Two debt payments of $2,000 each are due now and nine months from now. If money is worth 8%, what single payment six months from now is required to settle the debt?
A) $4,042.34
B) $7,177.27
C) $6,127.48
D) $3,600.00
E) $4,040.78

Question

Quizplus · Accepted Answer

To find the equivalent single payment six months from now that would settle the debt, we need to calculate the present value of the two $2,000 payments and then find the future value of this amount six months from now at an 8% annual interest rate. First, calculate the present value (PV) of the two payments:- The first $2,000 payment is already at present value since it's due now.- For the second $2,000 payment due in nine months, we use the formula PV = FV / (1 + r)^n, where FV is the future value ($2,000), r is the periodic interest rate (8% annual rate divided by 12 months = 0.08/12 per month), and n is the number of periods (9 months). This gives us PV = $2,000 / (1 + 0.08/12)^9.Then, sum the present values of both payments to get the total present value.Finally, calculate the future value (FV) of this total present value six months from now using the formula FV = PV * (1 + r)^n, where PV is the total present value we just calculated, r is the periodic interest rate (0.08/12 per month), and n is the number of periods (6 months).This calculation will give us the equivalent single payment required six months from now, which is closest to the value given in option E, $4,040.78. This approach uses the principles of time value of money to equate the value of different payment schedules.

Two Debt Payments of $2,000 Each Are Due Now and Nine