See Also:
Effective Rate of Interest Calculation
When is Interest Rate Not as Important in Selecting a Loan?
Interest Expense
Nominal Interest Rate
Interest Rate Swaps

What is Compound Interest?

Compound interest is interest earned on the principal plus interest earned on prior interest. Compounding interest rates not only earn interest on the original money, but also on the interest itself. The interest earns interest. Or, as Benjamin Franklin put it, “The money that money makes, makes money.”
For example, if an investor invests $100 at a 10% interest rate compounded yearly, during the first year the investment would earn interest on the original $100, and the next year the investment would earn interest on the original $100 plus the $10 of interest earned in the prior year.

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Compounding Periods

You can compound compound interest at different intervals, such as yearly, semi-annually, quarterly, monthly, daily, or continuously.
For yearly compounding interest rates, the original capital earns interest at the stated annual rate over the course of the year. The following year, the interest earned during the first year is added to the original capital, and the investment earns interest on the new amount.
For semi-annual, quarterly, monthly, or daily compounding interest rates, the original capital earns interest for the stated time period. At the end of that stated time period, the interest earned is added to the capital, and for the next period interest is earned on that new amount. This continues and the amount of money that earns interest gets larger and larger each period.
For a continuously compounding rate, the compounding period is an instant. In this case, compound the interest an infinite number of times during the course of a year.

Compound Interest and Simple Interest

There is a difference between compound interest and simple interest. An investment with compound interest grows faster than an investment with simple interest. Simple interest is interest earned on the original amount of capital. Each time period, the stated interest rate applies only to the principal amount. With simple interest, the interest itself does not earn interest.
For example, if $100 is invested at 10% yearly simple interest rate, then the investment earns $10 of interest each year. Each year, the interest rate applies only to the original $100 dollars and not to the accumulating interest.
Compound interest, as stated above, earns interest on the principal as well as the interest earned in prior periods. For example, if an investor invests $100 at a 10% interest rate compounded yearly, during the first year the investment would earn interest on the original $100, and the next year the investment would earn interest on the original $100 plus the $10 of interest earned in the prior year.

Compound Interest Formula

Here is how you calculate the value of an investment with compound interest after a certain number of years. First, divide the annual interest rate by the number of compounding periods. Then add one to that number. Next raise that value to the product of the number of compounding periods multiplied by the number of years of the investment. Take the value, and multiply it by the principal value. This gives you the ending value of the investment including compounded interest.

Investment Value = Principal x (1 + (Annual Rate/Periods))^{periods x years}

Compound Interest Monthly Formula

Use the following formula to calculate compound interest on a monthly basis:

Investment Value = Principal x (1 + (Annual Rate/12))¹²

For example, if you invest $100 at an annual rate of 6% that compounds monthly, then at the end of one year, the value of the investment would be $106.17.

$106.17 = $100 x (1 + (.06/12))¹²

Compound Interest Formula Quarterly

Use the following formula to calculate compound interest on a quarterly basis:

Investment Value = Principal x (1 + (Annual Rate/4))⁴

For example, if you invest $100 at an annual rate of 6% that compounds quarterly, then at the end of one year, the value of the investment would be $106.14.

$106.14 = $100 x (1 + (.06/4))⁴