# Annualizing a Multi-year Return

When you’re reviewing your portfolio to determine which of your investments have been the biggest winners and losers, using percentages helps you compare investments of different amounts. After all, it wouldn’t be fair to say a \$100 investment that returned \$10 performed worse than a \$1,000 investment that returned \$100 because if you had invested the same amount in both stocks, you would have generated the same 10 percent return. In the same way, it’s not fair to compare your returns on an investment you’ve owned for 10 years to another investment you just purchased two years ago without annualizing the returns first. In order to annualize a multi-year return, you will need to calculate the return per year of your investment, factoring in all compounding interest.

#### TL;DR (Too Long; Didn't Read)

Annualizing a multi-year return requires proper accounting for compounded interest in addition to the total number of years the investment has been held.

## Compound Interest Effects

When figuring your annualized return, you can’t just divide the multi-year return by the number of years you’ve held the investment because that ignores the effects of interest compounding. Interest compounding refers to the fact that when your investment grows each year, those returns generate additional returns in the future. For example, if you hold an investment for 10 years, the returns generated in the first year have nine more years to generate additional returns, and that money can really add up. If you don’t take into account the effects of interest compounding, you will overestimate your annual return.

## The Formula to Annualize a Multi-Year Return

To annualize a multi-year return, the first set is to convert it to a decimal by dividing it by 100. Second, add 1. Third, raise the result to the power of 1 divided by the number of years you’ve held the investment. On a calculator, use the exponent key, usually represented by a “^” or “x^y” key, to perform the calculation. Fourth, subtract 1 from the result. Fifth, multiply by 100 to convert it back to a percentage.

For example, say you have an investment that has grown by 80 percent over the last 10 years. First, divide 80 by 100 to get 0.8. Second, add 1 to get 1.8. Third, raise 1.8 to the 1/10th power to get 1.061. Fourth, subtract 1 from 1.061 to get 0.061. Fifth, multiply 0.061 by 100 to find the average annual return over the 10 years is 6.1 percent. If you had simply divided 80 percent by 10 years, you would have calculated a return of 8 percent per year – significantly higher than the actual 6.1 percent return.