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 Question from ameeta, a student: I need assistance on calculating principals interest rate and etc. i forgot how to do this. my question is joanna invest 500 dollars. She received 6 percent interest compounded monthly. how much interest did she earn with this investment after 3 years. the answer i calculated out to be was 90 dollars but could you please show me the steps.

Ameeta,

Since the annual interest rate is 6% the monthly rate is 6/12 = 0.5% or 0.5/100 = 0.005. Joanna invests $500 so at the end of the first month her return is$500 × 1.005 = $502.50. This is the amount she has to inverts at the beginning of the second month so at the end of the second month her return is$502.50 × 1.005 = $500 × 1.005 × 1.005 =$500 × (1.005)2.

This is the amount she has to inverts at the beginning of the third month so at the end of the third month her return is

$500 × (1.005)2 × 1.005 =$500 × (1.005)3.

Can you see the pattern now? At the end of the 36th month she will have $500 × (1.005)36. Penny Ameeta: If you work this out the way Penny Nom suggests, you will get a different answer than the$90 you got the first time. What you worked out is the _simple_ interest - that is, what Joanna would get if the interest was paid straight to her and not reinvested. If the interest is "compounded" that means that it is reinvested so in the second month she gets interest on the first month's interest,and so on. In the long run of course that yields more money.

-RD

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