{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0001","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[100,1],\"rate\":[-2,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(100, -1/10, 9/10, 1000/9)","explanation_zh":"結構基礎核對=(100, -1/10, 9/10, 1000/9)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222001,"parameters":{"future":[100,1],"rate":[-2,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[100,1],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0002","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[103,2],\"rate\":[-1,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(103/2, -1/20, 19/20, 1030/19)","explanation_zh":"結構基礎核對=(103/2, -1/20, 19/20, 1030/19)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222002,"parameters":{"future":[103,2],"rate":[-1,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[103,2],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0003","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[106,3],\"rate\":[0,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(106/3, 0, 1, 106/3)","explanation_zh":"結構基礎核對=(106/3, 0, 1, 106/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222003,"parameters":{"future":[106,3],"rate":[0,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[106,3],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0004","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[109,1],\"rate\":[1,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(109, 1/20, 21/20, 2180/21)","explanation_zh":"結構基礎核對=(109, 1/20, 21/20, 2180/21)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222004,"parameters":{"future":[109,1],"rate":[1,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[109,1],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0005","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[112,2],\"rate\":[2,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(56, 1/10, 11/10, 560/11)","explanation_zh":"結構基礎核對=(56, 1/10, 11/10, 560/11)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222005,"parameters":{"future":[112,2],"rate":[2,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[112,2],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0006","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[115,3],\"rate\":[-2,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(115/3, -1/10, 9/10, 1150/27)","explanation_zh":"結構基礎核對=(115/3, -1/10, 9/10, 1150/27)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222006,"parameters":{"future":[115,3],"rate":[-2,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[115,3],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0007","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[118,1],\"rate\":[-1,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(118, -1/20, 19/20, 2360/19)","explanation_zh":"結構基礎核對=(118, -1/20, 19/20, 2360/19)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222007,"parameters":{"future":[118,1],"rate":[-1,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[118,1],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0008","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[121,2],\"rate\":[0,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(121/2, 0, 1, 121/2)","explanation_zh":"結構基礎核對=(121/2, 0, 1, 121/2)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222008,"parameters":{"future":[121,2],"rate":[0,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[121,2],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0009","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[124,3],\"rate\":[1,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(124/3, 1/20, 21/20, 2480/63)","explanation_zh":"結構基礎核對=(124/3, 1/20, 21/20, 2480/63)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222009,"parameters":{"future":[124,3],"rate":[1,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[124,3],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0010","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[127,1],\"rate\":[2,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(127, 1/10, 11/10, 1270/11)","explanation_zh":"結構基礎核對=(127, 1/10, 11/10, 1270/11)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222010,"parameters":{"future":[127,1],"rate":[2,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[127,1],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0011","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[130,2],\"rate\":[-2,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(65, -1/10, 9/10, 650/9)","explanation_zh":"結構基礎核對=(65, -1/10, 9/10, 650/9)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222011,"parameters":{"future":[130,2],"rate":[-2,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[130,2],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0012","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[133,3],\"rate\":[-1,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(133/3, -1/20, 19/20, 140/3)","explanation_zh":"結構基礎核對=(133/3, -1/20, 19/20, 140/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222012,"parameters":{"future":[133,3],"rate":[-1,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[133,3],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0013","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[136,1],\"rate\":[0,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(136, 0, 1, 136)","explanation_zh":"結構基礎核對=(136, 0, 1, 136)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222013,"parameters":{"future":[136,1],"rate":[0,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[136,1],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0014","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[139,2],\"rate\":[1,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(139/2, 1/20, 21/20, 1390/21)","explanation_zh":"結構基礎核對=(139/2, 1/20, 21/20, 1390/21)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222014,"parameters":{"future":[139,2],"rate":[1,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[139,2],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0015","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[142,3],\"rate\":[2,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(142/3, 1/10, 11/10, 1420/33)","explanation_zh":"結構基礎核對=(142/3, 1/10, 11/10, 1420/33)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222015,"parameters":{"future":[142,3],"rate":[2,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[142,3],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0016","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[145,1],\"rate\":[-2,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(145, -1/10, 9/10, 1450/9)","explanation_zh":"結構基礎核對=(145, -1/10, 9/10, 1450/9)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222016,"parameters":{"future":[145,1],"rate":[-2,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[145,1],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0017","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[148,2],\"rate\":[-1,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(74, -1/20, 19/20, 1480/19)","explanation_zh":"結構基礎核對=(74, -1/20, 19/20, 1480/19)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222017,"parameters":{"future":[148,2],"rate":[-1,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[148,2],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0018","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[151,3],\"rate\":[0,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(151/3, 0, 1, 151/3)","explanation_zh":"結構基礎核對=(151/3, 0, 1, 151/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222018,"parameters":{"future":[151,3],"rate":[0,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[151,3],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0019","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[154,1],\"rate\":[1,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(154, 1/20, 21/20, 440/3)","explanation_zh":"結構基礎核對=(154, 1/20, 21/20, 440/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222019,"parameters":{"future":[154,1],"rate":[1,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[154,1],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0020","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[157,2],\"rate\":[2,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(157/2, 1/10, 11/10, 785/11)","explanation_zh":"結構基礎核對=(157/2, 1/10, 11/10, 785/11)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222020,"parameters":{"future":[157,2],"rate":[2,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[157,2],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0021","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[160,3],\"rate\":[-2,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(160/3, -1/10, 9/10, 1600/27)","explanation_zh":"結構基礎核對=(160/3, -1/10, 9/10, 1600/27)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222021,"parameters":{"future":[160,3],"rate":[-2,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[160,3],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0022","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[163,1],\"rate\":[-1,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(163, -1/20, 19/20, 3260/19)","explanation_zh":"結構基礎核對=(163, -1/20, 19/20, 3260/19)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222022,"parameters":{"future":[163,1],"rate":[-1,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[163,1],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0023","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[166,2],\"rate\":[0,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(83, 0, 1, 83)","explanation_zh":"結構基礎核對=(83, 0, 1, 83)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222023,"parameters":{"future":[166,2],"rate":[0,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[166,2],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0024","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[169,3],\"rate\":[1,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(169/3, 1/20, 21/20, 3380/63)","explanation_zh":"結構基礎核對=(169/3, 1/20, 21/20, 3380/63)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222024,"parameters":{"future":[169,3],"rate":[1,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[169,3],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0025","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-one-period-discount；資料={\"future\":[172,1],\"rate\":[2,20]}。請依 [future,rate,factor,present] 欄序回答。","answer":{"kind":"expression","value":"(172, 1/10, 11/10, 1720/11)","explanation_zh":"結構基礎核對=(172, 1/10, 11/10, 1720/11)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222025,"parameters":{"future":[172,1],"rate":[2,20],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-one-period-discount","semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[172,1],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0026","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[100,1],\"rate\":[-2,20],\"periods\":0}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(100, -1/10, 0, 1, 100)","explanation_zh":"結構基礎核對=(100, -1/10, 0, 1, 100)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222026,"parameters":{"future":[100,1],"rate":[-2,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[100,1],\"periods\":0,\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0027","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[103,2],\"rate\":[-1,20],\"periods\":1}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(103/2, -1/20, 1, 19/20, 1030/19)","explanation_zh":"結構基礎核對=(103/2, -1/20, 1, 19/20, 1030/19)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222027,"parameters":{"future":[103,2],"rate":[-1,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[103,2],\"periods\":1,\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0028","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[106,3],\"rate\":[0,20],\"periods\":2}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(106/3, 0, 2, 1, 106/3)","explanation_zh":"結構基礎核對=(106/3, 0, 2, 1, 106/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222028,"parameters":{"future":[106,3],"rate":[0,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[106,3],\"periods\":2,\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0029","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[109,1],\"rate\":[1,20],\"periods\":0}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(109, 1/20, 0, 1, 109)","explanation_zh":"結構基礎核對=(109, 1/20, 0, 1, 109)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222029,"parameters":{"future":[109,1],"rate":[1,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[109,1],\"periods\":0,\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0030","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[112,2],\"rate\":[2,20],\"periods\":1}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(56, 1/10, 1, 11/10, 560/11)","explanation_zh":"結構基礎核對=(56, 1/10, 1, 11/10, 560/11)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222030,"parameters":{"future":[112,2],"rate":[2,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[112,2],\"periods\":1,\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0031","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[115,3],\"rate\":[-2,20],\"periods\":2}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(115/3, -1/10, 2, 81/100, 11500/243)","explanation_zh":"結構基礎核對=(115/3, -1/10, 2, 81/100, 11500/243)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222031,"parameters":{"future":[115,3],"rate":[-2,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[115,3],\"periods\":2,\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0032","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[118,1],\"rate\":[-1,20],\"periods\":0}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(118, -1/20, 0, 1, 118)","explanation_zh":"結構基礎核對=(118, -1/20, 0, 1, 118)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222032,"parameters":{"future":[118,1],"rate":[-1,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[118,1],\"periods\":0,\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0033","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[121,2],\"rate\":[0,20],\"periods\":1}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(121/2, 0, 1, 1, 121/2)","explanation_zh":"結構基礎核對=(121/2, 0, 1, 1, 121/2)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222033,"parameters":{"future":[121,2],"rate":[0,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[121,2],\"periods\":1,\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0034","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[124,3],\"rate\":[1,20],\"periods\":2}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(124/3, 1/20, 2, 441/400, 49600/1323)","explanation_zh":"結構基礎核對=(124/3, 1/20, 2, 441/400, 49600/1323)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222034,"parameters":{"future":[124,3],"rate":[1,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[124,3],\"periods\":2,\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0035","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[127,1],\"rate\":[2,20],\"periods\":0}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(127, 1/10, 0, 1, 127)","explanation_zh":"結構基礎核對=(127, 1/10, 0, 1, 127)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222035,"parameters":{"future":[127,1],"rate":[2,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[127,1],\"periods\":0,\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0036","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[130,2],\"rate\":[-2,20],\"periods\":1}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(65, -1/10, 1, 9/10, 650/9)","explanation_zh":"結構基礎核對=(65, -1/10, 1, 9/10, 650/9)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222036,"parameters":{"future":[130,2],"rate":[-2,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[130,2],\"periods\":1,\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0037","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[133,3],\"rate\":[-1,20],\"periods\":2}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(133/3, -1/20, 2, 361/400, 2800/57)","explanation_zh":"結構基礎核對=(133/3, -1/20, 2, 361/400, 2800/57)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222037,"parameters":{"future":[133,3],"rate":[-1,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[133,3],\"periods\":2,\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0038","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[136,1],\"rate\":[0,20],\"periods\":0}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(136, 0, 0, 1, 136)","explanation_zh":"結構基礎核對=(136, 0, 0, 1, 136)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222038,"parameters":{"future":[136,1],"rate":[0,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[136,1],\"periods\":0,\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0039","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[139,2],\"rate\":[1,20],\"periods\":1}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(139/2, 1/20, 1, 21/20, 1390/21)","explanation_zh":"結構基礎核對=(139/2, 1/20, 1, 21/20, 1390/21)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222039,"parameters":{"future":[139,2],"rate":[1,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[139,2],\"periods\":1,\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0040","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[142,3],\"rate\":[2,20],\"periods\":2}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(142/3, 1/10, 2, 121/100, 14200/363)","explanation_zh":"結構基礎核對=(142/3, 1/10, 2, 121/100, 14200/363)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222040,"parameters":{"future":[142,3],"rate":[2,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[142,3],\"periods\":2,\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0041","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[145,1],\"rate\":[-2,20],\"periods\":0}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(145, -1/10, 0, 1, 145)","explanation_zh":"結構基礎核對=(145, -1/10, 0, 1, 145)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222041,"parameters":{"future":[145,1],"rate":[-2,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[145,1],\"periods\":0,\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0042","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[148,2],\"rate\":[-1,20],\"periods\":1}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(74, -1/20, 1, 19/20, 1480/19)","explanation_zh":"結構基礎核對=(74, -1/20, 1, 19/20, 1480/19)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222042,"parameters":{"future":[148,2],"rate":[-1,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[148,2],\"periods\":1,\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0043","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[151,3],\"rate\":[0,20],\"periods\":2}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(151/3, 0, 2, 1, 151/3)","explanation_zh":"結構基礎核對=(151/3, 0, 2, 1, 151/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222043,"parameters":{"future":[151,3],"rate":[0,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[151,3],\"periods\":2,\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0044","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[154,1],\"rate\":[1,20],\"periods\":0}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(154, 1/20, 0, 1, 154)","explanation_zh":"結構基礎核對=(154, 1/20, 0, 1, 154)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222044,"parameters":{"future":[154,1],"rate":[1,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[154,1],\"periods\":0,\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0045","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[157,2],\"rate\":[2,20],\"periods\":1}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(157/2, 1/10, 1, 11/10, 785/11)","explanation_zh":"結構基礎核對=(157/2, 1/10, 1, 11/10, 785/11)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222045,"parameters":{"future":[157,2],"rate":[2,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[157,2],\"periods\":1,\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0046","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[160,3],\"rate\":[-2,20],\"periods\":2}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(160/3, -1/10, 2, 81/100, 16000/243)","explanation_zh":"結構基礎核對=(160/3, -1/10, 2, 81/100, 16000/243)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222046,"parameters":{"future":[160,3],"rate":[-2,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[160,3],\"periods\":2,\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0047","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[163,1],\"rate\":[-1,20],\"periods\":0}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(163, -1/20, 0, 1, 163)","explanation_zh":"結構基礎核對=(163, -1/20, 0, 1, 163)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222047,"parameters":{"future":[163,1],"rate":[-1,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[163,1],\"periods\":0,\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0048","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[166,2],\"rate\":[0,20],\"periods\":1}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(83, 0, 1, 1, 83)","explanation_zh":"結構基礎核對=(83, 0, 1, 1, 83)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222048,"parameters":{"future":[166,2],"rate":[0,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[166,2],\"periods\":1,\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0049","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[169,3],\"rate\":[1,20],\"periods\":2}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(169/3, 1/20, 2, 441/400, 67600/1323)","explanation_zh":"結構基礎核對=(169/3, 1/20, 2, 441/400, 67600/1323)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222049,"parameters":{"future":[169,3],"rate":[1,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[169,3],\"periods\":2,\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0050","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-n-period-discount；資料={\"future\":[172,1],\"rate\":[2,20],\"periods\":0}。請依 [future,rate,periods,accumulation,present] 欄序回答。","answer":{"kind":"expression","value":"(172, 1/10, 0, 1, 172)","explanation_zh":"結構基礎核對=(172, 1/10, 0, 1, 172)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222050,"parameters":{"future":[172,1],"rate":[2,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-n-period-discount","semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[172,1],\"periods\":0,\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0051","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[50,1],\"rate\":[-2,20],\"periods\":0}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(50, -1/10, 0, 50, 50, 是)","explanation_zh":"結構基礎核對=(50, -1/10, 0, 50, 50, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222051,"parameters":{"principal":[50,1],"rate":[-2,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[50,1],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0052","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[52,2],\"rate\":[-1,20],\"periods\":1}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(26, -1/20, 1, 247/10, 26, 是)","explanation_zh":"結構基礎核對=(26, -1/20, 1, 247/10, 26, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222052,"parameters":{"principal":[52,2],"rate":[-1,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[52,2],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0053","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[54,3],\"rate\":[0,20],\"periods\":2}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(18, 0, 2, 18, 18, 是)","explanation_zh":"結構基礎核對=(18, 0, 2, 18, 18, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222053,"parameters":{"principal":[54,3],"rate":[0,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[54,3],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0054","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[56,1],\"rate\":[1,20],\"periods\":0}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(56, 1/20, 0, 56, 56, 是)","explanation_zh":"結構基礎核對=(56, 1/20, 0, 56, 56, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222054,"parameters":{"principal":[56,1],"rate":[1,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[56,1],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0055","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[58,2],\"rate\":[2,20],\"periods\":1}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(29, 1/10, 1, 319/10, 29, 是)","explanation_zh":"結構基礎核對=(29, 1/10, 1, 319/10, 29, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222055,"parameters":{"principal":[58,2],"rate":[2,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[58,2],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0056","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[60,3],\"rate\":[-2,20],\"periods\":2}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(20, -1/10, 2, 81/5, 20, 是)","explanation_zh":"結構基礎核對=(20, -1/10, 2, 81/5, 20, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222056,"parameters":{"principal":[60,3],"rate":[-2,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[60,3],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0057","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[62,1],\"rate\":[-1,20],\"periods\":0}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(62, -1/20, 0, 62, 62, 是)","explanation_zh":"結構基礎核對=(62, -1/20, 0, 62, 62, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222057,"parameters":{"principal":[62,1],"rate":[-1,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[62,1],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0058","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[64,2],\"rate\":[0,20],\"periods\":1}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(32, 0, 1, 32, 32, 是)","explanation_zh":"結構基礎核對=(32, 0, 1, 32, 32, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222058,"parameters":{"principal":[64,2],"rate":[0,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[64,2],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0059","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[66,3],\"rate\":[1,20],\"periods\":2}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(22, 1/20, 2, 4851/200, 22, 是)","explanation_zh":"結構基礎核對=(22, 1/20, 2, 4851/200, 22, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222059,"parameters":{"principal":[66,3],"rate":[1,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[66,3],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0060","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[68,1],\"rate\":[2,20],\"periods\":0}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(68, 1/10, 0, 68, 68, 是)","explanation_zh":"結構基礎核對=(68, 1/10, 0, 68, 68, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222060,"parameters":{"principal":[68,1],"rate":[2,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[68,1],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0061","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[70,2],\"rate\":[-2,20],\"periods\":1}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(35, -1/10, 1, 63/2, 35, 是)","explanation_zh":"結構基礎核對=(35, -1/10, 1, 63/2, 35, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222061,"parameters":{"principal":[70,2],"rate":[-2,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[70,2],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0062","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[72,3],\"rate\":[-1,20],\"periods\":2}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(24, -1/20, 2, 1083/50, 24, 是)","explanation_zh":"結構基礎核對=(24, -1/20, 2, 1083/50, 24, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222062,"parameters":{"principal":[72,3],"rate":[-1,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[72,3],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0063","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[74,1],\"rate\":[0,20],\"periods\":0}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(74, 0, 0, 74, 74, 是)","explanation_zh":"結構基礎核對=(74, 0, 0, 74, 74, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222063,"parameters":{"principal":[74,1],"rate":[0,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[74,1],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0064","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[76,2],\"rate\":[1,20],\"periods\":1}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(38, 1/20, 1, 399/10, 38, 是)","explanation_zh":"結構基礎核對=(38, 1/20, 1, 399/10, 38, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222064,"parameters":{"principal":[76,2],"rate":[1,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[76,2],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0065","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[78,3],\"rate\":[2,20],\"periods\":2}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(26, 1/10, 2, 1573/50, 26, 是)","explanation_zh":"結構基礎核對=(26, 1/10, 2, 1573/50, 26, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222065,"parameters":{"principal":[78,3],"rate":[2,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[78,3],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0066","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[80,1],\"rate\":[-2,20],\"periods\":0}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(80, -1/10, 0, 80, 80, 是)","explanation_zh":"結構基礎核對=(80, -1/10, 0, 80, 80, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222066,"parameters":{"principal":[80,1],"rate":[-2,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[80,1],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0067","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[82,2],\"rate\":[-1,20],\"periods\":1}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(41, -1/20, 1, 779/20, 41, 是)","explanation_zh":"結構基礎核對=(41, -1/20, 1, 779/20, 41, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222067,"parameters":{"principal":[82,2],"rate":[-1,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[82,2],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0068","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[84,3],\"rate\":[0,20],\"periods\":2}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(28, 0, 2, 28, 28, 是)","explanation_zh":"結構基礎核對=(28, 0, 2, 28, 28, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222068,"parameters":{"principal":[84,3],"rate":[0,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[84,3],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0069","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[86,1],\"rate\":[1,20],\"periods\":0}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(86, 1/20, 0, 86, 86, 是)","explanation_zh":"結構基礎核對=(86, 1/20, 0, 86, 86, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222069,"parameters":{"principal":[86,1],"rate":[1,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[86,1],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0070","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[88,2],\"rate\":[2,20],\"periods\":1}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(44, 1/10, 1, 242/5, 44, 是)","explanation_zh":"結構基礎核對=(44, 1/10, 1, 242/5, 44, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222070,"parameters":{"principal":[88,2],"rate":[2,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[88,2],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0071","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[90,3],\"rate\":[-2,20],\"periods\":2}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(30, -1/10, 2, 243/10, 30, 是)","explanation_zh":"結構基礎核對=(30, -1/10, 2, 243/10, 30, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222071,"parameters":{"principal":[90,3],"rate":[-2,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[90,3],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0072","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[92,1],\"rate\":[-1,20],\"periods\":0}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(92, -1/20, 0, 92, 92, 是)","explanation_zh":"結構基礎核對=(92, -1/20, 0, 92, 92, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222072,"parameters":{"principal":[92,1],"rate":[-1,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[92,1],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0073","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[94,2],\"rate\":[0,20],\"periods\":1}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(47, 0, 1, 47, 47, 是)","explanation_zh":"結構基礎核對=(47, 0, 1, 47, 47, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222073,"parameters":{"principal":[94,2],"rate":[0,20],"periods":1,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[94,2],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0074","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[96,3],\"rate\":[1,20],\"periods\":2}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(32, 1/20, 2, 882/25, 32, 是)","explanation_zh":"結構基礎核對=(32, 1/20, 2, 882/25, 32, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222074,"parameters":{"principal":[96,3],"rate":[1,20],"periods":2,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[96,3],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0075","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-forward-backward-audit；資料={\"principal\":[98,1],\"rate\":[2,20],\"periods\":0}。請依 [principal,rate,periods,future,recovered,roundtrip] 欄序回答。","answer":{"kind":"expression","value":"(98, 1/10, 0, 98, 98, 是)","explanation_zh":"結構基礎核對=(98, 1/10, 0, 98, 98, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222075,"parameters":{"principal":[98,1],"rate":[2,20],"periods":0,"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-forward-backward-audit","semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[98,1],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0076","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[100,1],\"rate\":[-1,10],\"periods\":0,\"candidate\":[101,1]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(100, -1/10, 0, 100, 101, 否)","explanation_zh":"結構基礎核對=(100, -1/10, 0, 100, 101, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222076,"parameters":{"future":[100,1],"rate":[-1,10],"periods":0,"candidate":[101,1],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[101,1],\"future\":[100,1],\"periods\":0,\"rate\":[-1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0077","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[103,2],\"rate\":[-1,20],\"periods\":1,\"candidate\":[1030,19]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(103/2, -1/20, 1, 1030/19, 1030/19, 是)","explanation_zh":"結構基礎核對=(103/2, -1/20, 1, 1030/19, 1030/19, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222077,"parameters":{"future":[103,2],"rate":[-1,20],"periods":1,"candidate":[1030,19],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[1030,19],\"future\":[103,2],\"periods\":1,\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0078","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[106,3],\"rate\":[0,1],\"periods\":2,\"candidate\":[106,3]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(106/3, 0, 2, 106/3, 106/3, 是)","explanation_zh":"結構基礎核對=(106/3, 0, 2, 106/3, 106/3, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222078,"parameters":{"future":[106,3],"rate":[0,1],"periods":2,"candidate":[106,3],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[106,3],\"future\":[106,3],\"periods\":2,\"rate\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0079","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[109,1],\"rate\":[1,20],\"periods\":0,\"candidate\":[109,1]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(109, 1/20, 0, 109, 109, 是)","explanation_zh":"結構基礎核對=(109, 1/20, 0, 109, 109, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222079,"parameters":{"future":[109,1],"rate":[1,20],"periods":0,"candidate":[109,1],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[109,1],\"future\":[109,1],\"periods\":0,\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0080","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[56,1],\"rate\":[1,10],\"periods\":1,\"candidate\":[561,11]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(56, 1/10, 1, 560/11, 51, 否)","explanation_zh":"結構基礎核對=(56, 1/10, 1, 560/11, 51, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222080,"parameters":{"future":[56,1],"rate":[1,10],"periods":1,"candidate":[561,11],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[561,11],\"future\":[56,1],\"periods\":1,\"rate\":[1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0081","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[115,3],\"rate\":[-1,10],\"periods\":2,\"candidate\":[11500,243]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(115/3, -1/10, 2, 11500/243, 11500/243, 是)","explanation_zh":"結構基礎核對=(115/3, -1/10, 2, 11500/243, 11500/243, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222081,"parameters":{"future":[115,3],"rate":[-1,10],"periods":2,"candidate":[11500,243],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[11500,243],\"future\":[115,3],\"periods\":2,\"rate\":[-1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0082","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[118,1],\"rate\":[-1,20],\"periods\":0,\"candidate\":[118,1]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(118, -1/20, 0, 118, 118, 是)","explanation_zh":"結構基礎核對=(118, -1/20, 0, 118, 118, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222082,"parameters":{"future":[118,1],"rate":[-1,20],"periods":0,"candidate":[118,1],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[118,1],\"future\":[118,1],\"periods\":0,\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0083","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[121,2],\"rate\":[0,1],\"periods\":1,\"candidate\":[121,2]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(121/2, 0, 1, 121/2, 121/2, 是)","explanation_zh":"結構基礎核對=(121/2, 0, 1, 121/2, 121/2, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222083,"parameters":{"future":[121,2],"rate":[0,1],"periods":1,"candidate":[121,2],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[121,2],\"future\":[121,2],\"periods\":1,\"rate\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0084","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[124,3],\"rate\":[1,20],\"periods\":2,\"candidate\":[49601,1323]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(124/3, 1/20, 2, 49600/1323, 49601/1323, 否)","explanation_zh":"結構基礎核對=(124/3, 1/20, 2, 49600/1323, 49601/1323, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222084,"parameters":{"future":[124,3],"rate":[1,20],"periods":2,"candidate":[49601,1323],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[49601,1323],\"future\":[124,3],\"periods\":2,\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0085","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[127,1],\"rate\":[1,10],\"periods\":0,\"candidate\":[127,1]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(127, 1/10, 0, 127, 127, 是)","explanation_zh":"結構基礎核對=(127, 1/10, 0, 127, 127, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222085,"parameters":{"future":[127,1],"rate":[1,10],"periods":0,"candidate":[127,1],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[127,1],\"future\":[127,1],\"periods\":0,\"rate\":[1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0086","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[65,1],\"rate\":[-1,10],\"periods\":1,\"candidate\":[650,9]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(65, -1/10, 1, 650/9, 650/9, 是)","explanation_zh":"結構基礎核對=(65, -1/10, 1, 650/9, 650/9, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222086,"parameters":{"future":[65,1],"rate":[-1,10],"periods":1,"candidate":[650,9],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[650,9],\"future\":[65,1],\"periods\":1,\"rate\":[-1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0087","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[133,3],\"rate\":[-1,20],\"periods\":2,\"candidate\":[2800,57]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(133/3, -1/20, 2, 2800/57, 2800/57, 是)","explanation_zh":"結構基礎核對=(133/3, -1/20, 2, 2800/57, 2800/57, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222087,"parameters":{"future":[133,3],"rate":[-1,20],"periods":2,"candidate":[2800,57],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[2800,57],\"future\":[133,3],\"periods\":2,\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0088","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[136,1],\"rate\":[0,1],\"periods\":0,\"candidate\":[137,1]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(136, 0, 0, 136, 137, 否)","explanation_zh":"結構基礎核對=(136, 0, 0, 136, 137, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222088,"parameters":{"future":[136,1],"rate":[0,1],"periods":0,"candidate":[137,1],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[137,1],\"future\":[136,1],\"periods\":0,\"rate\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0089","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[139,2],\"rate\":[1,20],\"periods\":1,\"candidate\":[1390,21]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(139/2, 1/20, 1, 1390/21, 1390/21, 是)","explanation_zh":"結構基礎核對=(139/2, 1/20, 1, 1390/21, 1390/21, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222089,"parameters":{"future":[139,2],"rate":[1,20],"periods":1,"candidate":[1390,21],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[1390,21],\"future\":[139,2],\"periods\":1,\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0090","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[142,3],\"rate\":[1,10],\"periods\":2,\"candidate\":[14200,363]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(142/3, 1/10, 2, 14200/363, 14200/363, 是)","explanation_zh":"結構基礎核對=(142/3, 1/10, 2, 14200/363, 14200/363, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222090,"parameters":{"future":[142,3],"rate":[1,10],"periods":2,"candidate":[14200,363],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[14200,363],\"future\":[142,3],\"periods\":2,\"rate\":[1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0091","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[145,1],\"rate\":[-1,10],\"periods\":0,\"candidate\":[145,1]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(145, -1/10, 0, 145, 145, 是)","explanation_zh":"結構基礎核對=(145, -1/10, 0, 145, 145, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222091,"parameters":{"future":[145,1],"rate":[-1,10],"periods":0,"candidate":[145,1],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[145,1],\"future\":[145,1],\"periods\":0,\"rate\":[-1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0092","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[74,1],\"rate\":[-1,20],\"periods\":1,\"candidate\":[1481,19]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(74, -1/20, 1, 1480/19, 1481/19, 否)","explanation_zh":"結構基礎核對=(74, -1/20, 1, 1480/19, 1481/19, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222092,"parameters":{"future":[74,1],"rate":[-1,20],"periods":1,"candidate":[1481,19],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[1481,19],\"future\":[74,1],\"periods\":1,\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0093","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[151,3],\"rate\":[0,1],\"periods\":2,\"candidate\":[151,3]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(151/3, 0, 2, 151/3, 151/3, 是)","explanation_zh":"結構基礎核對=(151/3, 0, 2, 151/3, 151/3, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222093,"parameters":{"future":[151,3],"rate":[0,1],"periods":2,"candidate":[151,3],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[151,3],\"future\":[151,3],\"periods\":2,\"rate\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0094","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[154,1],\"rate\":[1,20],\"periods\":0,\"candidate\":[154,1]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(154, 1/20, 0, 154, 154, 是)","explanation_zh":"結構基礎核對=(154, 1/20, 0, 154, 154, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222094,"parameters":{"future":[154,1],"rate":[1,20],"periods":0,"candidate":[154,1],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[154,1],\"future\":[154,1],\"periods\":0,\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0095","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[157,2],\"rate\":[1,10],\"periods\":1,\"candidate\":[785,11]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(157/2, 1/10, 1, 785/11, 785/11, 是)","explanation_zh":"結構基礎核對=(157/2, 1/10, 1, 785/11, 785/11, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222095,"parameters":{"future":[157,2],"rate":[1,10],"periods":1,"candidate":[785,11],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[785,11],\"future\":[157,2],\"periods\":1,\"rate\":[1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0096","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[160,3],\"rate\":[-1,10],\"periods\":2,\"candidate\":[16001,243]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(160/3, -1/10, 2, 16000/243, 16001/243, 否)","explanation_zh":"結構基礎核對=(160/3, -1/10, 2, 16000/243, 16001/243, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222096,"parameters":{"future":[160,3],"rate":[-1,10],"periods":2,"candidate":[16001,243],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[16001,243],\"future\":[160,3],\"periods\":2,\"rate\":[-1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0097","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[163,1],\"rate\":[-1,20],\"periods\":0,\"candidate\":[163,1]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(163, -1/20, 0, 163, 163, 是)","explanation_zh":"結構基礎核對=(163, -1/20, 0, 163, 163, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222097,"parameters":{"future":[163,1],"rate":[-1,20],"periods":0,"candidate":[163,1],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[163,1],\"future\":[163,1],\"periods\":0,\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0098","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[83,1],\"rate\":[0,1],\"periods\":1,\"candidate\":[83,1]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(83, 0, 1, 83, 83, 是)","explanation_zh":"結構基礎核對=(83, 0, 1, 83, 83, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222098,"parameters":{"future":[83,1],"rate":[0,1],"periods":1,"candidate":[83,1],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[83,1],\"future\":[83,1],\"periods\":1,\"rate\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0099","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[169,3],\"rate\":[1,20],\"periods\":2,\"candidate\":[67600,1323]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(169/3, 1/20, 2, 67600/1323, 67600/1323, 是)","explanation_zh":"結構基礎核對=(169/3, 1/20, 2, 67600/1323, 67600/1323, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222099,"parameters":{"future":[169,3],"rate":[1,20],"periods":2,"candidate":[67600,1323],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[67600,1323],\"future\":[169,3],\"periods\":2,\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r02-present-value-discounting-0100","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","language":"zh-Hant","source_mko_ids":["mko-present-value-discounting"],"title_zh":"固定因子現值","stem_zh":"固定期率、固定期數且無現金流。操作=presentvalue-candidate-audit；資料={\"future\":[172,1],\"rate\":[1,10],\"periods\":0,\"candidate\":[173,1]}。請依 [future,rate,periods,present,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(172, 1/10, 0, 172, 173, 否)","explanation_zh":"結構基礎核對=(172, 1/10, 0, 172, 173, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；累積因子必須為正；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定因子現值"]},"variant":{"family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222100,"parameters":{"future":[172,1],"rate":[1,10],"periods":0,"candidate":[173,1],"domain":"Exact_fixed_factor_discounting","operation":"presentvalue-candidate-audit","semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[173,1],\"future\":[172,1],\"periods\":0,\"rate\":[1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}