Investment
Present value of a single amount
The inverse of compounding. Divide the future amount by the growth factor it would have accumulated over n periods at rate r.
The Formula
PV = FV / (1 + r)^n
The inverse of compounding. Divide the future amount by the growth factor it would have accumulated over n periods at rate r.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| FV | Future value | currency | The single amount to be received at the end, including any final repayment of principal. |
| r | Discount rate per period | decimal | As a decimal, and matched to the period length: if periods are months, use a monthly rate. |
| n | Number of periods | count | Must be counted in the same unit as r years with an annual rate, months with a monthly rate. |
| PV | Present value | currency | The discounted worth today of that future amount. |
What Each Symbol Means
FVcurrency
Future value
The single amount to be received at the end, including any final repayment of principal.
rdecimal
Discount rate per period
As a decimal, and matched to the period length: if periods are months, use a monthly rate.
ncount
Number of periods
Must be counted in the same unit as r years with an annual rate, months with a monthly rate.
PVcurrency
Present value
The discounted worth today of that future amount.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate present 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 Present Value, filed under Finance. Every number the guide produces comes from substituting into this one line.