Present Value Interest Factor of Annuity (PVIFA)

Present Value Interest Factor of an Annuity (PVIFA)

The present value interest factor of an annuity (PVIFA) is a factor used to calculate the present value of a series of equal, periodic payments (an ordinary annuity). It helps compare the value of receiving a lump sum today versus receiving a sequence of future payments by applying the time value of money.

Formula

PVIFA = (1 − (1 + r)^−n) / r

Where:
* r = period interest (discount) rate
* n = number of payments

Multiply the PVIFA by the payment amount to get the present value of the annuity.

How it works

• PVIFA discounts each future payment back to today and sums those present values into a single multiplier.
• A higher discount rate (r) reduces the PVIFA, meaning future payments are worth less today.
• PVIFA applies when payments are fixed in amount and timing (predetermined amount and term).

Annuity due (payments at period start)

If payments occur at the beginning of each period (annuity due), adjust the ordinary annuity PVIFA by multiplying by (1 + r):

PVIFA_due = PVIFA_ordinary × (1 + r)

Tools and tables

• PVIFA calculators compute the factor for any r and n.
• PVIFA tables list common r and n combinations for quick lookup; tables may introduce rounding error and are less flexible than calculators.

PVIF vs PVIFA

• PVIF (present value interest factor) discounts a single future lump sum back to today.
• PVIFA discounts and sums a series of equal periodic payments (an annuity).

Quick example

For r = 5% and n = 10:
PVIFA = (1 − (1.05)^−10) / 0.05 ≈ 7.722

The present value of a $1,000 annual payment for 10 years at 5% is:
$1,000 × 7.722 ≈ $7,722

Key takeaways

• PVIFA simplifies computing the present value of equal periodic payments.
• Use the PVIFA formula or a calculator to compare lump-sum offers with annuity streams.
• Adjust PVIFA by (1 + r) for annuity-due payments.
• The discount rate choice materially affects the present value and the decision between lump sum and annuity.