Suppose a certain amount of money is deposited into an account paying 4%, compounded annually. For each non-negative integer n, let S(n)= the total amount in the account after n years, and let S(0) be the initial amount deposited. (a) Find a recurrence relation for S(0),S(1),S(2),⋯ assuming no additional deposits or withdrawals for n years; provide your answer as a recurrence formula with base case. (b) If S0=$5000, find the amount of money on deposit at the end of 4 years.
