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# How to Calculate Compound Interest

## Compounding the interest on a savings account can build a nice nest egg. Here's the formula.

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

In the initial stages of securing a loan, the frequency at which the interest is compounded is established. Ordinarily, interest is calculated on an annual basis; however, other terms can be established at the time of the loan. By compounding interest, a principal amount can grow at a faster rate than it would if it only accumulated simple interest, which is only the percentage of the principal amount.

## Compound interest calculator

Compound interest is calculated differently from simple interest. For example, with a \$4,000 deposit and an annual interest rate of 8 percent, 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): 4,000 x 0.08 x 4 = 1,280.

Compound interest is calculated by applying the interest to the principal, as well as the 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 principal is \$5,038.85. Applying this math formula again at the end of the fourth year gives a new principal of \$5,441.96, or with a total interest earned of \$1,441.96. Compared to the simple interest, the compound interest is \$161.96 more.

The above math is just to help show the concept of compound interest. There is a formula that is much simpler than calculating for each year and adding on. This formula is, with P meaning present value, r meaning interest rate as a decimal, and t as the time period expressed as an exponent:

P x (1+r)t = Future value

This formula can also be used to work backwards. This is useful if you want to establish a goal to save a specific amount of money in a specific amount of time. In other words, if you know your future value (FV), and would like to figure out your present value, simply work the formula backwards, which looks like:

P = FV/(1+r)t

If you don't want to do the math yourself, the U.S. Securities and Exchange Commission has a Compound Interest Calculator at investor.gov.

## Patience pays off

Compound interest is most useful for those looking to save money over a long-term period. Through regular investments, a savings account can grow to quite a large amount. When it comes to investing with compounding interest, you should start early. The younger you start saving and contributing, the more time compounding can work in your favor. You should also make regular and disciplined investments. By making saving for retirement a priority, you could end up with an excellent nest egg.

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

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