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# Concepts of Compound Interest

Original post by Jonathan Langsdorf of Demand Media

Compound interest is a powerful force for use to grow the value of an investment portfolio. Once the concept of compounding interest is understood, an investor can take extra steps to incorporate investments or techniques to allow compound growth of her portfolio. Knowledge of the function of compound interest can lead to real money growth.

## Basics of Compound Interest

The basic idea of compound interest is an investment earns interest that adds to the value of the investment. As the value increases the amount of interest earned increases, based on the new higher value. Compounding can be thought of as earning interest not only on the original investment amount, but also on all interest previously earned. An investment only compounds if the earned interest stays in the investment to increase the value of the investment.

## Details of Compounding

The results of a compound interest investment are dependent on the interest rate and the compounding frequency. The interest rate is usually quoted as an annual rate, but may be provided as a per compounding period rate. The compounding frequency is how often interest is added into the investment value and interest starts to be calculated on the new, higher value. Compounding frequency may be daily, weekly, monthly, quarterly, semi-annually or annually. The periodic interest rate is the annual rate divided by the number of compound periods. For example, a 6 percent rate compounding semi-annually, has a periodic interest rate of 3 percent.

## Compounding Example

An example shows how compound interest works. A \$1,000 investment earns 8 percent compounded semi-annually. The periodic rate is 4 percent. After 6 months the investment has earned \$40 and is worth \$1,040. In the next period, 4 percent is earned on the new balance, producing interest of \$41.60, providing an account value of \$1,081.60. Interest for the next 6 months would be \$43.26, bringing the investment value up to \$1,124.86. If the investment was left to compound for 10 years, the value would grow to \$2,191.12. The periodic interest earning would be over double the initial amounts.

## Rule of 72

The rule of 72 allows a quick calculation of how long it takes for an investment to double in value at a specific interest rate. Divide 72 by the interest rate and the result is how many years it will take an investment to double, compounding annually at that rate. So at 7 percent, an amount will double in 72 divided by 7 or about 10 years. The rule assumes annual compounding. Using the rule on the 8 percent, semi-annual compounding, divide 72 by the periodic rate of 4. The investment will double in 18 semi-annual periods or 9 years.

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