Say that you have $500 in the bank and are getting 5% interest a year on your money compounded each year. How much would he have after 10 years?

After 1 year he would have 500 + 500 * .05 which is $525.

After year 2 he would have 525 * 1.05 = 551.25

After year 3 he would have 551.25 * 1.05 = 578.81

As you can see we are getting interest on our original amount and on the interest that we have .

We can use a formula to help us with this problem.

money = original x ((1 + interest rate) ^ 10)

1.05 ^ 10 is 1.63 (rounded to nearest hundredth), so after 10 years at that interest rate we will get 163% of our original amount.

500 x ((1 + .04)^10) is $814.45

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If we are compounding the interest monthly then we have a different problem. Say that Pete has $400 and he is getting 4% yearly interest, compunded monthly. Every month he gets interest, so we will be getting more interest than if it was compounded yearly.

The formula is :

money = original x (1 + (interest rate / 12)) ^ 36)

Every month he will not get 4% interest, he will get 4%/12 or .04/12. We must do it 36 times because there are 36 times we get interest (12 times each year for 3 years).

Note : (1 + .04/12)^36 = 1.127 while (1 + .04)^3 is 1.124 so you will make more money (just a little more) by compounding monthly instead of yearly

If you take the interest yearly you will end up with $449.95. If you take the interest monthly then you will end up with 450.91.

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Say you were putting $500 in the bank at 4% interest compounded yearly, and you wanted to find out how many years it would take you to make $100 in interest.

We could set up an equation :

500 x (1.04) ^ x = 600

1.04 ^ x = 1.2

x = log(1.2) / log(1.04)

Remember - if it was 10 ^ x = 1.2 we would just take the log of 1.2 but since we have a different base we must divide by the log of 1.04 to convert it to that base.

Answer is 4.65 years