In financial terms, compound interest is the interest calculated on the initial principal, plus the accumulated interest of previous periods. Perhaps put more simply, compound interest is “interest on (interest + the principal).” Let’s first illustrate the concept of simple interest, and then move on to compounded interest.

## Simple Interest

Say you deposit \$1,000 into a savings account with a 5% annual simple interest rate. After 1 year, you will have \$1,050 in that account.

End of Year 1: (5% of 1,000 = 50) so (\$1,000 + \$50 = \$1,050)

After 2 years you’ll have \$1,100, and after 3 years you’ll have \$1,150. Every year you would gain \$50 of interest unless you added to the principal amount.

For instance, if after 2 years you decide to add another \$1,000 into your savings account, putting it at \$2,100, the next year you would earn interest on the principal of \$2,000 instead of \$1,000, bringing your annual interest to \$100. So with that newly added principal at the end of year 3, you would have \$2,200 in that account.

## Compound Interest

Let’s see what would happen if we take that same initial \$1,000 deposit and compound the interest annually at a 5% rate instead. At the end of year 1 will have \$1,050 (the same as with simple interest). But at the end of year 2 you will have \$1,102.50, and at the end of year 3 it will be \$1,157.62. So what’s happening here?

With compounded interest, you are treating your \$1,050 balance at the end of year 1 as your new principal balance, and calculating your interest based on that number.

End of Year 2: (5% of 1,050 = 52.50) so (\$1,050 + \$52.50 = \$1,102.50)
End of Year 3: (5% of 1,102.50 = ~55.12) so (\$1,102.50 + \$55.12 = \$1,157.62)