# How to Figure Out How Long It Takes an Investment to Grow

by C. Taylor

Most investments, such as savings accounts, stock markets and some bonds, grow using compounded interest, which means accrued interest gains in value. How long an investment requires to reach a certain goal depends on the interest rate and the compounding period. If you know these variables, the compound interest formula allows you to calculate exactly how long is required to reach your goal.

1. Divide the future value of your investment, which is your investment goal, by the amount you originally invested. This gives you the overall growth factor. As an example, If you invested \$10,000 and wanted it to grow to \$20,000, you would divide \$20,000 by \$10,000 to get a growth factor of 2.

2. Take the natural log of this number. On a business or scientific calculator, enter the number and press the "ln" key. In the example, this gives you 0.693147.

3. Take the natural log of 1 plus the periodic interest rate. The periodic interest rate is simply the annual interest rate divided by the number of periods in a year. In the example, if your investment offered 8 percent interest, compounded monthly, you would divide 0.08 by 12 to get a monthly compounded interest rate of 0.0066667. Therefore, you would take the natural log of 1.0066667 to get 0.0066445.

4. Divide this number into the growth factor's natural log to calculate the number of periods to reach your goal. In the example, this gives you 104.32 periods, or 8.69 years.