Pmt = PV x i / ((1 + i) x (1 - 1 / (1 + i)n))
PV = Present Value
Pmt = Periodic payment
i = Discount rate
n = Number of periods
This annuity due payment formula PV calculates the annuity payment required to provide a given value today PV (present value). The annuity due formula assumes payments are made at the start of each period for n periods, and a discount rate i is applied.
The annuity due formula can be used for example to determine the regular periodic payments which can be withdrawn from a savings account at the start of each of n periods before the balance (PV) is reduced to zero.
The Excel PMT function can be used instead of the annuity due payment formula PV, and has the syntax shown below.
PMT(Rate, Nper, PV, FV, Type)
*In this instance, the FV argument is not used when using the Excel annuity due payment function.
Example Using Annuity Due Payment Formula PV
A savings account balance of 6,000 (PV) is used to make regular annuity payments at the start of each period for 10 periods, at an interest rate of 5%. The amount of the annuity payment to reduce the savings account balance to zero after 10 periods is given by the annuity due payment formula PV as follows:
Annuity due payment = Pmt = PV x i / ((1 + i) x (1 - 1 / (1 + i)n)) Annuity due payment = Pmt = 6000 x 5% / ((1 + 5%) x (1 - 1 / (1 + 5%)10)) Annuity due payment = Pmt = 740.03
The same answer can be obtained using the Excel PMT function as follows:
Annuity due payment = PMT(Rate, Nper, PV, FV, Type) Annuity due payment = PMT(5%,10,-6000,,1) Annuity due payment = 740.03
* As the payments are at the start of each period, the Type argument in the Excel PMT function must be set to 1.
The annuity due payment formula PV 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 in 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 BSc from Loughborough University.