Suppose a certain amount of money is deposited into an account paying 4% annual

Question

Suppose a certain amount of money is deposited into an account paying 4% annual interest, compounded quarterly. For each positive integer n, let S_n = the amount on deposit at the end of the nth quarter, 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 a 4-year period. (b) If S_0 = exist5000, find the amount of money on deposit at the end of 4 years. (c) Find the APR for the amount. A sequence c_0, c_1, c_2, ... is defined as follows: c_0 = 1 and c_k = 7c_k - 1 + 2 for integer k greaterthanorequalto 1. (a) Find c_1 and c_2. (b) Use one of the reference formulas given at the end of this exam to simplify the expression 7^n + 2 * 7^n - 1 + ellipsis + 2 * 7^2 + 2 * 7 + 2. (c) Use iteration to guess an explicit formula for the sequence c_0, c_1, c_2....

Explanation / Answer

4) compounded quaterly i.e..,4% divided into quarters = 1% (times 4)

a) So for each quarter you get 1%
S[n+1] = S[n] * 1.01

b) S0 = 5000; In 4 years i.e..,16 quarters

5000 * (1.01)16 = 5000 * 1.1726 = 5862.89

c) APR = 1.014 = 1.040604 = 4.06 %

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