PVIFA Calculator
Compute the present value interest factor of an annuity. Enter the interest rate per period as a percent and the number of periods, choose ordinary annuity or annuity due, and optionally add a payment amount in dollars to see the present value of the whole stream.
Example: with Interest rate per period (%) 5 · Number of periods 10 · Payment timing Ordinary annuity (end of period) · Payment per period (optional, $) 1000 → PVIFA: 7.7217.
- Present value of the payments$7,721.73
- Total of all payments$10,000.00
- Discount vs total$2,278.27 less than the sum of payments
Computed by the calculator below using its default values. Change any input to see your own numbers.
PVIFA = (1 − (1 + r)^−n) ÷ r with r as the per-period rate. Multiply any level payment by this factor to get its present value.
What PVIFA does
PVIFA answers one question: what is a stream of identical payments worth today? Because a dollar arriving later is worth less than a dollar now, each payment is discounted by (1 + r) for every period you wait, and PVIFA is the sum of all those discount factors. At 5% per period for 10 periods the factor is 7.7217 — ten $1,000 payments are worth $7,721.73 today, not $10,000.
The same factor runs in both directions. Multiply a payment by PVIFA to value an annuity; divide a loan balance by PVIFA to find the level payment that retires it. Every fixed-payment mortgage, car loan, and structured settlement is priced on this identity.
Getting the per-period rate right
The r in the formula is the rate per payment period, not per year. For monthly payments quoted with a 6% annual rate, use r = 0.5% and n = number of months; for quarterly payments, divide the annual rate by 4. An annuity due (payments at the start of each period, like rent) is worth more — multiply the ordinary factor by (1 + r), which this calculator does when you switch the timing.
How it’s calculated
PVIFA (ordinary) = (1 − (1 + r)^−n) ÷ r, where r is the interest rate per period as a decimal and n the number of periods; when r = 0 the factor equals n. Annuity due multiplies the ordinary factor by (1 + r). Present value = payment × PVIFA; total of payments = payment × n; the discount line is their difference. Standard TVM notation, payments level and at the stated timing.
Assumes a constant per-period rate and identical payments — growing payments, changing rates, or taxes need a full cash-flow model like NPV.
PVIFA reference values (ordinary annuity)
| Periods (n) | PVIFA at 5% | PVIFA at 8% |
|---|---|---|
| 5 | 4.3295 | 3.9927 |
| 10 | 7.7217 | 6.7101 |
| 20 | 12.4622 | 9.8181 |
| 30 | 15.3725 | 11.2578 |
Computed with PVIFA = (1 − (1 + r)^−n) ÷ r; multiply by the payment per period for present value.
Common mistakes
- Using the annual rate with monthly periods — a 6% APR paid monthly needs r = 0.5% and n in months, or the factor is far too small.
- Confusing PVIFA with FVIFA: PVIFA discounts payments back to today, FVIFA compounds them forward to the end.
- Forgetting the (1 + r) multiplier for annuities due, which under-values start-of-period payment streams like rent or insurance premiums.
- Entering the rate as a decimal (0.05) in a field that expects percent, shrinking r by 100×.
Frequently asked questions
What is the PVIFA formula?
PVIFA = (1 − (1 + r)^−n) ÷ r, where r is the interest rate per period as a decimal and n is the number of periods. At r = 5% and n = 10 it equals 7.7217, so $1 per period is worth $7.72 today.
How do I get the per-period rate?
Divide the annual nominal rate by the number of payments per year: 6% annual with monthly payments is r = 0.5% with n counted in months. Mixing an annual rate with monthly periods is the most common PVIFA error.
What is the difference between an ordinary annuity and an annuity due?
Ordinary annuities pay at the end of each period (loans, bonds); annuities due pay at the start (rent, leases). Each due payment is discounted one period less, so PVIFA-due = PVIFA-ordinary × (1 + r).
How does PVIFA relate to loan payments?
They are inverses: payment = loan amount ÷ PVIFA. A $300,000 mortgage at 0.5% per month for 360 months has PVIFA 166.7916, giving a $1,798.65 monthly payment.
What happens when the rate is zero?
With no discounting, every payment is worth face value, so PVIFA simply equals n — ten periods give a factor of exactly 10.