## Formula

n to double = LN(2) / LN(1 + i)

**Variables used in the formula**

i = Discount rate

n = Number of periods to double the investment

LN = natural logarithm

## Use

The doubling time formula is used to work out the amount of time (n) it takes to double the value of a lump sum investment allowing for a given discount rate (i%).

## Excel Function

The Excel NPER function can be used instead of the doubling time formula, and has the syntax shown below.

NPER(i,pmt,PV,FV,type)

*The pmt and type arguments are not used when calculating the doubling time for a lump sum. In addition, as FV = 2 x PV when the investment doubles in value, PV should be set to -1, and FV should be set to 2 as follows:

NPER(i,pmt,-1,2,type)

## Doubling Time Formula Example

If an investment is made at the start of period 1, and the discount rate is 5%, then the number of periods it takes to double the value of the investment is given by the doubling time formula as follows:

n to double = LN(2) / LN(1 + i) n to double = LN(2)/ LN(1 + 5%) n to double = 14.21 periods

The same answer can be obtained using the number of periods formula in Excel as follows:

n = NPER(i,,PV,-FV) n to double = NPER(5%,,-1,2) n to double = 14.21 periods

*don’t forget the minus sign on PV

The Rule of 72 can be used as an approximation to the doubling time formula.

The doubling time formula 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 Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years in 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.