# Doubling Time Formula

## 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.

Doubling Time Formula November 6th, 2016

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