# How to Calculate Investment Rates of Return

by Kimberlee Leonard ; Updated July 27, 2017Looking at a year-end statement that shows the "rate of return" on investments only tells part of the story on return. Whether it is an annual percentage yield (APY) or compound annual growth rate (CAGR), it is important for the investor to understand how these are calculated to make sure the numbers they are reading are what they expect. These are two of many rates of return and are most often used with personal finance investment calculations.

Assume, for example, a $10,000 investment with a 6 percent return that compounds quarterly to be held for three years.

Convert the interest rate into a decimal point by dividing it by 100. In our example, 6%/100 = .06.

Determine the number of compounds in the year. Since our example is quarterly, this number is 4. Divide this into the number derived in Step 2. Example: .06/4 = .015.

Add one (1) to the number determined in Step 3. Example: 1 + .015 = 1.015.

Multiply the number of compounds per year with the number of years the investment will be held. Example: 4 x 3 = 12. Raise the number from Step 4 by this exponent. Example: 1.015 to the 12th power = 1.19561817.

Multiply the number in Step 5 with the amount invested. Example: $10,000 x 1.19561817 = $11,956.18. This is the amount the original investment will earn over the three years of compounding quarterly interest.

## How to Calculate CAGR

Assume in this example an investment of $10,000 is worth $12,000 at the end of year 1, $13,000 at the end of year 2 and $15,000 at the end of year 3.

Divide the initial amount by the ending value. Example: $15,000 / $10,000 = 1.5.

Divide the number of years invested by 1. Then use this number as the exponent to raise the value derived in Step 2. In the example: 1/3 years of investment = .3333. Then 1.5 raised .3333 = 1.14469877.

Subtract 1 from this number and then multiply this by 100. Example: 1.14469877 – 1 = .1446. The compound growth rate is 14.46 percent.