A $4,000 payment has to be made 3 years from now and another $6,000 payment 5 years from now. Using the financial functions on the calculator, determine what lump sum payment 40 months from now will be equivalent to these two payments if interest is 5.2% compounded quarterly.
A) $11,654.38
B) $11,253.35
C) $9,574.45
D) $9,224.69
E) $8,62.74

Question

Quizplus · Accepted Answer

To find the equivalent lump sum payment 40 months from now for the two future payments, we use the present value formula for each payment, discounting them back to the 40-month point, and then sum these present values. Since the interest is compounded quarterly, we adjust the interest rate and the number of periods accordingly. The annual interest rate is 5.2%, so the quarterly rate is 5.2% / 4 = 1.3%. For a $4,000 payment due in 3 years (36 months), it will be discounted back 4 months (since 40 - 36 = 4 months). For a $6,000 payment due in 5 years (60 months), it will be discounted back 20 months (since 60 - 40 = 20 months). Using the financial calculator functions for present value with these inputs gives us the equivalent lump sum payment, which matches choice C, $9,574.45.

A $4,000 Payment Has to Be Made 3 Years from Now