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 Sn = the amount on deposit at the end of the nth quarter, and let S0 be the initial amount deposited.
(a) Find a recurrence relation for S0, S1, S2, . . ., assuming no additional deposits or withdrawals for a 3-year period.
(b) If S0 = $5000, find the amount of money on deposit at the end of three years.
(c) Find the APR for the account.
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