  # Compound Interest

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## What Is Compound Interest and Why Does It Matter?

Compound interest can be quite confusing for most people.

When a person takes out any loan, the interest is calculated on the principal of the loan. The same is true when you put money in a savings account or invest it and the initial deposit earns interest. In a nutshell, compound interest allows you to earn interest on the interest you earned in previous years.

## Compound Interest Definition

Basically, the way compound interest works is that the interest is added to the principal balance for each term. This means that interest is then earned on the additional interest added to the original sum over the course of the next compounding period.

You can see an example of how the compound interest effect works on a \$1,000 investment below. As you can see in the graph, compound interest grows exponentially over the years.

The primary benefit of compound interest is that you can earn interest on money you never invested, allowing your investments to grow quicker than they could without it.

The above graph shows the compound interest impact over a period of 40 years.

## Annual Compound Interest Formula

The annual compound interest formula is as follows:

Compound Interest Formula

A = P (1 + r/n) (nt)

In this case:

A = The future value of the loan or investment,  including interest
P = The initial principal amount
r = The annual interest rate
n = The number of times the interest will compound on an annual basis
t = The number of years the money is borrowed or invested

This compound interest equation will yield the future value of a loan or investment, which is the principal plus compound interest.

To calculate only the compound interest, the formula is as follows:

Total compound interest = P (1 +r/n) (nt) – P

## How Does the Compound Interest Formula Work?

Let’s take a look at an example to see the compound formula at work:

If you deposit \$1,000 into a savings account with a 5% annual interest rate that’s compounded monthly, then the investment value after five years could be calculated as follows:

P = \$1,000
r = 5/100 = 0.05
n = 12
t = 5

A = \$1,000 (1 +0.05/12) ^ (12(5)) = \$1,283.36

Of course, no one is expected to break out this equation every time you need to figure out compound interest. Instead, you can use our free compound interest calculator. found at the top of this page for your convenience. 