Compounding interest is essentially interest on interest.

If we take an example of a $1000 investment earning 5% interest, that would mean $50 per year. So simple interest over 5 years would be:

Year 1: $1000 * 5% = $50

Year 2: $1000 * 5% = $50

Year 3: $1000 * 5% = $50

Year 4: $1000 * 5% = $50

Year 5: $1000 * 5% = $50

Total interest = $250

Instead, compound interest happens when we reinvest the $50 each year, back into the pot. So the 5 year run looks like:

Year 1: $1000 * 5% = $50

Year 2: $1000 + $50 ⇒ $1050 * 5% = $52.50

Year 3: $1050 + $52.50 ⇒ $1102.50 * 5% = $55.13

Year 4: $1102.50 + $55.13 ⇒ $1157.63 * 5% = $57.88

Year 5: $1157.63 + $57.88 ⇒ $1215.51 * 5% = $60.78

Total interest = $276.29

In this simple 5 year example, compound interest earned $26.29 or 10.5% more than under the simple interest model. The only difference between is that rather than taking out your earning each year, you reinvest them and let them compound. One can therefore imagine if this is the impact over only 5 years, what the impact over extended periods can be.

The impact of compound interest can be calculated using the future value formula

$FV = PV*(1+i)^n$

To break this down for our example:

Future Value (FV) is what we are trying to calculate

i = interest rate per period

n = number of periods

Present Value (PV) is the amount we invested = $1000

the interest rate (i) is 5% per year = 0.05

the number of periods is 5 years = 5

Which gives us $FV = 1000 * (1+.05)^5$ = $1276.28

**the 1 cent discrepancy is because in the annual breakdown I was rounding each year, whereas when calculated the rounding occurs only at the end. *

If you're interested in calcualating different scales of compounding, like monthly just adjust accordingly. So for our example, let's assume interest is compounded monthly:

We need to calculate what the applicable monthly interest rate is = 5% / 12 = 0.417% = 0.00417

And we no longer have 5 periods of compounding but rather 5 years * 12 = 60

So $FV = 1000 * (1 + .00417)^{60}$ = $1283.61

You'll note here that even though we used the same interest rate and the same 5 year investment period, because interest was compounded monthly instead of annually, we earned even more total interest. In this case, $7.33 or 0.57% more than with annual compounding.