Formula
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,. The function 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.
Number of Periods Annuity Formula FV Examples
Example 1
To illustrate, suppose an amount of 5,000 (Pmt) is deposited into a savings account at the end of each period. Additionally the discount rate (i) is 4% and the balance required at the end of the term is 120,000 (FV). The number of periods (n) it will take for the saving account to reach the balance 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
Example 2
To further illustrate, suppose an amount of 3,000 (Pmt) is deposited into a savings account at the end of each year. Additionally the discount rate (i) is 3% and the balance required at the end of the term is 90,000 (FV). The number of years (n) it will take for the saving account to reach the balance is given as follows.
n = LN ((FV x i + Pmt) / Pmt) / LN(1 + i) n = LN ((90000 x 3% + 3000) / 3000) / LN(1 + 3%) n = 21.71 years
Again the same answer can be obtained using the Excel NPER function as follows:
n = NPER(i,pmt,PV,FV,type) n = NPER(3%,-3000,,90000) n = 21.71 years
The number of periods is an important factor in the calculation of the future value of an annuity. It determines the total amount of the payments and the amount of interest that will be paid. The formula can be used to calculate the number of periods for annuities relating to pension plans, loans, leases, and other contracts with regular payments.
This annuity formula FV is one example of an annuity formula used in time value of money calculations, discover another at the link 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.