## Formula

n = LN ((FV x i + Pmt) / Pmt) / LN(1 + i)

**Variables used in the annuity formula**

FV = Future Value

Pmt = Periodic payment

i = Discount rate

n = Number of periods

LN = Natural logarithm

## Use

This number of periods annuity formula FV calculates the number of periods required for an annuity payment (Pmt) made at the end of each period to produce a future value (FV) when a discount rate (i) is applied.

The number of periods annuity formula FV can be used for example, to determine the number of periods is will take for a savings account balance to reach a given value assuming regular periodic deposits are made into the account at the end of each period.

## Excel Function

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

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

*In this instance, the PV and type arguments are not used when using the Excel number or periods function.

## Example Using Number of Periods Annuity Formula FV

An amount of 5,000 (Pmt) is deposited into a savings account at the end of each period. If the discount rate (i) is 4%, calculate the number of periods (n) it will take from the saving account to reach a balance of 120,000 (FV). The number of periods is given as follows:

n = LN ((FV x i + Pmt) / Pmt) / LN(1 + i) n = LN ((120000 x 4% + 5000) / 5000) / LN(1 + 4%) n = 17.16 periods

The same answer can be obtained using the Excel NPER function as follows:

n = NPER(i,pmt,PV,FV,type) n = NPER(4%,-5000,,120000) n = 17.16 periods

The number of periods annuity formula FV is one example of an annuity formula used in time value of money calculations, discover another at the link below.