Concept guide
Present value and discounting: proving that discounting inverts compounding, and the three-year present value of 1331
For a fixed rate i per period (1+i>0) and a period count n, prove that (1+i)^n>0, so the present value PV_n(F)=F/(1+i)^n is defined; prove that PV_n and compounding A_n(P)=P(1+i)^n are inverse functions of each other. Then, with i=1/10 per year, n=3 and F=1331, compute the present value 1000, cross-check by year-by-year discounting and a round trip, and explain why writing discounting as a multiplication, or mixing annual and monthly rates, is wrong.