Suppose a Certain Amount of Money Is Deposited into an Account

Essay

Suppose a certain amount of money is deposited into an account paying $4 \%$ annual interest, compounded quarterly (i.e., four times a year). For each positive integer $n$ , let $S _ { n } =$ the amount on deposit at the end of the $n$ th quarter, and let $S _ { 0 }$ be the initial amount deposited.
(a) Find a recurrence relation for $S _ { 0 } , S _ { 1 } , S _ { 2 } , \ldots$ , assuming no additional deposits or withdrawals for a 3-year period.
(b) If $S _ { 0 } = \$ 5000$ , find the amount of money on deposit at the end of three years.
(c) Find the APR for the account.