PVIFA Calculator (Present Value Annuity Factor)

PVIFA is the present-value multiplier for an annuity of $1 per period. Multiply it by the actual periodic payment to get the annuity’s present value.

PVIFA(r, n) = [1 - (1 + r)^-n] / r

Where r is the periodic interest rate and n is the number of periods. To value an annuity:

Present Value = Payment × PVIFA(r, n)

For example, a 30-year loan with monthly payments of $2,000 at 6% annual (0.5% monthly) for 360 months:

• PVIFA(0.005, 360) = [1 - 1.005^-360] / 0.005 = 166.79
• PV = 2,000 × 166.79 = $333,580 (the loan principal at origination)

Why the factor is useful. Once you have PVIFA, you can quickly value any annuity at the same r and n. Lease payments, retirement annuities, mortgage principals, structured settlements: all of them reduce to “what is PVIFA × payment?”

Common PVIFA values:

• 10 years at 5%: 7.722
• 20 years at 5%: 12.462
• 30 years at 5%: 15.372
• 10 years at 7%: 7.024
• 20 years at 7%: 10.594
• 30 years at 7%: 12.409
• 10 years at 10%: 6.145
• 20 years at 10%: 8.514
• 30 years at 10%: 9.427

Two annuity types, and using the wrong one is a real error.

• Ordinary annuity (payments at END of period): standard PVIFA above. Mortgages, most bonds.
• Annuity due (payments at BEGINNING of period): PVIFA × (1 + r). Rents, leases, insurance premiums.

Worked example: a mortgage payment. What monthly payment amortizes a $300,000 30-year mortgage at 6.5%?

Monthly rate = 6.5% / 12 = 0.541667% per month n = 360 months PVIFA(0.00541667, 360) = [1 - 1.00541667^-360] / 0.00541667 = 158.2108

Monthly payment = 300,000 / 158.2108 = $1,896.20

Keep the rate to more than four decimals here. Entering the rounded 0.5417% instead gives a factor of 158.2042 and a payment of $1,896.28, eight cents a month adrift. That is $29 across the life of the loan, from a rounding decision that looks harmless. On a corporate lease portfolio the same rounding is worth real money, which is why lease accounting standards are specific about the rate you use.

Worked example: bond pricing. A 10-year bond pays $50 semiannually with face value $1,000. Yield to maturity is 5% (so semiannual yield is 2.5%, n = 20 periods).

Coupon PV = 50 × PVIFA(0.025, 20) = 50 × 15.589 = $779.46 Face PV = 1,000 / 1.025^20 = 1,000 / 1.6386 = $610.27 Bond price = 779.46 + 610.27 = $1,389.73

The bond trades above face because coupons exceed the YTM-implied required return.

The intuition. PVIFA is a sum of discount factors: 1/(1+r) + 1/(1+r)² + … + 1/(1+r)^n. Each future $1 is worth less than $1 today; PVIFA tells you the cumulative present value of n future dollar payments.

Sensitivity. PVIFA decreases as r increases (higher discount = lower present value). It also approaches 1/r as n grows large, so a perpetuity is worth exactly 1/r times the payment. At 5% rate, perpetuity factor is 20; at 30 years it is already 15.37, so most perpetuity value is captured in the first 30 years.

Common mistake. Using annual r with n in months (or vice versa). Always match: monthly r with monthly n, semiannual r with semiannual n. Mixing them produces a number that looks reasonable but is wildly wrong.