Retirement
Present value of an ordinary annuity
Each payment is discounted back to today and the results are added.
The Formula
PV = PMT x (1 - (1 + i)^-n) / i
Each payment is discounted back to today and the results are added.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| PMT | Payment per period | currency | The equal payment made at each interval. |
| i | Rate per period | decimal | Annual rate divided by the number of payments a year. |
| n | Number of periods | count | Years multiplied by the payments per year. |
What Each Symbol Means
PMTcurrency
Payment per period
The equal payment made at each interval.
idecimal
Rate per period
Annual rate divided by the number of payments a year.
ncount
Number of periods
Years multiplied by the payments per year.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate annuity future value page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Annuity Future Value, filed under Finance. Every number the guide produces comes from substituting into this one line.