# How to Calculate the Number of Years for an Investment

by C. Taylor

People, in general, are goal oriented, which applies to investments as well. Although you may have found formulas for valuing an investment, they may not give you the information you really want: How long will it take to reach your investment goal? If you wanted to double your initial investment, you are probably curious how many years it will take. By modifying the standard formula for compound interest, you can calculate how long you must remain in an investment before reaching your goal. This applies to both interest earning investments and those with an expected annual return on investment (ROI). In the latter case, the expected annual ROI is effectively the interest rate.

## Compound Interest

1. Research the investment to determine the annual return on investment and the number of compounding periods in a year. Your bank, stock broker or financial planner can help you with this information. As an example, you might invest in a savings bond that offers 6 percent interest and compounds quarterly, or four times per year. Also determine the amount you are willing to invest and your monetary target, which is the amount you wish to have after a certain period of time. If there is no compounding period, because the investment continuously grows, then use the continuous compounded interest calculation in Section 2. Stock investments would use this continuous compounded interest method with the expected annual ROI serving as the interest rate.

2. Divide the interest rate by the number of periods to calculate periodic interest. In the example, 0.06 divided by 4 gives you 0.015.

3. Add one to this figure. In the example, you have 1.015.

4. Take the natural logarithm of this number. On a business or scientific calculator, you would press the "Ln" key. In the example, you would have 0.0148886.

5. Multiply this figure by the number of periods. In the example, you would multiply 0.0148886 by 4 to get 0.0595544. Save this figure, because you'll need it again later. On most calculators, you can press "M+" to save it in memory.

6. Divide the investment target value by the initial investment. In the example, if you invested \$10,000 and wanted to achieve \$20,000, then you would divide \$20,000 by \$10,000 to get 2.0.

7. Take the natural logarithm of this figure. In the example, this gives you 0.693147.

8. Divide this figure by the interest rate, or expected annual ROI, to calculate the number of years. If you saved the number on your calculator's memory, press "MR" to recall it. In the example, it would take you 11.64 years to double your investment.

## Continuous Compounded Interest

1. Divide the investment target value by the initial investment. Using the previous example, divide \$20,000 by \$10,000 to calculate 2.0.

2. Take the natural logarithm of this figure. In the example, this gives you 0.693147.

3. Divide this figure by the interest rate, or expected ROI, to calculate the number of years. In the example, it would take 11.55 years to double your initial investment.