A bank pays 6% interest compounded annually on its passbook savings accounts. Suppose that you deposit $800 in one of these accounts and make no further deposits or withdrawals. Write a recurrence relation and initial conditions for b(sub)n, the balance of the account after n years.
I'm a bit nervous about this problem because it included a percentage rather than other arithmetic.
I imagine b(sub)0=800. Then b(sub)n = b(sub)n-1 * 1.06, n>=1. This seems to calculate the conditions of the question, but I'm not so sure that it actually solves the equation for compound interest. I don't know if any money can be added other than the initial 800.
edit: the next problem is for a credit card with compound interest.... the answer is bn = bn-1 + (1.5%)bn-1 - 25. => bn = (1.015)bn-1 - 25. It supposedly factors in the compound interest each month minus the monthly $25 payment.
By using compound interest, one gets $$ b_n=(1+0.06)^n \times b_0 $$ or $$ b_n=800 \times1.06^n. $$