Formula and Use
This number of periods annuity formula PV calculates the number of periods required for an annuity payment (Pmt) made at the end of each period to produce a present value (PV) when a discount rate (i) is applied.
The number of periods annuity formula PV can be used for example to determine the number of annuity payments required to clear the balance on a loan account.
Excel NPER Function
The Excel NPER function can be used instead of the number of periods annuity formula PV, and has the syntax shown below.
NPER(i,pmt,PV,FV,type)
*In this instance, the FV and type arguments are not used when using the Excel number or periods function.
Number of Periods Annuity Formula PV Examples
Example 1 – Period Payments
A loan account balance of 50,000 (PV) is paid off with regular period end payments of 6,000 (Pmt). Consequently, if the interest rate on the loan is 6%, the number of periods (n) it would take to clear the loan balance is given as follows:
n = LN (Pmt / (Pmt - PV x i)) / LN(1 + i) n = LN (6000 / (6000 - 50000 x 6%)) / LN(1 + 6%) n = 11.90 periods
The same answer can be obtained using the Excel NPER function as follows:
n = NPER(i,pmt,PV,FV,type) n = NPER(6%,-6000,50000,,) n = 11.90 periods
Example 2
A loan account balance of 36,000 (PV) is paid off with regular periodic month end payments of 1,500 (Pmt). Additionally the annual nominal interest rate on the loan is 7% and interest is compounded monthly. Consequently the number of periods (n) it would take to clear the loan balance is given as follows:
n = LN (Pmt / (Pmt - PV x i)) / LN(1 + i) n = LN (1500 / (1500 - 36000 x 7%/12)) / LN(1 + 7%/12) n = 25.93 months
Again the same answer can be obtained using the Excel NPER function as follows:
n = NPER(i,pmt,PV,FV,type) n = NPER(7%/12,-1500,36000,,) n = 25.93 months
The number of periods is an important factor in the calculation of the present 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.
The annuity formula is one of many annuity formulas 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.