## Compound Interest

Compound interest is the method of finding the total interest where interest is charged on the amount borrowed (the principal) as well as the interest already accumulated. The formula for calculating compound interest is:

- Compound Interest = (Principal x (1 + Rate)

^{Periods}) – Principal

So what happens if you aren’t that good with math? You are in luck — there is an alternate way to calculate compound interest!

If you recall, simple interest (where the interest is only charged on the principal) is found using this formula:

- Simple Interest = Principal x Rate x Time

We can use the simple interest formula (which is much easier to work with) to find the compound interest by using the simple interest formula for each period, adding the interest from the previous period to the principal amount for the next period. Let’s look at an example to illustrate the method.

## Example of Compound Interest

Let’s assume a five year loan of $12,000 at 7% interest compounded annually. For the first year, plug the numbers into the simple interest formula:

- First Year Interest = $12,000 x 7% x 1 year, or
- First Year Interest = $840.00

Now for the second year, add this interest to the principal in the simple interest formula, reflecting that the second year interest rate applies both the the original principal and the first year’s interest:

- Second Year Interest = ($12,000 + $840.00) x 7% x 1 year, or
- Second Year Interest = $12,840 x 7% x 1 year, or
- Second Year Interest = $898.80

Again, for the third year add this interest to the principal we used last year, reflecting that the third year interest rate applies both the the original principal and the interest from the first two years:

- Third Year Interest = ($12,840 + $898.80) x 7% x 1 year, or
- Third Year Interest = $13,738.80 x 7% x 1 year, or
- Third Year Interest = $961.72

Almost finished… For the fourth year add this interest to the principal we used last year:

- Fourth Year Interest = ($13,738.80 + $961.72) x 7% x 1 year, or
- Fourth Year Interest = $14,700.52 x 7% x 1 year, or
- Fourth Year Interest = $1,029.04

For the fifth and final year add this interest to the principal we used last year:

- Fifth Year Interest = ($14,700.52 + $1,029.04) x 7% x 1 year, or
- Fifth Year Interest = $15,729.56 x 7% x 1 year, or
- Fifth Year Interest = $1,101.07

Now if we add up all the annual interest amounts we get $840.00 + $898.80 + $961.72 + $1,029.04 + $1,101.07 = $4,830.63 as the total compounded interest. (If we plug the numbers into the more complicated compound interest formula we get $4,830.62 — a penny off due to rounding.)

This method will make it easier to calculate compounded interest if you aren’t very good at math or if you don’t happen to have a calculator handy.