Concept guide
Compound-interest model: principal 1000 at 2% per year for three years, compared with simple 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.