Formula and Use
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 the following.
- Payments are made at the start of each period for n periods.
- 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The annuity due formula can be used for example to determine the regular periodic payments which can be withdrawn from a savings account at the start of each of n periods before the balance (PV) is reduced to zero.
Excel Function
The Excel PMT function can be used instead of the annuity due payment formula PV. The Excel PMT function 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. Assume 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 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
Accordingly, if the opening balance on the account is 6,000 and the interest rate is 5%, then regular payments of 740.03 can be made at the beginning of each period for 10 periods,
Furthermore 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.
This annuity due payment formula is one of many annuity formulas used in time value of money calculations. Further information on additional time value of money formulas is avalable 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.