$3,500 borrowed one year ago, is to be settled by payments of $500 today, $1,500 six months from now, and a final payment eighteen months from now. What is the amount of the final payment if the interest rate on the loan is 12% compounded monthly?
A) $3,625.31
B) $1,500.00
C) $7,005.78
D) $1,427.01
E) $2,429.16

Question

Quizplus · Accepted Answer

To find the final payment, we need to calculate the present value of each payment and ensure they sum to the original loan amount. The interest rate is 12% compounded monthly, which is 1% per month. The present value of the $500 payment today is $500. The present value of the $1,500 payment six months from now is $1,500 / (1.01)^6. The final payment is made 18 months from now, so its present value is X / (1.01)^18. Setting the sum of these present values equal to $3,500 and solving for X gives the final payment amount.

$3,500 Borrowed One Year Ago, Is to Be Settled by Payments