Formula and Use
Doubling time is a measure of the time it takes for a value or quantity to double in size. 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 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
To illustrate suppose an investment is made at the start of period 1, and the discount rate is 5%. In this case the number of periods it takes to double the investment is given by the formula as follows:
n to double = LN(2) / LN(1 + i) n to double = LN(2)/ LN(1 + 5%) = 14.21 periods
As can be seen this means that it will take approximately 14.21 periods for the investment to double in value at a growth rate of 5% per year.
Additionally 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) = 14.21 periods
*don’t forget the minus sign on PV
Additionally the Rule of 72 can be used as an approximation to the doubling time formula. In this case the rule is used as follows.
n to double = 72 / i n to double = 72 / 5 = 14.40 periods
Overall, the doubling time formula is a simple and useful tool for calculating the time it takes for a value to double in size, given a fixed rate of return or growth rate.
The doubling time formula is one of many used in the 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 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.