When setting savings goals, it's helpful to know how long it's going to take for your investment to reach your target. Say, for example, you want to put aside some money now so that you'll be able to buy a new car for $15,000. To figure how long it's going to take that money to grow to $15,000, you have to know the interest rate, how often interest compounds, and how much you're putting in.
Step 1
Divide the target amount by the amount you're investing. Say you want to invest $9,000 today and have it grow to $14,000: Divide $14,000 by $9,000 to get 1.5555.
Step 2
Figure the natural log of the result with a scientific calculator. The natural log function is usually represented by "ln" on the calculator. In this example, the natural log of 1.5555 is 0.4418.
Step 3
Divide the annual interest rate by the number of times per year interest compounds to figure the periodic rate. For example, if you have an annual interest rate of 3.6 percent and it compounds monthly, divide 0.036 by 12 to get a periodic rate of 0.003.
Step 4
Add 1 to the periodic rate. In this example, add 1 to 0.003 to get 1.003.
Step 5
Raise the result to the power of the number of times each year interest compounds. In this example, since your interest compounds monthly, or 12 times per year, raise 1.003 to the 12th power to get 1.0366.
Step 6
Figure the natural log of the result. In this example, take the natural log of 1.0366 to get 0.0359.
Step 7
Divide the Step 2 result by the Step 6 result to figure the time, in years, it takes to reach your investment goal. Finishing the example, divide 0.4418 by 0.0359 to find it will take about 12.3 years for your $9,000 to grow to $14,000 at 3.6 percent interest.
