**Compute the future value of $100 at 8 percent interest rate 5, 10, and 15 years in the future. What would the future value be over these time horizons if the interest rate were 5 percent?**

### 7 Answers | Add Yours

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.

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.

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

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.

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?

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.

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

Thanks for your post, it being very helpful for me to have an understanding on the book and to be able to implemente into that questions. I hope we are in the same page in this anwser. I did my calculation and they're the same so wish me luck in this one.

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes