# What Is Compound Interest?

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)