Question

Ian loaned his friend $25,000 to start a new business. He considers this loan to be an investment, and therefore requires his friend to pay him an interest rate of 9% on the loan. He also expects his friend to pay back the loan over the next four years by making annual payments at the end of each year. Ian texted and asked that you help him calculate the annual payments that he should expect to receive so that he can recover his initial investment and earn the agreed-upon 9% on his investment.

Calculate the annual payment and complete the following capital recovery schedule

Answer 1

In this case loan of $ 25000 is given @ 9% and it is to be pay back over next 4 years by making annual payments at the end of year each.

Calculation of annual payment and capital recovery schedule is as follow:

Annual Payment = Loan / PVAF (r%, n year)

Loan = $ 25000

PVAF (r%, n year) signifies Present Value annuity factor where r% is rate on interest and n is no. of years.

PVAF (9%, 4 years) = ((1+ r%)ⁿ - 1) / (r% * (1+r%)ⁿ)

= ((1+ 9%)⁴ - 1) / (0.09 * (1+9%)⁴)

= (1.411582 - 1)/ (0.09*1.4112)

= 0.411582 / 0.127042

= 3.23972

Therefore Annual Payment = 25000/ 3.23972

= $ 7716.72

Recovery Schedule:

Period	Annual Payment (a)	Interest Component (b)	Principal Component (a-b)	Closing O/s
0	-	-	-	25000
1	7716.72	(25000*9%) = 2250.00	5466.72	(25000-5466.72) = 19533.28
2	7716.72	(19533.28 *9%) = 1758.00	5958.72	(19533.28-5958.72) = 13574.56
3	7716.72	(13574.56*9%) = 1221.71	6495.01	(13574.56-6495.01) = 7079.56
4	7716.72	(7079.56*9%) = 637.16	7079.56	(7079.56-7079.56) = 0.00