# Rule of 72 and Rule of 115

**Rule of 72**

The rule of 72 is a shorthand method of determining how long it will take for an investment to *double* in value when the annual rate of return is known. It is also a shorthand method for determining what the annual interest rate is when the time it took for an investment to double is known. The rule of 72 states that the approximate amount of time (in years) needed for an amount of money to double is 72 divided by the interest rate (expressed as a percentage). For example, suppose you have invested $1,000 that will earn 6% per year. How long will it take to double in value to $2,000? Simply divide 72 by 6 (the interest rate). The answer is 12, that is, it will take 12 years for the $1,000 investment to grow to $2,000. Conversely, suppose you have invested $1,000 eight years ago and it has grown to $2,000. What was the annual rate of return? Simply divide 72 by 8 (the number of years). The answer is 9%, that is, for an investment to double in value over 8 years, the annual rate of return is 9%. **Note**: the solution derived from this method is an approximation based on annual compounding. To determine an approximate answer using continuous compounding use 69.3 instead of 72.

**Rule of 115**

To approximate the time (in years) it will take for an investment to *triple* in value uses the rule of 115. The rule of 115 states that the approximate amount of time (in years) needed for an amount of money to triple is 115 divided by the interest rate (expressed as a percentage). For example, suppose you have invested $1,000 that will earn 5% per year. How long will it take to triple in value to $3,000? Simply divide 115 by 5 (the interest rate). The answer is approximately 23, that is, it will take roughly 23 years for the $1,000 investment to grow to $3,000. Conversely, suppose you have invested $1,000 ten years ago and it has grown to $3,000. What was the annual rate of return? Simply divide 115 by 10 (the number of years). The answer is 11.5%, that is, for an investment to triple in value over 8 years, the annual rate of return must be 11.5%. Again, this a rough approximation. Using a time value calculator, the actual annualized rate of return is 11.6%.

**Bookstore**: Books on Investment Performance Measurement

Also see:

Geometric average vs. arithmetic average return

Time-weighted vs. dollar-weighted return

Real (inflation-adjusted) vs. nominal return