M = P( 1 + i )^n

M is the final amount including the principal.

P is the principal amount.

i is the rate of interest per year.

n is the number of years invested.

Stolen from

http://math.about.com/od/formulas/a/compound.htmSo, if we take the example of someone who invests $1000, at 5%, and it compounds annually.

In year 1, they would have

M = P( 1 + i )^n

M = 1000(1.05)^1 = 1050

In year 2, there are 2 ways to calculate it.

Using the formula above

M = P( 1 + i )^n

M = 1000(1.05)^2 = 1000(1.1025) = 1102.5

Or we can use the 1050 from the first year, as the new P number

M = P( 1 + i )^n

M = 1050(1.05)^1 = 1102.5

So, if you can see what is happening here, the interest earned at the end of the first compounding period (here it is a year), becomes the input as the principal in the second year. That rolling over of the interest, into the principal for the next compounding period, is how compounding interest works.

Let's do another example to illustrate just how much compounding can make a difference!

Say you have 1000 to invest, and it will earn 5% annually (from an very stable fund, for example), and it will pay out that interest rate for 25 years. You are given the option to let that interest compound (roll over) or you can take it out annually, whichever you prefer.

If you take the interest out every year, the formula doesn't need to compound (simple interest), so it will look like this:

M = P*i*n + P

M = (1000 x 0.05 x 25) + 1000 = 1250 + 1000

M = 2250

But, in this case, you need to remember, that you were taking the interest out every year, so you would have collected $50/year for 25 years, meaning you earned $1250 in interest, plus you have your original $1000 left at the end.

But, if you let the interest compound, it would look like this:

M = P( 1 + i )^n

M = 1000(1.05)^25 = 3386.35

So, if the interest compounds, you wind up with $1136.35 of EXTRA growth at the end of the 25th year.

If that has helped at all, (or not) please let me know.

Other things that are important, that will make your money grow faster are:

-higher interest rates (even 0.1% can make a big difference, after a large number of compounding cycles)

-shorter compounding cycles