How to solve this compound interest problem?

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How to solve this compound interest problem?

Postby student101 » Mon Apr 27, 2015 10:33 am

A man deposited 2,000 into a bank that paid compound interest of 3.28% compound half yearly. He continued depositing $2,000 into the bank every six months.Calculate the amount of money he had after he made his fifth deposit of $2,000,giving your answer correct to the nearest cent.

I need help to solve this question in an easy way acceptable for O level. Also I have a doubt about whether the interest given(3.28%) is annual interest or half year interest as in the question,it is not mentioned clearly.

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Re: How to solve this compound interest problem?

Postby » Wed Jun 10, 2015 2:12 am

Interest given usually annual interest. The interest rate given in this question is annual interest rate.

Compound interest formula:

(principal + interest) = Principal * (1+ interest rate per period(%) / 100) to the power of n period

Since the interest rate provided by the bank is compounded half yearly, so one period is half year.

So the interest rate per period for this question we have to use interest rate per half year. Given in the question, interest rate is 3.28% per year, then the interest rate per half year would be (3.28% divided by 2 = 1.64%)

The number of period would be the number of half years that the principal money is deposited in the bank.

For the first deposit, the money would be compounded for 4 times.
{because he will only get his first interest for his first $2,000 after 6 months ( when he made second deposit of $2,00),and then second interest after 1 year (we he made third deposit of $2,000) ...and four interest at his deposit}

(Principal + int) for 1st $2,000 deposit = 2000(1+ 1.64/100) to power 4
= 2134.46

Following the same concept,

(Principal + int) for 2nd $2,000 deposit = 2000(1+ 1.64/100) to power 3
= 2100.02

and following same concept get [ 3rd deposit = 2066.14] [4th deposit =2032.8]
fifth deposit didnt earn any interest because it is just deposited. So total is =10333.42
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