Formula and Use
An annuity is a series of equal payments made at equal intervals of time. The annuity payment formula PV calculates the annuity payment required to provide a given value today PV (present value). The formula assumes payments are made at the end of each period for n periods, and a discount rate i is applied.
The annuity formula can be used to determine the regular periodic payments required to clear a loan balance (PV). The formula for the annuity payment assumes that the discount rate remains constant over the entire period of the annuity. If the discount rate changes, then a new calculation will be necessary to determine the updated annuity payment. Additionally it is important to realize that the formula only applies to annuities received at the end of each period. For annuities that are received at the beginning of each period, a different formula is used.
Excel Function
The Excel PMT function can be used instead of the annuity payment formula PV, and has the syntax shown below.
PMT(Rate, Nper, PV, FV, Type)
*In this instance, the FV and type arguments are not used when using the Excel annuity payment function.
Example Using Annuity Payment Formula PV
A loan balance (PV) of 6,000 is cleared with regular annuity payments for 10 periods at an interest rate of 5%. The amount of the annuity payment is given by the annuity payment formula as follows:
Annuity payment = Pmt = PV x i / (1 - 1 / (1 + i)n) Annuity payment = Pmt = 6000 x 5% / (1 - 1 / (1 + 5%)10) Annuity payment = Pmt = 777.03
The same answer can be obtained using the Excel PMT function as follows:
Annuity payment = PMT(Rate, Nper, PV, FV, Type) Annuity payment = PMT(5%, 10, -6000) Annuity payment = 777.03
In conclusion, the annuity payment formula is a useful tool for calculating the stream of equal payments needed over a specified period of time to produce a given present value.
The annuity payment formula PV is one of many used in time value of money calculations, discover another at the links 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.