Sharon wishes to have $30,000 in 4 years' time. If she deposits a lump sum of $3,500 now, then what monthly deposits need to be made if interest is at 2.7% compounded annually?
A) $495.16
B) $505.45
C) $515.99
D) $520.67
E) $565.20

Question

Quizplus · Accepted Answer

First, calculate the future value of the initial deposit. Using the formula FV = PV(1 + r)^n, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years, we get FV = $3,500(1 + 0.027)^4 ≈ $3,918.23. Subtract this from the desired future amount to find the total amount needed from monthly deposits: $30,000 - $3,918.23 = $26,081.77. Next, use the future value of a series formula: FV = P[((1 + r)^nt - 1) / r], where P is the monthly deposit, r is the monthly interest rate (2.7% annual rate means 0.027/12 per month), and nt is the total number of deposits (4 years * 12 months = 48 deposits). Rearranging the formula to solve for P gives P = FV / [((1 + r)^nt - 1) / r]. Plugging in the numbers: P = $26,081.77 / [((1 + 0.027/12)^48 - 1) / (0.027/12)] ≈ $515.99.

Sharon Wishes to Have $30,000 in 4 Years' Time