Free present value of an annuity calculator
See what a stream of future payments is worth today. Enter the payment, the discount rate, and the number of years, and the calculator returns the present value of the annuity — for both ordinary annuities and annuities due, with the lump-sum-vs-payments comparison built in — updated live, as you type.
On this page15 sections
Estimates only, based on the values you enter. Not financial advice.
Results are estimates. Consult a professional.
What is the present value of an annuity?
The present value of an annuity is what a stream of equal future payments is worth in today's money. Because a dollar you receive years from now is worth less than a dollar in your hand today — it could have been invested and earned a return — every future payment has to be discounted back to the present. This present value of an annuity calculator does that discounting for you: enter the payment, the rate, and the number of payments, and it returns the single lump sum today that is financially equivalent to the whole stream.
That lump sum is the number a lottery winner sees as the "cash option," the figure a structured-settlement buyer offers for your payments, and the amount a lender hands over as loan principal in exchange for your future installments. They are all the same idea: the present value of an annuity.
Present value of an annuity formula
The standard formula for the present value of an ordinary annuity — payments made at the end of each period — is the one used by CalculatorSoup, Corporate Finance Institute, and every finance textbook:
The bracketed term, [1 − (1 + r)^−n] / r, is the annuity factor (or PV annuity factor). Multiply any payment by it and you get the present value of the whole stream. The calculator above evaluates this exact expression live as you type.
The annuity-due variant
If payments arrive at the start of each period instead — rent, leases, and many insurance premiums work this way — every payment is discounted one period less, so it is worth slightly more. The fix is a single multiplier:
Ordinary annuity vs. annuity due
The only difference between the two is when each payment lands — and that timing changes the present value. An annuity due always has a higher present value than an otherwise-identical ordinary annuity, because you receive every payment one period sooner and money in hand earlier is worth more.
| Ordinary annuity | Annuity due | |
|---|---|---|
| Payment timing | End of each period | Start of each period |
| Typical examples | Mortgages, car loans, bonds | Rent, leases, insurance premiums |
| Present value | Lower | Higher (× (1 + r)) |
| Default in this tool | Yes | Optional toggle |
Same payments, same rate — only the timing differs. Source: Corporate Finance Institute; Bankrate.
How to calculate the present value of an annuity
Calculating the present value of an annuity by hand is a four-step process. The calculator collapses it into one, but seeing the steps makes the number trustworthy.
- Find the periodic rate (r). Divide the annual rate by the number of payments per year. A 6% annual rate with monthly payments gives r = 0.5% per month.
- Find the number of periods (n). Multiply the years by payments per year. Five years of monthly payments is n = 60.
- Build the annuity factor. Compute [1 − (1 + r)^−n] / r.
- Multiply by the payment. PV = PMT × annuity factor. If it is an annuity due, multiply once more by (1 + r).
A worked example using the present value of an annuity calculator
You win a $1,000,000 jackpot paid as $50,000 a year for 20 years. The lottery also offers a single cash payout today. To judge whether that cash offer is fair, you need the present value of the 20-year payment stream at a realistic discount rate — say 5%. Here is how the calculator gets there.
Step 1 — Enter the payment and term
Set the payment to $50,000, the frequency to annual, and the term to 20 years. The calculator reads this as 20 payments (n = 20).
Step 2 — Enter the discount rate
Enter 5% as the annual rate. With annual payments the periodic rate is also 5%, so r = 0.05. Leave the toggle on "Ordinary" — jackpot installments are paid at the end of each year.
Step 3 — Read the present value
| Input | Value |
|---|---|
| Payment per year (PMT) | $50,000 |
| Discount rate (r) | 5% |
| Number of payments (n) | 20 |
| Annuity factor [1 − (1.05)^−20] / 0.05 | 12.4622 |
| Present value (PMT × factor) | $623,110.52 |
$50,000 × 12.4622 = $623,110.52 — the present value of the 20-year stream at 5%.
Now use it to decide. If the lottery's cash option is above $623,111, the lump sum is the better deal at a 5% discount rate; if it is below, the annuity wins. The next section turns that comparison into a rule you can reuse.
Lump sum vs. payments: how present value decides
Whenever you are offered "a lump sum now or payments over time," the present value of the annuity is the apples-to-apples number that lets you compare them. The rule is simple:
- If the lump sum offered > the present value of the payments, take the lump sum — you are being paid more than the stream is worth.
- If the lump sum offered < the present value, keep the payments — they are worth more than the cash offer.
- The discount rate is the lever. A higher rate (you can invest well) shrinks the present value and favors taking the lump sum; a lower rate favors the payments.
This is exactly why a lottery's advertised jackpot is so much larger than its cash option, and why a structured-settlement buyer offers less than the sum of your future checks. The cash figure is the present value — almost always 30–50% below the headline total, depending on the rate and the term. The same logic prices a pension buyout, a retirement-income stream, and the principal of a loan.
How the discount rate changes the present value
The discount rate is the single biggest driver of an annuity's present value. The table below holds the payment fixed at $50,000 a year for 20 years and varies only the rate, so you can see how sensitive the answer is. Raise the rate and the present value falls sharply; lower it and the stream is worth far more today.
| Discount rate | Annuity factor | Present value of $50,000 × 20 years |
|---|---|---|
| 3% | 14.8775 | $743,873.74 |
| 4% | 13.5903 | $679,516.32 |
| 5% | 12.4622 | $623,110.52 |
| 6% | 11.4699 | $573,496.06 |
| 8% | 9.8181 | $490,907.37 |
Same $1,000,000 in nominal payments, discounted at five different rates. The undiscounted total is always $1,000,000.
The term matters too. Stretching the same payment over more years adds present value, but each added year contributes less than the one before it, because payments far in the future are discounted the hardest.
Where the present value of an annuity is used
The same calculation shows up across personal finance and investing whenever a stream of equal payments needs a price tag today:
- Lottery and prize payouts — pricing the cash option against the multi-year annuity.
- Retirement income — what an income annuity or pension stream is worth as a lump sum.
- Loan principal — the amount a lender advances equals the present value of your future payments at the loan rate.
- Structured settlements — what a buyer will pay today for your future legal-settlement checks.
- Bond and lease valuation — the present value of coupon or lease payments, before adding any final balloon or face value.
For the mirror-image question — what a stream of payments will grow to — use the future value calculator. To price a single future amount rather than a stream, use present value.
Limitations and what the present value leaves out
The present value of an annuity is precise math on a set of assumptions — and those assumptions are where real-world decisions get complicated. Keep these limits in mind:
- Payments are assumed equal and certain. If amounts grow each year (many lottery annuities rise about 5% annually) or could stop, the simple formula understates or overstates the value.
- The rate is assumed constant. One discount rate is applied to every period; real reinvestment rates move.
- Taxes are not included. A lump sum is often taxed all at once at a high rate, while payments can spread the tax over years — this can flip the after-tax decision.
- Inflation is separate. Use a real (inflation-adjusted) rate if you want today's purchasing power rather than today's nominal dollars.
- Payer credit risk is ignored. The math assumes every payment is made; a shaky payer deserves a higher discount rate.
Formula sources and methodology
This calculator uses the standard time-value-of-money formula for the present value of an annuity, PV = PMT × [1 − (1 + r)^−n] / r, with the annuity-due adjustment × (1 + r) for start-of-period payments. The frequency selector converts the annual rate and term into a periodic rate and a period count before the formula is applied. Figures match the conventions documented by Corporate Finance Institute and Annuity.org and the output of the Excel PV function.
Frequently asked questions about the free present value of an annuity calculator
About this present value of an annuity calculator
This present value of an annuity calculator runs entirely in your browser. Every figure you enter stays on your device — nothing is sent to a server, logged, or shared. It applies the standard formula PV = PMT × [1 − (1 + r)^−n] / r, converts your annual rate and term to a periodic rate and period count by frequency, and multiplies by (1 + r) when you choose annuity due — all updating instantly as you type.
Calculators Cloud offers 400+ free tools with no sign-up. The whole Finance calculators shelf includes Present value, Future value, and Annuity tools alongside this one. Or browse the full calculator directory.