The Ajax Co. just decided to save $1,500 a month for the next five years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 3.25% interest compounded monthly. It deposits the first $1,500 today. If the company had wanted to deposit an equivalent lump sum today,how much would it have had to deposit?
A) $82,964.59
B) $83,189.29
C) $83,428.87
D) $83,687.23
E) $84,998.01

Question

Quizplus · Accepted Answer

Using the formula for future value of an annuity:

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

Where FV = future value, PMT = payment (in this case $1,500), r = annual interest rate (3.25%), n = number of compounding periods per year (12), and t = time in years (5).

Plugging in the numbers, we get:

FV = 1,500 * (((1 + 0.0325/12)^(12*5))-1) / (0.0325/12) = $83,189.29

Therefore, the equivalent lump sum deposit today would be $83,189.29, which is option B.