Quick answer
The present value interest factor of an annuity is PVIFA = (1 − (1 + r)^−n) ÷ r. At 5% for 10 periods PVIFA is 7.721735 (and the future value factor FVIFA is 12.577893).
Enter the rate per period and the number of periods. The calculator returns PVIFA and FVIFA.
Related tools: Investment Calculator: Project investment growth from a rate of return you choose. Financial Calculator: Time-value-of-money solver for N, rate, present value, payment or future value. IRR Calculator: Internal rate of return of an investment from its yearly cash flows.
How to use the PVIFA Calculator
- Enter rate per period (%) (between 0 and 1000).
- Enter number of periods (a whole number, between 1 and 1200).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Rate per period | A number, in % | ≥ 0, ≤ 1000 |
| Number of periods | A whole number | ≥ 1, ≤ 1200 |
Formula and method
Formula
PVIFA = (1 − (1 + r)^−n) ÷ r
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Multiply the factor by the payment amount to get the present value of an ordinary annuity.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Rate per period = 5; Number of periods = 10.
| Result | Value |
|---|---|
| PVIFA | 7.721735 |
| FVIFA | 12.577893 |
Example 2
Inputs: Rate per period = 8; Number of periods = 20.
| Result | Value |
|---|---|
| PVIFA | 9.818147 |
| FVIFA | 45.761964 |
Example 3
Inputs: Rate per period = 0; Number of periods = 12.
| Result | Value |
|---|---|
| PVIFA | 12 |
| FVIFA | 12 |
The first line is the headline result (pVIFA). Below it the pVIFA Calculator lists fVIFA, which describe the same case from other angles. IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Using the factor
Multiply a payment by PVIFA to get its present value: $100 × 7.7217 = $772.17. Multiply by FVIFA for the future value: $100 × 12.5779 = $1,257.79. Tables of these factors were used before calculators.
Zero rate
At 0% PVIFA equals n. Rate and periods must match the payment frequency. FVIFA = PVIFA × (1 + r)ⁿ.
How the result changes with rate per period
Holding every other input at the first worked example, this table changes only rate per period. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Rate per period | PVIFA | FVIFA |
|---|---|---|
| 2.5 | 8.752064 | 11.203382 |
| 5 | 7.721735 | 12.577893 |
| 10 | 6.144567 | 15.937425 |
| 20 | 4.192472 | 25.958682 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Number of periods: entering "0" shows "Number of periods must be at least 1." beside that field and no result.
- Rate per period: entering "-1" shows "Rate per period must be at least 0." beside that field and no result.
Choosing between the PVIFA Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Investment Calculator](/finance/investment-calculator/) | initial amount, annual interest rate and years | Projected value |
| [Financial Calculator](/finance/financial-calculator/) | solve for, periods per year and payments | Future value (FV) |
| [IRR Calculator](/finance/irr-calculator/) | initial investment and cash flows | IRR |
| [CAGR Calculator](/finance/cagr-calculator/) | beginning value, ending value and years | CAGR |
| [Present Value Calculator](/finance/present-value-calculator/) | future value, annual discount rate and years | Present value |
Background: interest, saving and investing
A nominal rate (APR) does not include the effect of compounding; the annual percentage yield (APY) does: APY = (1 + r/n)^n − 1. A 5% nominal rate compounded annually is 5.000%, semi-annually about 5.063%, quarterly about 5.095% and monthly about 5.116%, so more frequent compounding helps, but with diminishing returns.
The rate you enter in a projection is an assumption, not a promise: real returns vary and can be negative. Fees and taxes are not modelled unless the page says so.
Assumptions and limitations
- 0% rate gives PVIFA = n
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for number of periods and rate per period to confirm this.
Frequently asked questions
What is FVIFA?
The future value interest factor of an annuity.
Why use factors?
They simplify repeated calculations.
How is a loan payment found from PVIFA?
Loan amount ÷ PVIFA.
What does the PVIFA Calculator calculate?
Present value interest factor of an annuity. It returns PVIFA and FVIFA.
What formula does the PVIFA Calculator use?
PVIFA = (1 − (1 + r)^−n) ÷ r. Multiply the factor by the payment amount to get the present value of an ordinary annuity.
What do I need to enter in the pVIFA Calculator?
You enter Rate per period (%) and Number of periods.
How is the result rounded or limited?
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice. 0% rate gives PVIFA = n.
What is an example of a pVIFA result?
With rate per period 5 and number of periods 10, the pVIFA is 7.721735.
Can I rely on this calculator for a decision?
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser. For this calculator in particular: 0% rate gives PVIFA = n.
Related calculators
- Investment Calculator — Project investment growth from a rate of return you choose.
- Financial Calculator — Time-value-of-money solver for N, rate, present value, payment or future value.
- IRR Calculator — Internal rate of return of an investment from its yearly cash flows.
- CAGR Calculator — Compound annual growth rate between two values.
- Present Value Calculator — Today's value of a future amount at a given discount rate.
- Mutual Fund Calculator — Growth of a fund investment after its expense ratio.
Sources
- Standard time-value-of-money relations (e.g. Brealey, Myers & Allen, Principles of Corporate Finance)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.