PVIFA Calculator
A 10-period annuity at an 8% periodic rate has a PVIFA of about 6.71. This PVIFA calculator finds the present value interest factor of annuity from a periodic interest rate and a number of periods, then uses that factor to show the present value of a fixed periodic payment. Enter the rate per period, the number of periods, and an optional payment amount to see both numbers at once.
Quick answer
PVIFA converts a stream of equal future payments into a single multiplier you can apply to one payment amount.
What this tells you
- •PVIFA converts a stream of equal future payments into a single multiplier you can apply to one payment amount.
- •A higher periodic rate or fewer periods produces a smaller PVIFA, because future payments get discounted more.
- •Multiply PVIFA by the periodic payment to get the present value of the whole annuity.
How to Use
- 1Enter the interest rate per period as a percent, such as 8 for 8% per period.
- 2Enter the number of periods in the annuity, such as 10 for 10 years or 10 months.
- 3Enter an optional periodic payment amount to see its present value using the PVIFA factor.
- 4Calculate to see the PVIFA factor and, if you entered a payment, the present value of that payment stream.
How It Works
Formula
PVIFA = [1 - (1 + r)^-n] / r
Present value = Payment x PVIFAr is the interest rate per period as a decimal and n is the number of periods. The formula discounts each of the n equal future payments back to today and adds them together into one factor. When r is 0, PVIFA equals n, because payments with no discounting simply add up to the number of periods.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Ordinary annuity at 8% for 10 periods
A payment of $1,000 at the end of each of 10 periods, discounted at 8% per period, is worth about $6,710.08 today.
Longer annuity at a lower rate
Even though this annuity runs twice as long, the lower 5% rate and smaller payment bring the present value in close to the first example.
PVIFA Factor at Common Rates and Terms
These factors show how the present value interest factor of annuity shrinks as the rate or the term changes.
| Periods | 5% per period | 8% per period | 10% per period |
|---|---|---|---|
| 5 | 4.3295 | 3.9927 | 3.7908 |
| 10 | 7.7217 | 6.7101 | 6.1446 |
| 20 | 12.4622 | 9.8181 | 8.5136 |
| 30 | 15.3725 | 11.2578 | 9.4269 |
Figures are rounded to 4 decimal places. Use the calculator above for an exact factor at your own rate and term.
Common mistakes
- Entering an annual rate when the payments are monthly or quarterly, instead of converting to a per-period rate first
- Confusing PVIFA with the future value interest factor of annuity, which compounds forward instead of discounting back
- Assuming payments happen at the start of each period, when this factor assumes payments happen at the end of each period