# Compound interest: formula and definition

Compound interest is the interest that accumulates on the original principal and the interest accrued on a principal deposit, loan or debt. Interest is the fee paid by borrowers for the use of the owner’s assets. It applies to loans, credit cards and other debts, as well as bank accounts. Banks pay interest to the account holder for the use of deposited funds. The percentage of principal that is paid over time is the interest rate.

In the early stages of obtaining a loan, the frequency with which interest is compounded is established. Normally, interest is calculated on an annual basis; however, other conditions may be established at the time of the loan. By compounding interest, a principal amount can grow at a faster rate than if it accrued only simple interest, which is only a percentage of the principal amount.

## Compound interest calculator

Compound interest is calculated differently from simple interest. For example, with a deposit of \$ 4,000 and an annual interest rate of 8%, the simple interest after four years would be \$ 1,280. This is calculated by multiplying the principal (P) by the rate (R) and by the rate of time (T): 4000 x 0.08 x 4 = 1280.

Compound interest is calculated by applying interest on the principal, plus accrued interest, after each year. So after the first year, P x R x T = 320, so the new principal would be \$ 4,320. At the end of the second year, P x R x T = \$ 345.60, which is added to the old principal, creating a new principal of \$ 4,665.50. At the end of the third year, P x R x T = \$ 373.25, which, added to the old capital, is \$ 5,038.85. Applying this mathematical formula again at the end of the fourth year results in a new principal of \$ 5,441.96, for a total interest earned of \$ 1,441.96. Compound interest is \$ 161.96 more than simple interest.

The above calculations are just to help show the concept of compound interest. There is a formula which is much simpler than calculating for each year and adding. This formula is, with P signifying the current value, r signifying the interest rate in decimal number and t as the period of time expressed as an exponent:

Px (1 + r)t = future value

This formula can also be used to work backwards. This is useful if you want to set a goal to save a specific amount of money within a specific amount of time. In other words, if you know your future value (FV) and want to determine your current value, just work the formula backwards, which looks like:

P = VF / (1 + r)t

If you don’t want to do the math yourself, the United States Securities and Exchange Commission has a compound interest calculator on Investor.gov.

## Patience pays

Compound interest is particularly useful for those looking to save money over a long period of time. With regular investments, a savings account can grow to quite a large amount. When it comes to investing with compound interest, you should start early. The younger you start to save and contribute, the more time capitalization can work in your favor. You also need to make regular and disciplined investments. By making retirement savings a priority, you could end up with a great nest egg.

Keep an eye on your credit report to maximize your compound interest investments. You should also be patient and not touch the money you have set aside for compound interest. Compounding only works if the investment is allowed to grow. While the results may seem slow at first, persistence can really pay off. For example, an annual contribution of \$ 5,000 to an IRA for 45 years, with an average return of 8%, can generate retirement savings of over \$ 1.93 million, or more than eight times the amount contributed.