Compute PVIFA and optional present value for ordinary or due annuities using rate per period and number of periods.
Compute the Present Value Interest Factor of Annuity (PVIFA) and optional present value for a fixed periodic payment.
PVIFA (ordinary annuity):
PVIFA = [1 − (1 + r)^(-n)] / r
PVIFA for an annuity due:
PVIFA_due = PVIFA × (1 + r)
Present value from a payment amount (PMT):
PV = PMT × PVIFA (or PMT × PVIFA_due)
Where r = rate per period (decimal) and n = number of periods.
Follow these steps to calculate the PVIFA and (optionally) the present value of an annuity on CalcMastery. You’ll set the rate per period, number of periods, and annuity timing.
Type the periodic rate in the “Interest Rate per Period (%)” box. If your APR is annual but payments are monthly, divide by 12 first (e.g., 6% APR → 0.5% per month; enter 0.5). Use a dot as the decimal separator (enter 7.5, not 7,5). Common mistake: entering the annual rate (6) instead of the per-period rate (0.5).
Use the “Number of Periods” slider or box to enter total payment periods, not years. For 10 years of monthly payments, enter 120. Avoid decimals—periods should be whole numbers.
Select “Ordinary (end of period)” if payments occur at each period’s end (typical for loans). Select “Due (beginning of period)” for rent/leases or payments made upfront; this applies the (1+r) adjustment. Mistake to avoid: picking the wrong timing, which over- or understates PV.
In “Payment per Period,” enter the fixed payment amount in currency units for each period (e.g., the monthly payment). Do not include thousands separators or currency symbols; enter 1250.75. Common error: entering an annual amount instead of the per-period payment.
Click “Calculate.” The tool shows PVIFA and, if you provided a payment, the Present Value (PV = payment × PVIFA). If r=0, PVIFA equals n (the number of periods); very small rates can make the factor large.
The Present Value Interest Factor of Annuity (PVIFA) is the discounting factor that converts a level payment made each period into its present value. For an ordinary annuity it equals the sum of per-period discount factors from period 1 to nn; for an annuity due it’s the same sum shifted one period earlier.
No. PVIF discounts a single future sum; PVIFA discounts a series of equal payments (an annuity).
Two core inputs: the interest (discount) rate per period and the number of periods. An option lets you choose timing: “ordinary annuity” (end-of-period payments) or “annuity due” (beginning-of-period payments).
Enter the rate for the same period as your payments. If your payments are monthly and you have a nominal annual rate with monthly compounding, use the annual nominal rate divided by 12. If you have an effective annual rate, convert it to a monthly rate by taking the 12th root of one plus the annual effective rate, then subtracting one.
If the rate is exactly zero, PVIFA equals the number of periods. Negative rates are allowed down to, but not including, −100% per period. Very large period counts or rates near −100% can reduce numerical precision; results are computed in double precision and rounded as described below.
Ordinary annuity assumes each payment occurs at the end of the period and uses the standard annuity-immediate factor. Annuity due assumes payments occur at the beginning of each period and applies one extra period of growth to the ordinary-annuity factor (i.e., it’s larger, all else equal).
The calculator computes PVIFA for an ordinary annuity by applying the standard closed-form annuity-immediate factor from finance texts; for an annuity due, it multiplies the ordinary-annuity factor by one plus the per-period rate. If the per-period rate is zero, the factor collapses to the number of periods.
When users supply non-annual payment frequencies, we treat the entered rate as the per-period rate; if users begin with a nominal annual rate compounded mm times, we convert to a per-period rate by dividing by mm; for an effective annual rate, we convert using the appropriate th root minus one (described in words here per request). All internal arithmetic is IEEE-754 double precision with the default “round to nearest, ties to even”; displayed PVIFA values are rounded to 10 significant digits.
When PVIFA is used to price currency amounts (payment × PVIFA), final monetary outputs should be rounded to the ISO 4217 minor unit for the selected currency code. Definitions of ordinary vs. due annuities and non-annual timing are aligned with the cited finance text.