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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