Formula library

Present Value of Annuity Due

Present Value of Annuity Due
\[PV=PMT\frac{1-(1+i)^{-n}}{i}(1+i)\]

Variables

PVpresent value of annuity due (currency)
PMTperiodic payment (currency)
iinterest rate per period (decimal)
nnumber of periods

Description

What is this formula?


The Present Value of an Annuity Due calculates the current value of a series of equal payments made at the beginning of each period.


Because payments are received or paid one period earlier than in an ordinary annuity, the present value is greater than the equivalent ordinary annuity.


When to use it


Use this formula when payments occur at the beginning of each period and you need to determine their equivalent value today.


Example


Suppose:


PMT = $1,000


i = 0.01 per month


n = 12 months


Formula:


PV=PMT((1-(1+i)^(-n))/i)(1+i)


Substitution:


PV=1000((1-(1.01)^(-12))/0.01)(1.01)


PV=11,367.63


Result:


Present Value = $11,367.63


Applications


Lease analysis


Insurance contracts


Retirement planning


Loan evaluation


Investment analysis


Financial planning


Note


This formula assumes equal payments made at the beginning of each period and a constant interest rate. Real financial arrangements may involve changing interest rates, fees, inflation, taxes, or irregular payment schedules that affect the actual present value.

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