Question

1. An individual is borrowing $100,000 at 8% compounded annually. The loan is to be repaid in equal annual payments over 30 years.

a. What is the annual payment?

b. If the individual paid P8,000 per year instead of the calculated amount in a, how long will it take to pay for the loan in full maintaining the same interest rate?

c. If the borrower wanted to pay P8,000 per year in 30 years, what is the rate of interest charged then?

Answer 1

A. The formula for EMI is (in our case its annual installment, but the formula remains same-except we will put yearly interest rate rather than monthly)

Putting our values in

and solving, we get

Annual installment=8882.74.

B. What the questtion is saying is that the annual payment is now 8000, but we need to find the number of years (n) which will result in the loan being finished. We can use the same formula as part A, except this time we know the answer to the formula but not n. This is shown below

solving for n, we get n=186 years.

C.

Lets say such an interest rate is x%, then the problem becomes

solving for x, we get

x=6.93%

Hence, the interest rate is 6.93%