Question

A person borrows $240 that he must repay in a lump sum no more than 10 years from now. The interest rate is 7.4% annually compounded. The borrower can repay the loan at the end of any earlier year with no prepayment penalty.

a. What amount will be due if the borrower repays the loan after 1 year?
b. How much would the borrower have to repay after 5 years?
c. What amount is due at the end of the tenth year?

Answer 1

- Amount borrowed = $240

The amount due will be repaid with a lumpsum payment at the end of any year with no prepayment penalty.

a). Calculating the amount due at the end of 1 year:-

Future Value = Loan amount*(1+r)^n

Where,

r = Periodic Interest rate = 7.4%

n= no of periods = 1 year

Future Value = $240*(1+0.074)^1

Future Value = $257.76

So, the amount will be due if the borrower repays the loan after 1 ​year is $257.76

b). Calculating the amount due at the end of 5 year:-

Future Value = Loan amount*(1+r)^n

Where,

r = Periodic Interest rate = 7.4%

n= no of periods = 5 year

Future Value = $240*(1+0.074)^5

Future Value = $240*1.42896439189

Future Value = $342.95

So, the amount  borrower have to repay after 5 years is $342.95

c). Calculating the amount due at the end of 10 year:-

Future Value = Loan amount*(1+r)^n

Where,

r = Periodic Interest rate = 7.4%

n= no of periods = 10 year

Future Value = $240*(1+0.074)^10

Future Value = $240*2.04193923328

Future Value = $490.07

So, the amount  borrower have to repay after 10 years is $490.07