Compound interest is a financial return that is earned on a previously earned financial return. It is interest that is earned on previously earned interest.
For example, suppose you put $1 in a savings account that pays 10% interest per year. In the real world, it would be difficult to obtain a 10% rate of return from a bank. It provides a fairly simple mathematical example, however.
Simple Example of Compound Interest with a 10% Rate of Return
Initial Deposit in the Savings Account $1.00
Interest Earned in the First Year ($1 times .10 ) $.10
Savings Account Balance After One Year $1.10
Interest Earned in the Second Year(1.10 times .10) $.11
Savings Account Balance After Two Years $1.21
Table 1. A simple example of compound interest.
Investing $1 at a 10 percent annual interest rate seems to suggest that the investment would earn 10 cents in interest each year. After two years, one might expect the value of the savings account to be $1.20. As this example illustrates, however, if the interest payments are left in the savings account, the interest earned in the second year will be 11 cents instead of 10 cents. The additional penny in interest is due to compounding. The extra penny is the interest earned in the second year on the 10 cents interest that was earned in the first year.
There is an equation that helps calculate the future value of investments based on the rate of return. This equation that relates the present value and future value of an investment is:
FV = PV (1 + i)n
where:
FV = future value of the investment
PV = present value of the investment
i = interest rate (i.e., rate of return)
n = number of years
In the example above, the present value of the investment is $1. The interest rate (i.e., rate of return) is .10. The dollar is invested for two years. Substitution into the equation above yields:
FV = ($1.00) (1.10)2
FV = ($1.00) (1.21)
FV = $1.21
This formula yields the same result that one dollar invested at 10 percent interest per year will be worth $1.21 after two years.
This equation can be used to develop a plan for one’s personal investments.
Consider the following three cases.
Compound interest is amazing. If you invest 200 dollars at 4% in fifty years you will have just 1100 dollars. But if you invest 200 at 10% a year thats the average return on stocks over long periods of time you would have 25000 dollars in fifty years.
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