Loan Interest Problem

blsbball wrote:Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.

• A. 360
  B. 390
  C. 400
  D. 410
  E. 420

I dont understand how to calculate when hes not repaying anything for the first 3 years. Thanks and Great Forum!

Though he is not paying for the first 3 years the interest rate is being calculated compounded annually. Its like Nathan has been given 1200 and he does not have to pay anything for the first 3 years. But at the end of the three years he has to pay the total amount which is Principal + the 3 years of interest.

Compunded annually = A*(1+r/100)^n, where A is the initila loan amount, r is the interest rate, n is the number of years.

Thus 1200 * (1+10/100)^3 = 1597.2

Hence he owes 1597.2 - 1200 = 397.2 approx 400

IMO C

Thanks that makes definitely sense. However calculating equations that intense is by no means my strength. Is there a way to go break it up year to year?

blsbball wrote:Thanks that makes definitely sense. However calculating equations that intense is by no means my strength. Is there a way to go break it up year to year?

Yes of course this can be broken down year by year. But keep the formula handy to calculate for a huge number of years.

Compunded annually = A*(1+r/100)^n, where A is the initila loan amount, r is the interest rate, n is the number of years.
Thus 1200 * (1+10/100)^3 = 1597.2

First year:

Loan amount = 1200, Interest amount = 10% of 1200 = 120.
End of the year the total loan to be paid = 1200 + 120 = 1320 (Because compounded annually)

Second year:

Loan amount = 1320, Interest amount = 10% of 1320= 132.
End of the year the total loan to be paid = 1320 + 132= 1452 (Because compounded annually)

Third year:

Loan amount = 1452, Interest amount = 10% of 1452 = 145.2.
End of the year the total loan to be paid = 1452 + 145.2 = 1597.2 (Because compounded annually)