# Compound Interest

In this lesson we will learn how to solve compound interest math problems. Click the play button to start the video.

## Compound Interest Calculator

To quickly find out the balance and the compound interest for any principal, interest rate, and time period, use this free compound interest calculator provided on this website.

## Important Facts

Unlike the simple interest, the compound interest pays interest on both the principal and the interest already earned. To find the final balance after a certain number of years, use the following important formula:

# B = p (1 + r)^t

B is the final balance
p is the initial principal
r is the interest rate per year
t is the time in years

## Example:

If you deposit \$5000, in an account that earns 8% compounded annually, find the compound interest at the end of the second year and find the final balance.

## Solution

At the end of the first year, the interest will be

Interest year 1 = 5000 x 8% x 1 = 5000 x 0.08 x 1 = \$400

Add \$400 to the initial principal (\$5000) to find the new principal for the second year: \$5400

The interest at the end of the second year will be:

Interest year 2 = 5400 x 8% x 1 = 5400 x 0.08 x 1 = \$432

Therefore, the total compound interest at the end of the year two will be

\$400 + \$432 = \$832

To find the final balance you can use the formula B = p (1 + r)^t :

B = p (1 + r)^t = 5000 (1 + 0.08)^2 = 5000 x (1.08)^2 = 5000 x 1.1664 = \$5832

If you do not want to use the above formula, you can also find the final balance by adding the compound interest earned at the end of the year two (\$432), to the second year principal (\$5400).

\$432 + \$5400 = \$5832

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