Suppose a certain amount of money is deposited into an accou

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.

The recurrence relation for S₀, S₁, S₂, . . ., assuming no additional deposits or withdrawals for a 3-year period is the following:

If S_k is the amount on deposit at the end of the kth quarter, then
S_k = S_{k-1 =} 1 + (0.01)S_k-1 = (1 + 0.01) S_k-1 = (1.01) S_k-1 for each integer k 1.

True

False

Solution

True