Answer to Question #306188 in Microeconomics 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

Determine the number of payments of $4,000 each to be made and the amount of the final payment.

Solution:

Total 8 numbers of installments each $4000 need to be paid and $358.95 will be paid as the final installment amount.

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?

The values of the future value(FV) on December 31, 2025, and the one-year compounding rate(CR) are identified.

FV on December 31, 2025 = $100, 890.12

CR = (1 + 0.12)

The FV on December 21, 2026, is the product of the FV on December 31, 2025, and OC. There are only 7 annual cash flows that end on December 31, 2025. Therefore, the interest is compounded for the FV on December 31, 2025, for another year( until December 31, 2026)

FV on December 31, 2026 = FV on Dec 31, 2025 × OC

FV on December 31, 2026 = $100890.12 × (1 + 0.12)

FV on December 31, 2026 = $ 112996.93

The FV is $ 112, 996.93