Hong Life CalculatorsUnderstanding the PVIFA calculator — concept and principle
PVIFA (present value interest factor of an annuity) is the number you multiply a regular payment by to get the present value of all the payments. This calculator gives PVIFA, FVIFA and the single-sum factor PVIF, and applies them to a payment you enter.
How it is calculated
- PVIFA = [1 − (1 + r)^−n] ÷ r, for payments at the end of each period.
- FVIFA = [(1 + r)^n − 1] ÷ r, the future value at the end of period n.
- PVIF = (1 + r)^−n, the present value of a single sum at period n.
- For an annuity due (payments at the start), both annuity factors are multiplied by (1 + r). At r = 0 they equal n.
The principle
The present value of one payment received in k periods is 1 ÷ (1 + r)^k. An annuity is a sum of such terms for k = 1 to n, a geometric series with a closed-form sum: PVIFA. FVIFA works the same way forward in time. Before calculators, finance textbooks printed these factors in tables; they are still a quick way to price loans, leases, bonds and pensions.
Worked example
Default inputs: rate 6% per period, 10 periods, ordinary annuity, payment 1,000 USD.
- PVIFA = [1 − 1.06^−10] ÷ 0.06 ≈ 7.3601.
- Present value of the payments = 1,000 × 7.3601 ≈ 7,360.09 USD.
- FVIFA = [1.06^10 − 1] ÷ 0.06 ≈ 13.1808; future value ≈ 13,180.79 USD.
- PVIF at period 10 = 1.06^−10 ≈ 0.5584.
- Total of the payments = 10,000 USD.
| Number of periods (n) | PVIFA |
|---|---|
| 2.5 | 2.2593 |
| 5 | 4.2124 |
| 7.5 | 5.9007 |
| 10 | 7.3601 |
| 12.5 | 8.6217 |
| 15 | 9.7122 |
| 20 | 11.4699 |
How to read the result
The gap between the total of the payments (10,000) and their present value (7,360) is the value of waiting: money paid later is worth less today. A higher rate or longer term widens the gap. To find a loan payment from an amount, divide the amount by PVIFA.
Common mistakes
- Using an annual rate with monthly periods (use the monthly rate and months).
- Mixing ordinary annuities and annuities due.
- Entering the rate as 6 instead of 6% in a formula.
- Confusing PVIFA with PVIF, the factor for one payment.
Frequently asked questions
What is PVIFA used for?
To find the present value of equal payments, such as the value of a pension or the amount a loan payment can support.
How do I find a loan payment with PVIFA?
Payment = loan amount ÷ PVIFA at the loan's periodic rate and number of payments.
What changes for payments at the start of each period?
Multiply PVIFA (and FVIFA) by (1 + r).
Sources: Brigham & Houston, Fundamentals of Financial Management (time value of money, annuity factors) · Ross, Westerfield & Jordan, Fundamentals of Corporate Finance (present value of annuities)