Compute the present value factor of an ordinary annuity paying 1 per period, and the resulting annuity present value.
Input Data
Results
At a glance:PVIFA discounts a series of end-of-period payments of 1 to today; the annuity present value is the factor times the payment.
Formula
factor = (1 − (1 + periodicRate)^−periods) / periodicRate
presentValue = factor × payment
$$PVIFA = \dfrac{1 - (1 + r)^{-n}}{r}$$$$PV = PMT \times PVIFA$$How to Use
- Enter the periodic rate and number of periods.
- Enter the per-period payment (or 1).
- Read the PVIFA factor and annuity present value.
FAQ
What is PVIFA used for?
PVIFA is the present-value factor of an ordinary annuity that pays 1 each period; multiply it by the per-period payment to get the annuity's present value directly. It is the standard building block for loan amortisation, lease valuation and any equal-payment cash-flow series.
Why enter the payment as 1?
Entering 1 isolates the pure factor, so you can reuse it for any payment amount or compare across rate/term scenarios. PV = factor × payment, so once you have the factor, scaling to the actual payment is a single multiplication.
How is PVIFA related to the annuity present value formula?
PVIFA = (1 − (1+r)^−n) ÷ r; the annuity present value = PVIFA × payment. This is exactly the discounted sum of n payments of 1, and it underpins the EMI and mortgage formulas.
Does PVIFA assume payments at period end?
Yes — it is for an ordinary annuity (end-of-period payments). If payments are at the beginning of each period (annuity due), the factor is PVIFA × (1 + r). Keep the timing convention consistent with your cash flows.
What happens as the rate or number of periods changes?
A higher periodic rate lowers PVIFA (future payments discounted more); a longer term raises PVIFA (more payments, though with diminishing effect as discounting accumulates). The factor is most sensitive when both rate and term are moderate, so test a few combinations when planning long-term liabilities.
References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.