Formula and Use
The present value of annuity due formula shows the value today of series of regular payments. The payments are made at the start of each period for n periods, and a discount rate i is applied.
It is important to realize that an annuity due is different from a regular annuity in that payments are made at the beginning of each period, rather than at the end of each period.
The formula shown discounts the value of each payment back to its value at the start of period one.
In the formula PV is the present value of the annuity due, PMT is the amount of each payment, i is the discount rate per period, and n is the number of periods.
The Excel PV function can be used instead of the present value of annuity formula. The function has the syntax shown below.
PV(i, n, pmt, FV, type)
*The FV argument is not used when using the Excel present value of an annuity due function.
Example Using the Present Value of Annuity Due Formula
To illustrate suppose a payment of 6,000 is received at the start of each period for 9 periods. Additionally the discount rate is 6%. In this case the value of the payments today is given by annuity due formula as follows:
PV = Pmt x (1 + i) x (1 - 1 / (1 + i)n) / i PV = 6,000 x (1 + 6%) x (1 - 1 / (1 + 6%)9) / 6% PV = 43,258.76
The same answer can be obtained using the Excel PV function as follows:
PV = PV(i, n, pmt,,1) PV = PV(6%,9,-6000,,1) PV = 43,258.76
Additionally our present value of an annuity due calculator can also be used to carry out the calculations shown above.
The present value of annuity due formula is one of many annuity formulas used in time value of money calculations. Discover another at the links below.
In summary, the PV of an annuity due formula is a useful tool for evaluating the value of a series of equal payments made at the beginning of each period. The formula takes into account the time value of money and the discount rate to determine the present value of the payments.
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.