A company wishes to accumulate $100,000.To do so,they will make quarterly deposits of $4000 into a fund paying interest at j₄ = 8%.It turns out they need to make 20 deposits,plus a smaller drop payment.What is the size of the drop payment needed?

Question

Quizplus · Accepted Answer

Using the formula for the future value of an annuity, we can find the total amount accumulated by the company:

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

where PV = 0 (no initial investment), PMT = 4000, r = 0.08, n = 4 (quarterly deposits), and t = 20 (number of deposit periods).

FV = 4000 * [(1 + 0.08/4)^(4*20) - 1] / (0.08/4) = 131,501.28

To find the size of the drop payment, we need to subtract the accumulated amount from the target amount of $100,000:

drop payment = 100,000 - 131,501.28 = -31,501.28

Since the result is negative, it means that the company has already exceeded its target amount and does not need to make a drop payment. Therefore, the answer is (D) 0.

A Company Wishes to Accumulate $100,000