Question

5 . Loan amortization and capital recovery Ian loaned his friend $20,000 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 6% 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 6% on his investment. Calculate the annual payment and complete the following capital recovery schedule:

Answer 1

Answer:

Ans. The annual payment to repay the loan at 6% annual, for 4 years is $5,771.83

Explanation:

Hi, in order to find the annual payment o the loan, we need to use the following equation and solve for "A".

$PresentValue=\frac{A((1+r)^{n} -1)}{r(1+r)^{n} }$

Where:

Present Value = Money loaned (in this case, $20,000)

A= Annual payments

r= interest rate (in our case, annual)

n = Number of periodic payments (4 payments, 1 each year)

Everything should look like this.

$20,000=\frac{A((1+0.06)^{4}-1) }{0.06(1+0.06)^{4} }$

$20,000=\frac{A(0.26247696)}{0.07574862}$

$20,000=A(3.46510561)$

$A=\frac{20,000}{3.46510561}$

$A=5,771.83$

Best of luck.