by Orlando Miami

Created on: January 10, 2007   Last Updated: January 08, 2008

I think the best way to explain compound interest is to contrast it with its counterpart, simple interest.

In simple interest, your principal doesn't grow and benefit from future credits of interest. Rather, you always earn the same rate on your original principal. For example, 6% of simple interest per year on $100 is $6. Every year your simple interest will be $6 because it is based upon your original, never increasing, principal ($100 in this example).

Compound interest, on the other hand, assumes that your principal compounds with your interest. In other words, if you earn 6% on $100 in year one, your principal will grow to $106 (or $100 of principal + $6 of interest). The next year, if you earn 6% again, this rate will now be applied to your new higher principal balance of $106 resulting in $112.36 (as opposed to only $112 with simple interest).

While this example is not particularly compelling, the truth is that the value of compound interest is very powerful. Over long periods of time, say 30 years, compounding interest can lead to a huge gap in the amount of money you would end up with vs. simple interest.

Compound interest can also be applied over a period of time less than one year. Many savings accounts pay interest compounded monthly. What this means is that each month 1/12 of your annual interest rate is applied to your month-end balance and that result is credited to your account. The next month, your principal balance will be larger (assuming no deposits/withdrawals) as a result of the previous month's interest credit. And again, your account will be credited with 1/12 of the annual interest rate.

To make the math easy, assume that your bank offers you a 12% annual rate of interest compounded monthly. What this means is that each month, your month-end savings balance will be credited with 1% interest.

It is important to note that compound interest will ALWAYS result in a higher value than simple interest (assuming all other variables are equal).

The formula to calculate compound interest is below:

FV = PV((1+(r/n))^(tn))

Where:

FV = Future Value
PV = Present Value (or your original principal)
r = percentage interest rate (10% = 0.10 for example)
n = number of compounding periods (12 for monthly, 4 for quarterly, etc.)
t = number of years

For example, $1,000 at 4% compounded monthly for 10 years would equal:

FV = $1,000((1+(.04/12))^(10x12)) = $1,490.83

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