PVIFA Calculator - Present Value Interest Factor of Annuity
Enter your interest rate per period, the number of periods, and an optional payment amount to get the present value interest factor of annuity (PVIFA) and the total present value of all future payments. Choose between an ordinary annuity (payments at the end of each period) or an annuity due (payments at the start). The step-by-step panel shows the full working, and the payment schedule breaks down each period.
Formula
Worked example
An ordinary annuity pays $1,000 at the end of each year for 8 years at 4% annual interest. r = 0.04, n = 8. (1 + 0.04)^(-8) = 0.730690. Numerator = 1 - 0.730690 = 0.269310. PVIFA = 0.269310 / 0.04 = 6.732745. Present value = 6.732745 x $1,000 = $6,732.74.
What is PVIFA?
The present value interest factor of annuity (PVIFA) is a multiplier that converts a stream of equal, evenly-spaced payments into a single present-day lump sum. It captures the core idea of the time value of money: a dollar received in the future is worth less than a dollar in hand today, because the dollar in hand can be invested and grow. PVIFA rolls up all those future payment discounts into one compact number. Multiply it by any equal periodic payment and you get the present value of the entire payment stream. This is used constantly in finance: to price bonds, evaluate loans, value leases, assess retirement income, and compare investment alternatives.
PVIFA formula - ordinary annuity vs annuity due
For an ordinary annuity (payments at the end of each period), PVIFA = [1 - (1 + r)^(-n)] / r, where r is the interest rate per period and n is the number of periods. For an annuity due (payments at the start of each period), multiply the ordinary PVIFA by (1 + r): PVIFA_due = PVIFA_ordinary x (1 + r). The annuity due is always larger because each payment arrives one period earlier and therefore has one fewer period of discounting. The difference matters most at high interest rates and long horizons: at 10% for 20 periods, the ordinary PVIFA is 8.5136 while the annuity due is 9.3649, a gap of about 10%.
How to use PVIFA in practice
If a bank offers you a choice between receiving $50,000 today or $6,000 per year for 10 years at a 6% discount rate, PVIFA answers whether the annuity is worth more. PVIFA = [1 - (1.06)^(-10)] / 0.06 = 7.3601. Present value of the annuity = 7.3601 x $6,000 = $44,160. Since $44,160 is less than $50,000, taking the lump sum is better at a 6% opportunity cost. Reverse the question: what annual payment over 10 years at 6% has a present value of exactly $50,000? Divide $50,000 by the PVIFA of 7.3601 to get approximately $6,793 per year. Loan amortization works the same way - the monthly mortgage payment is the loan principal divided by the PVIFA for the loan term and monthly rate.
Effect of interest rate and time horizon on PVIFA
PVIFA always rises as n increases (more payments add more present value) and always falls as r increases (a higher discount rate shrinks the value of each future payment). At very high interest rates, PVIFA approaches 1/r: even an infinite stream of payments converges to a finite present value called a perpetuity. For a perpetuity at 5%, PVIFA approaches 1/0.05 = 20, meaning any finite annuity at 5% has a PVIFA below 20 no matter how many periods. This ceiling effect explains why doubling the interest rate roughly halves the present value of long-dated annuities, while shorter annuities are far less sensitive to rate changes.
PVIFA table - common rates and periods
| Periods (n) | 1% | 2% | 3% | 4% | 5% | 6% | 7% | 8% | 10% | 12% |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.9901 | 0.9804 | 0.9709 | 0.9615 | 0.9524 | 0.9434 | 0.9346 | 0.9259 | 0.9091 | 0.8929 |
| 2 | 1.9704 | 1.9416 | 1.9135 | 1.8861 | 1.8594 | 1.8334 | 1.8080 | 1.7833 | 1.7355 | 1.6901 |
| 3 | 2.9410 | 2.8839 | 2.8286 | 2.7751 | 2.7232 | 2.6730 | 2.6243 | 2.5771 | 2.4869 | 2.4018 |
| 5 | 4.8534 | 4.7135 | 4.5797 | 4.4518 | 4.3295 | 4.2124 | 4.1002 | 3.9927 | 3.7908 | 3.6048 |
| 10 | 9.4713 | 8.9826 | 8.5302 | 8.1109 | 7.7217 | 7.3601 | 7.0236 | 6.7101 | 6.1446 | 5.6502 |
| 15 | 13.8651 | 12.8493 | 11.9379 | 11.1184 | 10.3797 | 9.7122 | 9.1079 | 8.5595 | 7.6061 | 6.8109 |
| 20 | 18.0456 | 16.3514 | 14.8775 | 13.5903 | 12.4622 | 11.4699 | 10.5940 | 9.8181 | 8.5136 | 7.4694 |
| 25 | 22.0232 | 19.5235 | 17.4131 | 15.6221 | 14.0939 | 12.7834 | 11.6536 | 10.6748 | 9.0770 | 7.8431 |
| 30 | 25.8077 | 22.3965 | 19.6004 | 17.2920 | 15.3725 | 13.7648 | 12.4090 | 11.2578 | 9.4269 | 8.0552 |
Ordinary annuity PVIFA values: present value of $1 per period at the given rate for the given number of periods. Multiply by your payment amount to find the total present value.
Frequently asked questions
What is the PVIFA formula?
For an ordinary annuity (payments at period end): PVIFA = [1 - (1 + r)^(-n)] / r, where r is the interest rate per period and n is the number of periods. For an annuity due (payments at period start), multiply the result by (1 + r). At a zero interest rate, PVIFA simply equals n.
What is the difference between PVIFA and PVIF?
PVIF (present value interest factor) discounts a single future payment to today: PVIF = 1 / (1 + r)^n. PVIFA discounts a series of equal payments and equals the sum of PVIF values for periods 1 through n. Use PVIF for a lump sum, and PVIFA for a recurring cash flow stream.
How do I use a PVIFA table?
A PVIFA table pre-computes the factor for combinations of interest rate and number of periods. Find the row for your period count, find the column for your rate, and read off the factor. Multiply that factor by your equal periodic payment to get the present value. This calculator generates the most common table values for you in the reference section below.
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period (mortgages, bonds, most loans). An annuity due pays at the start of each period (rent, insurance premiums, leases). Because payments arrive one period earlier, the annuity due is always worth more. Its PVIFA equals the ordinary PVIFA multiplied by (1 + r).
How is PVIFA used to calculate loan payments?
The monthly payment on a loan equals the loan principal divided by the PVIFA for the loan term. For example, a $200,000 mortgage at 0.5% per month for 360 months has PVIFA = [1 - (1.005)^(-360)] / 0.005 = approximately 166.79. Monthly payment = $200,000 / 166.79 = approximately $1,199. This calculator lets you work the math in either direction.
What happens to PVIFA at a zero interest rate?
When r = 0, future payments carry no discount at all, so each payment is worth exactly its face value today. PVIFA equals n (the number of periods), and the present value equals n times the payment amount. This makes sense: with no opportunity cost of money, the timing of payments is irrelevant.
What is the PVIFA of a perpetuity?
A perpetuity is an annuity that pays forever (n approaches infinity). As n grows very large, (1 + r)^(-n) approaches zero, so PVIFA approaches 1/r. For example, at a 5% rate, the PVIFA of a perpetuity is 1/0.05 = 20. This means a payment of $100 per year forever is worth $2,000 today at 5% interest.