Question

Victoria had $200 in her account at the end of one year. At the first of each subsequent year she deposits $15 into the account and earns 2% interest on the new balance, compounded annually. Which recursive formula represents the total amount of money in Victoria’s account at the end of the nth year?
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Answer 1

Let A_n be the balance at the end of the nth year. Since A_1 = 200 and each year she first adds $15 then the whole balance earns 2%,

A_n = 1.02(A_{n-1} + 15) for n ≥ 2.

(Equivalently A_n = 1.02 A_{n-1} + 15.3.)