Formula and Use
The present value of annuity formula shows the value today of series of regular payments. The payments are made at the end of each period for n periods, and a discount rate i is applied.
The formula discounts the value of each payment back to its value at the start of period 1 (present value).
In the formula the terms have the following meanings.
Periodic amount (Pmt). The payment amount is the amount of money that is paid at regular intervals, such as monthly, quarterly, or annually.
Interest rate per period (i). The interest rate per period is the rate at which the investment or loan is earning interest. It is typically expressed as an annual percentage rate (APR) and is divided by the number of payment periods to get the interest rate per period.
Total number of payment periods (n). The total number of payment periods is the number of payments made over the lifetime of the annuity. It can be calculated as the number of years times the number of payments per year.
Excel Function
The Excel PV function can be used instead of the present value of annuity formula, and has the syntax shown below.
PV(i, n, pmt, FV, type)
*The FV and type arguments are not used when using the Excel present value of an annuity function.
Present Value of Annuity Formula Example
If a payment of 5,000 is received at the end of each period for 10 periods, and the discount rate is 4%, then the value of the payments today is given by the annuity formula as follows:
PV = Pmt x (1 - 1 / (1 + i)n) / i PV = 5,000 x (1 - 1 / (1 + 4%)10) / 4% PV = 40,554.48
It is important to realize that the same answer can be obtained using the Excel PV function as follows:
PV = PV(i, n, pmt) PV = PV(4%,10,-5000) PV = 40,554.48
In conclusion the present value of an annuity calculates the present value of a stream of future payments made at regular intervals. As can be seen the present value of an annuity formula is based on several key parameters, including the interest rate (i), the number of payments (n), the payment amount (Pmt), and the time period. The formula takes into account the time value of money.
The present value of annuity formula 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 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.