A $4,000 obligation is to be repaid by three payments. The first payment is now, the second is 18 months from now, and the final payment is in 24 months. In addition, the second payment will be half the amount of the first, while the third payment will be twice as much as the first. Interest is 4.8% compounded quarterly. Using the financial functions on the calculator, determine the size of each payment.
A) Payment #1 = $1218.24; Payment #2 = $609.12; Payment #3 = $2436.48
B) Payment #1 = $500; Payment #2 = $250; Payment #3 = $1,000
C) Payment #1 = $2520.50; Payment #2 = $1,260.25; Payment #3 = $5,041
D) Payment #1 = $3,300.75; Payment #2 = $1,650.38; Payment #3 = $6,601.50
E) Payment #1 = $875.50; Payment #2 = $437.75; Payment #3 = $1,751

Question

Quizplus · Accepted Answer

To solve this problem, we need to calculate the present value of each payment and ensure their sum equals $4,000. Given the interest rate is 4.8% compounded quarterly, we convert it to a quarterly rate by dividing by 4, which gives us 1.2% per quarter. The first payment is immediate, so its present value is its face value. For the second and third payments, we discount them back to the present value using the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods. Given the conditions:- The second payment is half the first, and the third is twice the first.- The second payment occurs in 18 months (4.5 quarters), and the third in 24 months (6 quarters).Let's denote the first payment as P. Then the second payment is P/2, and the third payment is 2P. Using the present value formula for each and setting the sum to $4,000 allows us to solve for P, which leads to the payments outlined in option A when the calculations are correctly executed.

A $4,000 Obligation Is to Be Repaid by Three Payments