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Loan Interest Problem

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by blsbball » Tue Nov 30, 2010 10:14 am
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!
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by shovan85 » Tue Nov 30, 2010 11:20 am
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
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by blsbball » Tue Nov 30, 2010 11:35 am
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?
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by shovan85 » Tue Nov 30, 2010 11:46 am
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)
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