Equations · Finance and economics
Present value of an annuity
What a stream of equal payments is worth today.
PV = C (1 − (1 + r)⁻ⁿ) / r
Aethel says
P V equals C times the quantity 1 minus the quantity 1 plus r, to the power of negative n, over r
What it says
It is the sum of n discounted payments of C, each at the end of a period, collapsed into one expression with the geometric series. It prices loans, mortgages and pensions.
Symbol by symbol
| Symbol | Say it | Means |
|---|---|---|
| PV | P V | the present value |
| C | C | the payment each period |
| r | r | the interest rate per period |
| n | n | the number of payments |
Where you meet it
Corporate finance, mortgages and actuarial science.
Questions
How do you say Present value of an annuity out loud?
PV = C (1 − (1 + r)⁻ⁿ) / r is read: “P V equals C times the quantity 1 minus the quantity 1 plus r, to the power of negative n, over r.” That is exactly what Aethel says when it meets the formula in a book.
What does PV mean in Present value of an annuity?
PV (said “P V”) is the present value.
What does C mean in Present value of an annuity?
C (said “C”) is the payment each period.
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