# Lump Sum Number of Periods Formula

## Formula and 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.