Formula and Use
The doubling time formula continuous compounding works out the amount of time (n) it takes to double the value of a lump sum investment allowing for continuous compounding at a given discount rate (i%).
It is important to realize that in the formula shown above the period is defined by that used for the discount rate. To illustrate for example, if the discount rate is monthly then the answer is the number of months to double. In contrast if the discount rate is annual the answer will be the number of years to double.
Doubling Time Formula Continuous Compounding Example 1
To illustrate consider an investment made at the start of period 1 compounded continuously at a discount rate of 7% per period. The calculation of the number of months it takes to double the value of the investment is as follows:
n to double = LN(2) / i n to double = LN(2)/ 7% n to double = 9.90 periods
Doubling Time Formula Continuous Compounding Example 2
Consider an investment made at the start of period 1 compounded continuously at a discount rate of 1% per month. Accordingly the calculation of the number of months it takes to double the value of the investment is as follows:
n to double = LN(2) / i n to double = LN(2)/ 1% n to double = 69.31 months
This formula is used when compounding takes place on a continuous basis. If compounding is not continuous, then use the standard doubling time formula instead.
Tripling Time Formula Continuous Compounding
It is important to realize that the formula to calculate the doubling time is adaptable. By simply replacing LN(2) with LN(3) it is possible to calculate the time it takes to triple the value of a lump sum investment.
Consider an investment made at the start of period 1 compounded continuously at a discount rate of 1% per month. Accordingly the calculation of the number of months it takes to triple the value of the investment is as follows:
n to triple = LN(3) / i n to double = LN(3)/ 1% n to double = 109.86 months
The doubling time formula is one of many used in time value of money calculations. Additional formulas are available at the links below.
About the Author
Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a degree from Loughborough University.