This exercise certainly shows you the value of compount interest because each day the money grows, so the interest payment is higher. A sad reality check would be to do this same exercise with the "real" interest rate in today's economy. My standard bank savings account pays an interest rate of .1%. It makes the account merely a safe place to keep my money, but I don't earn enough to make it place to keep any substantial investment and would hardly be worse off if I kept the money in a cookie jar at home.

It would be helpful to me (and probably to the original asker of the question) if someone could explain the variations in the numbers cited above. Is one set of calculations correct and the other incorrect, or were the calculations done differently?

Certainly an understanding of interest rates is a great way of gaining money, and this is something that those shrewd enough to do so can use to their own benefit. However, the problem with this is you are dependent upon a healthy economy with good interest rates that will boost your savings. As #2 makes clear, you can make significant money out of your money, ending up with a total of $317.22 at the end of the entire period. Making money out of money you already have is obviously a good thing.

The future value of P at an interest rate r per year after t years is P*(1+r)^t

At 8 percent interest rate the future value of $100 after 5 the value would be $146.93, after 10 years it would be $125.89 and after 15 years it would be $317.21

If the interest rate were 5%, after 5 years the future value of $100 would be $127.62, after 10 years it would be $162.88 and after 15 years it would be $207.89

The longer you keep the money in an investment, the more interest you would make. However, considering the small amount of money, it probably is not worth it. I don't know where you'd get an 8% interest rate in this economy. There is also the opportunity cost of not using the money elsewhere.

For the 8% interest, your investment would be worth $146.93 in 5 years. In 10 years it would be worth $215.89. You'll notice that in the first 5 years you made about $47 in interest while you made about $68 in the next 5 years. This is why compound interest is such a great thing. In the third five years, you make even more, ending up with $317.22 at the end of that period.

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