The general compound interest formula is, P_{F} = P_{I}(1+ r/n)^{nt}. In this formula, P_{F} is the final amount of the investment or amount owed on a loan in dollars (or other currency) after time t, P_{I} is initial investment amount or principal, r is the interest rate expressed as a decimal, n is the number of compounding periods per period (the period is the unit in which the time, t is expressed in, perhaps months or years), and t is the number of time periods over which the interest is earned, usually in years.

The compound interest formula can be used to determine the additional amount of interest earned from an investment or owed on a loan. Let’s take a look at an example to illustrate how this formulation works.

Jason and Helen have $20,000 in a money market account at ABC bank. They earn an annual interest rate of 2.0%. The interest is compounded monthly or 12 times a year. How much money do they earn in interest for the first three years if no money is taken out or put into the account over this time period?

So our Principal, P_{I} is $20,000, the rate, r is 0.020 (2.0%/100), the time, t is 3 years, the interest is compounded 12 times per year so n is 12, and the interest that we are solving for can be obtained from P_{F }– P_{I}.

Now we just apply our formula, P_{F} = P_{I}(1+ r/n)^{nt}, to the situation in our example. P_{F} = ($20,000)(1+ 0.02/12)^{(12 x 3)}, so P_{F} = $21,235.67. If we subtract P_{I} from P_{F}, we get P_{F} – P_{I} = $21,235.67 - $20,000 = $1,235.67. So Jason and Helen earned $1,235 in interest on their $20,000 in the money market account over the three year time period with an interest rate of 2% compounded monthly.

Compound interest is quite possibly the most valuable tool for growing your money through savings and investments. The initial money you place in an investment will grow and yield interest, but when this interest is added back to the total, the investment has the ability to grow at an accelerated pace. This principle of increase can remain at work continually with your invested money earning interest and is the key to successful financial growth. For this reason it is beneficial if possible to avoid taking out loans that accrue a high rate of interest that is compounded.

REFERENCES / RESOURCES:

Calculate Compound Interest, Math Warehouse

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