You have a savings account into which you invest $100 at the end of every month and the account pays you an APR of 6% compounded monthly. Use the regular deposits balance formula to determine the balance in the account at the end of 3 years.

Question

Quizplus · Accepted Answer

Using the regular deposits balance formula:

FV = P * (((1 + r/n)^(n*t) - 1) / (r/n)) + PMT * (((1 + r/n)^(n*t) - 1) / (r/n))

Where:
P = initial balance = 0
r = annual interest rate = 6%
n = number of compounding periods per year = 12 (monthly)
t = time period = 3 years
PMT = regular deposit amount = $100

Plugging in the values:

FV = 0 * (((1 + 0.06/12)^(12*3) - 1) / (0.06/12)) + 100 * (((1 + 0.06/12)^(12*3) - 1) / (0.06/12))
FV = $3933.61

Therefore, the balance in the account at the end of 3 years is $3933.61, which is option B.

You Have a Savings Account into Which You Invest $100