# Computing Compound Return

## Compound return is one of the most frequently used terms in the investment world. But what does it mean? And how does one calculate it? This article will help you find out.

Compound return is a term thrown about frequently in advertisements for mutual funds and investment specialists. But what does it mean? And how do these financial types come up with these numbers? This article will explore these questions.

Before talking about how to compute compound return, it is important to talk about the idea of compound interest. Compound interest is simply this: interest that is paid on interest. This is different from simple interest, which only pays interest on the initial investment. For example, if you invested \$100 in a savings account with a 10% simple interest rate, at the end of the first year you would have \$110. This number is arrived at by adding the initial investment (\$100) with the interest accrued on that investment (100*.10). At the end of the second year, you would add the same interest (10% on the initial investment of \$100) to the total, raising the balance to \$120.

This is good, but not as good as compound interest, which works differently. For example, if you were to invest the same \$100 in a savings account at a compound interest rate of 10%, at the end of your first year you would have \$110 (100 + (100*.10)). At the end of the second year, the 10% compound interest rate would apply to the \$110, and you would now have \$121 (110 + (110*.10)). This extra dollar is a result of compounding interest.

There is a simple formula for figuring out the effect of compound interest on an investment. This is to take the interest rate, add it to 1, then multiply that number by itself once for each period the interest is compounded. Then multiply that number by the initial investment. On our above example, we would take the interest rate - 10%, or .10 - and add it to 1. This equals 1.1. Now following our formula, we get: 1.1*1.1 = 1.21. Multiply 1.21 by our initial investment, \$100, and we get a total of \$121. If we wanted to know how compound interest would affect our investment over 3 years, we would multiply 1.1 by itself three times (or 1.1 to the third power) before multiplying by the initial investment. Four years, four times (to the fourth power). And so on.

The equation for this is as follows: FV = IV(1 + R)^Y, where FV = Final Value, IV = Initial Value, R = Interest Rate, and Y = number of periods. The ^ symbol indicates exponentiation, or raising the value (1 + R) to the power Y.

This brings us to the notion of compound return. Computing compound return is essentially the same thing as computing the effect of compound interest, except reversing the process. Rather than figuring out how much money an investment will be worth knowing the compound interest rate and the number of periods, computing compound return is generating what the interest was based on the final and initial values of an investment.

For example, let's say you invested \$100 in a savings account. Three years later, your investment is worth \$172.80. What is the compound return on this investment? The process is simple, though you will probably need a good calculator. First, you need to figure out the factor by which your investment grew. This is done by dividing the end value by the beginning value. 172.8/100 = 1.728. Now, you need to find the third root of this number, since there were three years in the investment. In other words, what number raised to the third power will equal 1.728? Using a calculator, we find the number is 1.2 (1.2 * 1.2 * 1.2 = 1.728). Subtract 1 from this, and you get the answer - .2, or a 20% compound return.

There is, of course, an equation for this: TR = (1 + CR)^Y. Where TR = Total Return (Final Value/Initial Value), CR = Compound Return, and Y = Number of Periods. The ^ symbol indicates exponentiation, or raising the value (1 + CR) to the power Y. In our example we have TR = 1.728, CR = unknown, and Y = 3.

This may seem complicated at first, but with the help of a good calculator, or a spreadsheet program such as Excel, calculating compound interest and compound return is a snap. Knowing how to figure these numbers is a great skill to have when looking at different investments. It will help you become more financially savvy, and will help you navigate the complicated world that is financial planning.