Answer to Question #306187 in Macroeconomics for Jen

Question

On January 1, 2019, Joan Campbell borrows $20,000 from Susan Rone and agrees to repay this amount in payments of $4,000 a year until the debt is paid in full. Payments are to be of an equal amount and are to include interest at 12% on the unpaid balance of principal at the beginning of each period. Assuming that the first payment is to be made on January 1, 2020, determine the number of payments of $4,000 each to be made and the amount of the final payment.

What is the future value on December 31, 2026, of 7 annual cash flows of $10,000 with the first cash payment made on December 31, 2019, and interest at 12% being compounded annually?

Answer 1

1.) Repayment Schedule

$Year 1=4000+(0.12\times20000)=6,400$

$Year 2=4000+(0.12\times16000)=5920$

$Year 3=4000+(0.12\times12000)=5440$

$Year 4=4000+(0.12\times8000)=4960$

$Year 5=4000+(0.12\times4000)=4480$

5 payments will be done and final payment will be $4,480.00

2.) Future Value of Ordinary annuity.

$FV=A\times\frac{(1+r)^{7}-1}{r}$

$FV=10,000\times\frac{(1+0.12)^{7}-1}{0.12}=100,890.12$

Future Value will be $100,890