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.
Choosing the rate and period
The rate and payment period must use the same time unit. Monthly cash flows need a monthly discount rate and a number of months. Quarterly cash flows need a quarterly rate and a number of quarters. Entering an 8 percent annual rate beside 120 monthly payments would discount every month by 8 percent, which is far more aggressive than an 8 percent annual assumption.
Converting an annual rate depends on how that rate is stated. A nominal annual rate compounded monthly is often divided by 12 to find the monthly periodic rate. An effective annual rate requires the compound conversion (1 + annual rate)^(1/12) - 1. Contracts and investment quotes may use other day-count or compounding conventions. Match the source document rather than assuming every annual percentage converts the same way.
This calculator models an ordinary annuity, so each equal payment arrives at the end of its period. If payments arrive at the beginning, the stream is an annuity due. With a positive rate, its present value equals the ordinary-annuity result multiplied by 1 plus the periodic rate. A first payment made immediately should not be discounted as though it arrived one period later.
At a zero percent rate, the formula's usual division by the rate would be undefined. The implementation handles that case directly by setting PVIFA equal to the number of periods. Ten payments of $1,000 then have a present value of $10,000. The calculator rejects negative rates, noninteger periods, zero periods, and terms above 1,000 periods.
A present value changes when the discount rate changes. That rate may represent a required return, borrowing cost, opportunity cost, or a rate specified in a contract. None is automatically correct for every decision. A risky or uncertain payment stream may need probability adjustments or a different valuation method rather than simply using a higher rate without analysis.
The computed payment stream is level and certain in the model. Real arrangements may include missed payments, defaults, escalation clauses, inflation indexing, balloon amounts, taxes, expenses, surrender charges, or changing rates. Those cash flows should be modeled period by period. PVIFA is useful when the equal-payment assumptions genuinely fit the problem.
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
- Using a nominal annual rate divided by 12 without checking its compounding convention
- Treating the calculated present value as a market quote, guaranteed return, or sale price
- Ignoring credit risk, inflation, taxes, fees, or payment uncertainty when choosing the discount rate
Limitations
This calculator computes an ordinary annuity with equal end-of-period payments, a nonnegative constant periodic rate, and an integer term from 1 through 1,000 periods. It does not model beginning-of-period payments, irregular dates, growing or shrinking payments, variable rates, inflation, taxes, fees, default risk, liquidity, embedded options, terminal values, or currency effects. The payment amount may be zero. A zero rate returns a factor equal to the number of periods. The result depends entirely on the chosen rate and cash-flow assumptions and is not a market price or guaranteed valuation.
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