## Formula and Use

The doubling time formula continuous compounding is used to work 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%).

## Doubling Time Formula Continuous Compounding Example 1

If an investment is made at the start of period 1 and compounded continuously at a discount rate of 7% per period, then the number of periods it takes to double the value of the investment is given by the doubling time formula continuous compounding 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

If an investment is made at the start of period 1 and compounded continuously at a discount rate of 1% per month, then the number of months it takes to double the value of the investment is given by the doubling time formula continuous compounding 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 the standard doubling time formula should be used instead.

## Tripling Time Formula Continuous Compounding

It should be noted that the formula to calculate the doubling time can be adapted to calculate the time it takes to triple the value of a lump sum investment simply by replacing LN(2) with LN(3).

For example, if an investment is made at the start of period 1 and compounded continuously at a discount rate of 1% per month, then the number of months it takes to triple the value of the investment is given by the tripling time formula continuous compounding as follows:

n to triple = LN(3) / i n to double = LN(3)/ 1% n to double = 109.86 months

The doubling time formula continuous compounding is one of many used in time value of money calculations, discover another at the links below.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Plan Projections. 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 BSc from Loughborough University.