What this calculator does
PVIFA stands for present value interest factor of annuity. It is a single multiplier that turns a stream of equal, regular payments into what that stream is worth today, given a discount rate and a number of periods. Textbooks and finance courses often present it as a lookup table, with rate down one side and number of periods across the top, but it is just a formula: [1 minus (1 plus r) to the power of minus n] divided by r.
The factor on its own answers a narrower question than a full present-value calculation: it tells you what one dollar (or one unit of currency) per period is worth today, before you multiply by the actual payment amount. That is useful when a problem gives you the factor and asks you to apply it, or when you want the number itself rather than a dollar figure tied to one particular payment size.
The formula
Convert the rate to a decimal per period, raise (1 plus that rate) to the power of minus the number of periods, subtract the result from 1, then divide by the rate. If the rate is zero, the factor is simply the number of periods, since there is no discounting to apply. Multiplying the factor by a payment amount gives the present value of that whole payment stream.
| Term | Meaning |
|---|---|
| PVIFA | Present value interest factor of annuity: [1 - (1+r)^-n] / r. |
| r | The discount or interest rate per period, expressed as a decimal in the formula (entered here as a percentage). |
| n | The number of periods the equal payments run for. |
| Present value | PVIFA multiplied by the payment amount, giving what the whole stream of payments is worth today. |
The inputs explained
| Field | What to enter |
|---|---|
| Interest rate per period (%) | The interest or discount rate that applies to each period, as a percentage. Use a monthly rate for monthly payments, an annual rate for annual payments. |
| Number of periods | How many equal payments the annuity runs for, in the same period units as the rate. |
| Payment per period (optional) ($) | The payment made each period, if you want the present value in dollars as well as the bare factor. Leave it at 1 to read the factor on its own. |
When to use it
Textbook and exam problems
Many finance problems give a rate and a number of periods and ask for the PVIFA factor directly, or expect you to multiply it by a payment to reach the present value, without spelling out the underlying formula each time.
Valuing a fixed payment stream
A lease, a structured settlement, or a bond with equal coupon payments can be valued by multiplying the payment amount by the PVIFA factor for the relevant rate and term.
Comparing loan or annuity quotes
Because the factor isolates the effect of rate and term from the payment size, it is a quick way to see how much more (or less) a given payment stream is worth as either input changes.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the PVIFA factor changes with the interest rate
The factor for 10 equal periods, across a range of rates per period.
| Rate per period | PVIFA factor | Present value of the annuity |
|---|---|---|
| 2% | 8.983 | $8,982.59 |
| 4% | 8.111 | $8,110.90 |
| 6% | 7.360 | $7,360.09 |
| 8% | 6.710 | $6,710.08 |
| 10% | 6.145 | $6,144.57 |
| 12% | 5.650 | $5,650.22 |
How the PVIFA factor changes with the number of periods
The factor at a fixed 5% rate, as the number of periods increases.
| Number of periods | PVIFA factor | Present value of the annuity |
|---|---|---|
| 5 | 4.329 | $4,329.48 |
| 10 | 7.722 | $7,721.73 |
| 15 | 10.380 | $10,379.66 |
| 20 | 12.462 | $12,462.21 |
| 25 | 14.094 | $14,093.94 |
| 30 | 15.372 | $15,372.45 |
Questions
What is the difference between PVIFA and a normal present value of annuity calculation?
They are the same maths. PVIFA is the bare multiplying factor, [1 - (1+r)^-n] / r, before it is multiplied by a payment amount. A present-value-of-annuity result is that factor multiplied by the payment. This calculator shows both, so you can read off the factor on its own or the dollar present value.
What if the rate is zero?
With no discounting, each payment is worth exactly its face value today, so the PVIFA factor is simply equal to the number of periods, and the present value is just the payment multiplied by the number of periods.
Does PVIFA assume payments at the end or the start of each period?
This is the ordinary annuity form, which assumes payments at the end of each period. An annuity due, with payments at the start of each period, is worth slightly more because each payment is discounted for one fewer period.
Can the rate or number of periods be a fraction?
Yes. The formula works with any positive number of periods and any rate above -100%, so you can use a fractional period count or a fractional interest rate if your problem calls for one.
For payments that start at the beginning of each period instead of the end, see the annuity due calculator. To value a pot being drawn down over time rather than a fixed payment stream, see the annuity payout calculator.