# John invested $20,000 in a finance company that pays compound interest at a rate of 1.8% per annum.Find the total amount of interest he would receive after 3 years if the interest is compounded...

John invested $20,000 in a finance company that pays compound interest at a rate of 1.8% per annum.Find the total amount of interest he would receive after 3 years if the interest is compounded every 6 months

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### 1 Answer

The investment is $20,000 and it earns 1.8% annual interest rate compounded semiannually. How much interest after 3 years?

Let P be the principle -- then the amount of interest I is given by:

`I=P(1+r/m)^(nm)-P` where r is the annual interest rate, m is the number of compounding periods per year, and n is the number of years.

`I=20000(1+.018/2)^(2*3)-20000`

`~~21104.59-20000`

`=1104.59`

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So the interest earned is $1104.59

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