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Compound interest problems

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by gmattesttaker2 » Thu Jul 05, 2012 10:49 pm
Hello,

These are from MGMAT Guide 1 (5th edition):

4) A car loan is offered at 8% annual interest, compounded annually. After the first year, the interest due is $240. What is the principal on the loan?

[spoiler]Ans: $3000[/spoiler]

8) Lori deposits $10,000 in a savings account at 10% annual interest, compounded annually. After 3 years, what is the balance on the account? (Assume Lori makes no deposits or withdrawals)

[spoiler]Ans: $13,310[/spoiler]


Can you please explain how to solve these compound interest problems. Thanks for your help.

Best Regards,
Sri
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by eagleeye » Fri Jul 06, 2012 3:08 am
You need to know how to calculate simple and compound interest.

For simple interest: Simple Interest SI = P*r*t/100 (Where P is the principal, r is the rate and t is the time).

For compound interest: Total amount after time t = A = P*(1+r/100)^t.
So Compound interest = CI = A-P.

A car loan is offered at 8% annual interest, compounded annually. After the first year, the interest due is $240. What is the principal on the loan?
Since the loan is compounded annually, and the question asks for one year. Simple and compound interest are the same.

We have simple interest = 240 = P*8*1/100 => P = 100*240/8 = 3000$.


Lori deposits $10,000 in a savings account at 10% annual interest, compounded annually. After 3 years, what is the balance on the account? (Assume Lori makes no deposits or withdrawals)

Balance amount = A = P* (1+r/100)^3 = 10000* (1.1)^3 = 10*11^3 = 13310.
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by gmattesttaker2 » Fri Jul 06, 2012 10:21 pm
eagleeye wrote:You need to know how to calculate simple and compound interest.

For simple interest: Simple Interest SI = P*r*t/100 (Where P is the principal, r is the rate and t is the time).

For compound interest: Total amount after time t = A = P*(1+r/100)^t.
So Compound interest = CI = A-P.

A car loan is offered at 8% annual interest, compounded annually. After the first year, the interest due is $240. What is the principal on the loan?
Since the loan is compounded annually, and the question asks for one year. Simple and compound interest are the same.

We have simple interest = 240 = P*8*1/100 => P = 100*240/8 = 3000$.


Lori deposits $10,000 in a savings account at 10% annual interest, compounded annually. After 3 years, what is the balance on the account? (Assume Lori makes no deposits or withdrawals)

Balance amount = A = P* (1+r/100)^3 = 10000* (1.1)^3 = 10*11^3 = 13310.
Hello Eagleeye,

Thank you very much for your excellent explanation and also for the formula. It is clear now. Thanks again.

Best Regards,
Sri
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