# Concept derivation guides

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Concept guide



## [Compound-interest model: principal 1000 at 2% per year for three years, compared with simple interest](/en/derivations/derivation-mko-compound-interest-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-compound-interest)

In the model with one-year periods, rate i=1/50 (2%) per period and no deposits, withdrawals or fees, prove B_n=B_0(1+i)^n by induction, compute the balance after three years from B_0=1000, namely 132651/125 (that is 1061.208), and the interest; compare with simple interest B_0(1+ni)=1060 and prove by Bernoulli's inequality that the compound balance is never below the simple one for any n; explain how mixing period units and cash flows during the period break the single-power formula.

Compound-interest model

derivation-mko-compound-interest-01





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