If you invest money with the intention of funding a certain purchase, such as a fancy new car or a new home, or accumulating a retirement nest egg, you can calculate how many years it will take to reach your investment target if you know the annual rate of return. However, since returns are almost never guaranteed, the actual amount of time it takes to reach your goal could change depending on how your investments perform. The steps for figuring the time are derived from the formula for calculating the future value of a present amount.
Rearrange the formula for calculating the future value of a present amount, Future Value = Present Value * (1 + Interest Rate) ^ Number of Years, to Natural Log(Future Value / Present Value) / Natural Log (1 + Interest Rate). The only way to isolate the number of years value is to use the natural log function, because it is the inverse of the exponent function.
Divide your target value for the investment by the amount of the initial investment to find the increase expressed as a rate. For example, to figure how long it takes $16,000 to grow to $24,000, divide $24,000 by $16,000 to get 1.5.
Calculate the natural log, often abbreviated "ln" on calculators, of the result. The natural log function is the inverse of the exponent function and is used to isolate the time variable in the formula. You need to use a calculator to compute this value. In this example, calculate the natural log of 1.5 to get 0.4055.
Add 1 to the annual rate of return on the investment expressed as a decimal. For example, if you expect the investment to grow at 4.8 percent, add 1 to 0.048 to get 1.048.
Calculate the natural log of the result. In this example, calculate the natural log of 1.048 to get 0.04688.
Divide the step 2 result by the step 4 result to find the number of years it will take to reach your investment goal. Finishing the example, divide 0.4055 by 0.04688 to find it will take 8.65 years to reach your goal.
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