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

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

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

$FV=\$45637.57$