Quick answer
Present value of an ordinary annuity PV = PMT × (1 − (1 + r)^−n) ÷ r. Ten payments of $100 discounted at 5% per period are worth $772.17 today.
Enter the payment, rate per period and number of periods. The calculator returns the present value.
Related tools: Present Value Calculator: Today's value of a future amount at a given discount rate. Net Present Value Calculator: NPV of an initial outlay and a series of yearly cash flows. Future Value of Annuity Calculator: Future value of equal payments at the end of each period.
How to use the Present Value of Annuity Calculator
- Enter payment per period ($) (above 0).
- Enter rate per period (%) (0 or more).
- 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 |
|---|---|---|
| Payment per period | A number, in $ | > 0 |
| Rate per period | A number, in % | ≥ 0 |
| Number of periods | A whole number | ≥ 1, ≤ 1200 |
Formula and method
Formula
PV = PMT × (1 − (1 + r)^−n) ÷ r
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Ordinary annuity (payments at period end); r = 0 gives PMT × n.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Payment per period = 100; Rate per period = 5; Number of periods = 10.
| Result | Value |
|---|---|
| Present value | $772.17 |
Example 2
Inputs: Payment per period = 100; Rate per period = 0; Number of periods = 10.
| Result | Value |
|---|---|
| Present value | $1,000.00 |
The first line is the headline result (present value). IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Meaning
$772.17 is the lump sum that, invested at 5% per period, funds ten withdrawals of $100. The total of the payments is $1,000, so the discount is $227.83.
Rate per period
Use a rate for the same period as the payments. For monthly payments at 6% a year use 0.5%. The PVIFA calculator returns the factor 7.7217 alone.
How the result changes with payment per period
Holding every other input at the first worked example, this table changes only payment per period. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Payment per period | Present value |
|---|---|
| 50 | $386.09 |
| 100 | $772.17 |
| 200 | $1,544.35 |
| 400 | $3,088.69 |
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.
Choosing between the Present Value of Annuity 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 |
|---|---|---|
| [Present Value Calculator](/finance/present-value-calculator/) | future value, annual discount rate and years | Present value |
| [Net Present Value Calculator](/finance/net-present-value-calculator/) | discount rate, initial investment and cash flows | Net present value |
| [Future Value of Annuity Calculator](/finance/future-value-of-annuity/) | payment per period, rate per period and number of periods | Future value |
| [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) |
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 handled
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 to confirm this.
Frequently asked questions
What is an annuity?
A series of equal payments.
How is it used for loans?
The loan amount is the PV of the payments.
What if the rate is zero?
PV equals payment × periods.
What does the Present Value of Annuity Calculator calculate?
Present value of equal payments at the end of each period. It returns Present value.
What formula does the Present Value of Annuity Calculator use?
PV = PMT × (1 − (1 + r)^−n) ÷ r. Ordinary annuity (payments at period end); r = 0 gives PMT × n.
What do I need to enter in the present Value of Annuity Calculator?
You enter Payment per period ($), 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 handled.
What is an example of a present Value of Annuity result?
With payment per period 100, rate per period 5 and number of periods 10, the present value is $772.17.
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 handled.
Related calculators
- Present Value Calculator — Today's value of a future amount at a given discount rate.
- Net Present Value Calculator — NPV of an initial outlay and a series of yearly cash flows.
- Future Value of Annuity Calculator — Future value of equal payments at the end of each period.
- 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.
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.