Answer to Question #306183 in Accounting for Jen

Question #306183

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?


1
Expert's answer
2022-03-07T10:44:07-0500

a)

Periodic payment (pmt)= $4000

Present value (PV)=$20000

Interest rate (r)=12% or 0.12

n="\\frac{-log(1-\\frac{PV}{pmt}i)}{log(1+i)}"


The number of payments that would be made is:

"n=\\frac{-log(1-\\frac{\\$20000}{\\$4000}(0.12))}{log(1+0.12)}"

"n=8.09"

The number of payments to be made is approximately 8 times


B)"FV=\\frac{PV {(1-(1+r)^{-n})}}{r}"


Where

PV=$10000

r=0.12

n=7

"FV=\\frac{\\$10000{(1-(1+0.12)^{-7})}}{0.12}"

"FV=\\$45637.57"


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