## Formula

n = LN(FV / PV) / LN(1 + i)

**Variables used in the formula**

PV = Present Value

FV = Future Value

i = Discount rate

n = Number of periods

LN = natural logarithm

## Use

The lump sum number of periods formula is used to work out the amount of time (n) it takes to grow a lump sum from its present value (PV), to a future value (FV) allowing for a given discount rate (i%).

## Lump Sum Number of Periods Formula Excel Function

The Excel NPER function can be used instead of the lump sum number of periods formula, and has the syntax shown below.

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

*The pmt and type arguments are not used when calculating the number of periods for a lump sum.

## Example

If a lump sum of 1,000 is received at the start of period 1, and the discount rate is 10%, then the number of periods to increase the value of the lump sum to 2,000 is given by the lump sum number of periods formula as follows:

n = LN(FV / PV) / LN(1 + i) n = LN(2,000 / 1,000 / LN(1 + 10%) n = 7.27 periods

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

n = NPER(i,,PV,-FV) n = NPER(10%,,1000,-2000) n = 7.27 periods

*don’t forget the minus sign on FV

The lump sum number of periods formula is one of many used in time value of money calculations, discover another at the links below.