# How to Determine the Percentage Increase With a Relative Rate of Change

by Tim Plaehn

When looking at investment results, it is often better to convert value changes to percentages. The percentage change shows how much an investment gained or lost relative to the initial investment costs. The conversion of value change to a percentage works for any type of investment. Once you have learned the procedure to calculate percentage changes, you can apply the calculation to a wide range of value and rate changes.

## Simple Percentage Calculation

To calculate the percentage of any gain or loss, divide the amount of gain or loss into the initial value. For example, if a stock was purchased at \$90 per share and increased in value by \$10 per share, the \$10 is divided by the \$90 to calculate a gain percentage of 11.1 percent. A loss would be calculated in the same manner. It may be necessary to subtract the ending value from the initial value to determine the amount or rate of change. The important point to remember is that percentage gains or losses are always calculated from the starting value.

## Periodic and Annual Percentages

The calculation of a percentage increase is not dependent on the time frame. Often, it is desirable to convert the gain to an annual percentage. If the calculated percentage gain or loss is for a period less than one year, calculate the portion of a year in which the gain -- or loss -- was made and divide the percentage by the portion. For example, a stock went up 15 percent in eight months. Eight divided by 12 equals 0.75. Dividing the 15 percent by 0.75 produces an annualized gain of 20 percent.

## Long Term Gains

To calculate the annual return for a gain earned over a period longer than one year, an advanced rate of return calculation is required. The calculations can be done with either a handheld financial calculator or using the financial functions available in a spreadsheet program. Gains earned over a multi-year period should be calculated as if the annual returns compounded each year. For example, if an investment doubles -- a 100 percent gain -- in five years, the annual return percentage would be 14.87 percent. With long-term gains, the amount earned each year is added to the starting point to calculate the return for the following year.

## Compounding vs. Simple Gains

Rates of change or gains can be either compounding or simple gains. If the gain adds into to the value each year and also earns a return, the gain compounds. For example, a \$10,000 account earns 5 percent per year compounded. After one year the account would be worth \$10,500 and the interest earned in the second year increases to \$525 and the account is worth \$11,025 after two years. With simple interest the amount earned stays level each year. For example, a \$10,000 bond pays 5 percent interest, which cannot be reinvested. The bond will earn \$500, or 5 percent, every year until the bond matures.

#### About the Author

Tim Plaehn has been writing financial, investment and trading articles and blogs since 2007. His work has appeared online at Seeking Alpha, Marketwatch.com and various other websites. Plaehn has a bachelor's degree in mathematics from the U.S. Air Force Academy.

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