Compound Interest

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Compound Interest – What Does it Mean?

compound interest calculator

The subject of compound interest can be quite confusing for many people.

As you are probably already aware, when you take out a loan, interest is calculated on the principal of the loan. The same is true when you put money in a savings account. The initial deposit earns interest.

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.

Below you can see an example how the compound interest effect works on a $1000 amount. As you can see from the graph, the compound interest effect exponentially grows the initial principal amount.

Compound interest example

A graph shows the compound interest effect over a period of 40 years

Annual Compound Interest Formula

The annual compound interest formula is as follows:

compound interest formula

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 loan amount or deposit, referred to as the principal sum
r = the annual interest rate
n = the number of times the interest will be compounded on an annual basis
t = the number of years the money is borrowed or invested

It should be understood that this compound interest equation will yield the future value of a loan or investment. This is the principal plus the compound interest.

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

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

Example: How Does the Compound Interest Formula Work?

Let’s take a look at an example how the compound formula works:

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

P = 1,000
r = 5/100 = 0.05
t =5

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

If you have trouble with this formula, a compound interest calculator can help – scroll to the top of the page to find the calculator.

The primary benefit of compound interest is that the initial sum will earn more with compounded interest than it would without it.