Last updated: Oct 06, 2026
Present Value of Annuity Calculator
Present Value of Annuity Calculator: Find What Future Payments Are Worth Today
A present value of annuity calculator turns a series of equal future payments into one number: what that stream is worth today. This free tool does more than the basic formula. It handles monthly, quarterly and annual payments, ordinary and due timing, balloon payments, growing payments, deferred starts and perpetuities.
Use it if you are weighing a lottery annuity against a lump sum, valuing a pension, pricing a lease or settlement, or checking homework. It also helps if you are building a financial model.
It matters because money loses value while you wait for it. A dollar paid ten years from now is worth less than a dollar in your hand today. The calculator shows exactly how much less.
What Is the Present Value of an Annuity?
The present value of an annuity is the lump sum today that equals a series of equal payments made at regular intervals, discounted at a chosen interest rate. It is also called the PV of annuity, current value of an annuity, discounted value of an annuity or present worth of an annuity.
An annuity is any stream of equal payments at regular intervals. Rent, loan installments, pension checks and lottery payouts are all annuities.
The discount rate is the yearly return you could earn elsewhere. A higher rate makes future payments worth less today.
This idea comes from the time value of money: cash received sooner can be invested and grow. For example, 10 payments of $1,000 are worth less than $10,000 today, because the later payments have not earned anything yet.
How to Use the Present Value of Annuity Calculator
The calculator has twelve linked cards. Each card works alone. When you calculate one card, it suggests values for the cards below it, marked “Auto-filled.” You can overwrite any suggestion.
Start with Card 1, the main present value of annuity calculator, and follow these steps:
- Enter the payment amount.
- Pick how often payments are made.
- Enter the term and its unit.
- Enter the discount rate and choose its type.
- Choose end-of-period or beginning-of-period timing.
- Add a balloon payment if there is one.
- Press Calculate. Press Fill Example to see a sample first.
Turn on Show Steps in the settings to see the full working. That makes this a present value of annuity calculator with steps, which is useful for students and auditors.
Settings That Apply to Every Card
The top panel controls how all results look:
- Currency: USD, GBP, EUR, CAD, AUD, NZD, INR, PKR, AED, SAR, CHF or JPY.
- Decimal places: 0, 2, 4 or 6.
- Number format: 1,234.56, 1.234,56 or 1 234,56.
- Show steps: On or off.
- Rate entry type: Nominal APR, Effective Annual Rate (EAR) or periodic rate per payment.
Card 1 Inputs Explained
| Input | What it means | Tip |
|---|---|---|
| Payment amount (PMT) | The equal amount paid each period | Use the pre-tax amount unless you want an after-tax view |
| Payment frequency | Annual, semi-annual, quarterly, monthly, weekly, daily and more | Match the contract exactly |
| Term length and unit | How long payments last, in years, months, weeks or payment count | Use “Number of Payments” for exact schedules |
| Discount / interest rate | Your required return or the loan rate | Be realistic; see the rate section below |
| Rate type | Nominal APR, EAR or periodic rate | Check which one your source quotes |
| Compounding frequency | How often interest compounds; “Same as Payment Frequency” is the default | Choose continuous for theory problems |
| Payment timing | End of period (ordinary) or beginning (due) | Rent and insurance are usually due |
| Final / balloon payment | A lump sum at the end | Leave at 0 if none |
| Start date | When the schedule begins | Used for dated schedules |
Pro tip: Mixing up APR and EAR is the most common input error. A 5% APR compounded monthly is an effective annual rate of about 5.12%. The calculator converts between them, but you must pick the right type.
Card 1 Results Explained
The headline result is the present value of the annuity today. Below it, the calculator shows supporting figures:
- Total nominal payments: Every payment added with no discounting.
- Total discount: Face value minus present value. This is the price of waiting.
- Periodic rate × periods: Your rate converted to one payment period, times the number of payments.
- Effective annual rate: The true yearly return after compounding.
- PVIFA used: The present value interest factor of an annuity. Multiply it by the payment to get the value.
- PV of balloon: The final lump sum discounted back to today.
- If paid in advance (due): The same stream valued with each payment one period earlier.
- Macaulay duration: The weighted average time until cash arrives. Longer duration means more sensitivity to rate changes.
You also get a chart of discounted value by year, a yearly schedule table and a short expert-style commentary on the result.
The Present Value of Annuity Formula
The present value of annuity formula for an ordinary annuity is:
PV = PMT × [1 − (1 + i)^−n] ÷ i
- PV is the present value.
- PMT is the payment each period.
- i is the interest rate per period.
- n is the number of periods.
The part in brackets is the annuity factor, also written PVIFA (present value interest factor of an annuity). So the formula is simply PV = PMT × PVIFA.
For an annuity due, multiply the result by (1 + i). That is the present value of annuity due formula: PV(due) = PV(ordinary) × (1 + i).
Step-by-Step Sample Calculation
Find the present value of $1,000 paid monthly for 10 years at 5% APR, compounded monthly.
- Periodic rate: i = 5% ÷ 12 = 0.4167% = 0.004167.
- Number of periods: n = 10 × 12 = 120.
- Annuity factor: [1 − (1.004167)^−120] ÷ 0.004167 = 94.2814.
- Present value: $1,000 × 94.2814 = $94,281.35.
The payments total $120,000. The present value is $94,281.35, so waiting costs you $25,718.65 in discounting.
If the same payments arrive at the start of each month, the value rises to $94,674.19. That is the ordinary value times 1.004167.
Present Value of Annuity Table (PVIFA)
Before calculators, people used printed tables. A present value of annuity table lists PVIFA factors by rate and number of periods. You find the factor, then multiply by the payment.
Here is a small sample table, calculated with the exact formula:
| Periods (n) | 4% | 6% | 8% | 10% |
|---|---|---|---|---|
| 5 | 4.4518 | 4.2124 | 3.9927 | 3.7908 |
| 10 | 8.1109 | 7.3601 | 6.7101 | 6.1446 |
| 20 | 13.5903 | 11.4699 | 9.8181 | 8.5136 |
| 30 | 17.2920 | 13.7648 | 11.2578 | 9.4269 |
To use it, find 10 periods at 6%: 7.3601. A $1,000 yearly payment is worth $1,000 × 7.3601 = $7,360.10 today.
Card 4 of the calculator builds custom tables for any rate range. It covers PVIFA, FVIFA, PVIF, FVIF, capital recovery and sinking fund factors for both ordinary and due annuities. It also highlights your lookup cell, interpolates between rates and draws a heatmap.
Warning: Printed tables round factors to four decimals. On a large payment, this can shift the answer by several currency units. The calculator uses the exact formula.
Ordinary Annuity vs. Annuity Due
| Feature | Ordinary annuity | Annuity due |
|---|---|---|
| Payment timing | End of each period | Start of each period |
| Also called | Annuity in arrears, regular or immediate annuity | Annuity in advance |
| Typical examples | Loan payments, bond coupons, mortgage payments | Rent, insurance premiums, leases paid up front |
| Present value | Lower | Higher by a factor of (1 + i) |
| Future value | Lower | Higher by a factor of (1 + i) |
Paying one period earlier adds exactly one period of interest to the value. In the example above, that gap is 0.4167%, which equals the monthly rate.
Card 2 puts both side by side. It includes presets for rent in advance, leases, insurance premiums, tuition, subscriptions, pensions, lottery annuities and structured settlements. It also runs a “shift check” that confirms due equals ordinary × (1 + i).
Expert insight: Negotiating a payment date can be worth real money. Lessees prefer paying in arrears, and lessors prefer advance.
Present Value vs. Future Value of an Annuity
Present value discounts payments back to today. Future value grows them forward to the end of the term.
The future value of an ordinary annuity formula is:
FV = PMT × [(1 + i)^n − 1] ÷ i
The bracketed part is the FVIFA (future value interest factor of an annuity). The two values connect: FV = PV × (1 + i)^n.
Use present value when you ask, “What is this stream worth now?” Use future value when you ask, “How much will my savings reach?” Card 3 handles future value of an annuity. It adds a starting balance, inflation and a target goal, and it shows any surplus or shortfall. For a simple growth projection, try the Future Value Calculator.
Real-World Examples
Example 1: Lottery Annuity vs. Lump Sum
You win a prize. You can take $50,000 a year for 20 years, or $600,000 today. Which is better?
| Discount rate | PV of $50,000 × 20 years (ordinary) | Better choice vs. $600,000 |
|---|---|---|
| 3% | $743,874 | Annuity |
| 5% | $623,111 | Annuity (by $23,111) |
| 7% | $529,701 | Lump sum |
The lump sum implies a return of about 5.45% a year. If you can safely earn more than that, take the lump sum. If you cannot, the annuity is worth more.
If the first payment arrives right away (annuity due), the 5% value rises to $654,266. Always check the timing in your contract.
Warning: This ignores taxes and the risk of investing the lump sum. Card 10 adds marginal tax and inflation. Our Lottery Tax Calculator can help with the tax side.
Example 2: Lease Liability
A company leases equipment for $2,000 a month for five years. Its incremental borrowing rate is 6%.
- Paid at the end of each month: lease liability of $103,451.
- Paid at the start of each month: $103,968.
Under lease accounting rules (IFRS 16 and ASC 842), this liability starts the right-of-use asset. Card 11 builds the asset, the amortization schedule and an implied rate. The incremental borrowing rate (IBR) is the rate a lessee would pay to borrow similar funds over a similar term. For full loan schedules, use the Amortization Calculator.
Example 3: Settlement Offer (Case Study)
An insurer offers $280,000 now, or $2,000 a month for 15 years. You assume 4% a year.
The PV of the monthly stream is $270,384. The lump sum is $9,616 higher in today’s money. On numbers alone, the lump sum wins.
Many people still choose the stream for stability, so do not decide on present value alone. Our Settlement Calculator covers related cases.
Example 4: Deferred Retirement Income
You are 35 and want $30,000 a year for 20 years, starting at 65. You assume a 5.5% return.
- Value at age 65: $358,511.
- Value today (discounted 30 years): $71,933.
That is the present value of a deferred annuity. Waiting 30 years cuts the funding needed today by about 80%. Card 7 shows this directly, including the “cost of waiting.”
Special Annuity Types
Deferred Annuity
A deferred annuity starts paying later. Value it as a normal annuity at the start date, then discount that amount back to today. Card 7 covers retirement income, delayed tuition, no-payment financing and deferred income annuities.
Growing Annuity
A growing annuity has payments that rise at a steady rate. The present value of a growing annuity formula is:
PV = PMT₁ ÷ (i − g) × [1 − ((1 + g) ÷ (1 + i))^n]
Here, PMT₁ is the first payment and g is the growth rate.
Sample: $40,000 first payment, 3% growth, 7% discount rate, 20 years.
- Growing annuity PV: $533,267.
- Level annuity PV: $423,761.
- Value added by growth: $109,506, or 25.8%.
Card 5 supports fixed percent growth, fixed dollar steps, CPI-indexed payments, step-ups and a payment cap. It warns you when growth meets or exceeds the discount rate.
Perpetuity
A perpetuity pays forever. Its present value is simple:
PV = PMT ÷ i
At a 5% yield, $1,000 a year is worth $20,000. At 4%, it is worth $25,000. At 6%, it is worth $16,667.
For a growing perpetuity, use PMT₁ ÷ (i − g). This is the Gordon growth model. See our Gordon Growth Model Calculator and Dividend Discount Model Calculator.
Fact: At 5%, half of a perpetuity’s value arrives within about 14.2 years. Within 30 years, 76.9% has arrived. That is why very long annuities behave like perpetuities, and why Card 6 includes a share-of-value gauge.
NPV, IRR and Cash-Flow Streams
Net present value (NPV) adds the discounted value of all cash inflows and subtracts the outflows. A positive NPV means the investment earns more than your discount rate.
Card 9 stacks several annuities or accepts a custom list of cash flows. It returns NPV, IRR, MIRR, profitability index and payback. It also draws an NPV-versus-rate profile.
- IRR (internal rate of return): The rate that makes NPV equal zero.
- MIRR (modified IRR): IRR corrected for realistic reinvestment and financing rates.
- Profitability index: PV of inflows divided by PV of outflows. Above 1.00 is good.
Use NPV to rank projects of different sizes. For a payback view, try the Payback Period Calculator.
Solving for Payment, Rate or Number of Periods
Card 8 works backward. It can find:
- The payment from a present or future value.
- The interest rate from a present or future value.
- The number of periods from a present or future value.
Rates have no closed-form answer, so the solver uses Newton-Raphson iteration with a bisection fallback. It plugs the answer back into the formula to prove it matches.
Example: A $200,000 loan over 360 months at 6% APR needs a payment of $1,199.10. Multiply that by the annuity factor and you get $200,000 back. For loans, also try the Loan Calculator and Mortgage Calculator.
The capital recovery factor is the reverse of PVIFA. It turns a present sum into level payments. The sinking fund factor is the reverse of FVIFA. It turns a future goal into level deposits.
How the Discount Rate Changes the Answer
The rate you choose is the biggest driver of the result. Here is $1,000 a month for 10 years at different rates:
| Annual rate | Present value |
|---|---|
| 3% | $103,562 |
| 5% | $94,281 |
| 7% | $86,126 |
| 9% | $78,942 |
Moving from 5% to 6% cuts the value by about 4.5%. Higher rates always mean lower present values.
How to Pick a Discount Rate
- Loans and leases: Use the loan rate or your incremental borrowing rate.
- Personal choices: Use the return you could realistically earn safely.
- Business projects: Use your required return or cost of capital. See the WACC Calculator.
- Bond-like income: Use current market yields. See the Bond Yield Calculator.
Understand how quoted rates convert with the Effective Annual Rate Calculator, APR Calculator and APY Calculator.
Pensions, Lump Sums and Longevity
A pension or lifetime annuity pays as long as you live, so its true term is unknown. Card 10 handles this with an optional Gompertz survival model. This is a mathematical approximation of mortality, not an official life table.
It also covers joint-and-survivor annuities, period-certain-plus-life annuities, cost-of-living adjustments (COLA), taxes and inflation. It shows the lump sum’s implied return and a break-even term.
Warning: A pure present value comparison understates the value of a lifetime annuity. It insures you against outliving your money. If you live longer than expected, the annuity wins.
For older adults, health matters too. Shorter expected lifespans lower an annuity’s value, and longer ones raise it. Use realistic assumptions, and talk to a licensed adviser before you commit to an irrevocable choice.
Taxes and Inflation
Taxes reduce what you keep. Card 10 applies your marginal tax rate to show an after-tax present value. Inflation shrinks purchasing power, so a fixed payment buys less each year.
For a fixed $50,000 payment, 2.5% inflation means the payment in year 25 buys roughly half of what it does today. Indexed payments (COLA) protect against this, but they cost more to fund.
Check real values with the Inflation Calculator and Salary Inflation Calculator.
Verify Your Answer: Excel, BA II Plus and Tables
Card 12 checks any result five ways: the closed formula, a PVIFA table, summed discounted payments, the Excel identity and backward recursion. All exact methods should match to the cent.
Excel: Use the PV function. For the 10-year monthly example:
=PV(0.05/12, 120, -1000, 0, 0) returns 94,281.35.
Set the last argument to 1 for an annuity due.
BA II Plus (financial calculator):
- Press 2ND, P/Y, enter 12, then ENTER.
- Set N = 120 and I/Y = 5.
- Set PMT = −1,000 and FV = 0.
- Press CPT, then PV.
For an annuity due, press 2ND, BGN, 2ND, SET to switch to beginning mode. Forgetting this is the most common reason hand answers differ from software by exactly one period of interest.
Common Mistakes to Avoid
- Using the annual rate with monthly payments. Divide by the payments per year, or let the calculator convert it.
- Mixing up ordinary and due timing. This shifts the answer by one period of interest.
- Forgetting the balloon payment. Add it in the balloon field.
- Using a growth rate at or above the discount rate. The formula breaks down.
- Rounding factors from tables. Small rounding grows on large payments.
- Ignoring tax, inflation and risk. Present value shows math, not the whole decision.
Limitations and Assumptions
- The calculator assumes payments are certain. Real payments carry credit and default risk.
- It assumes one constant discount rate for the whole term.
- Survival results use an approximation, not an official mortality table.
- Tax results use one marginal rate, not a full tax return.
- Results are estimates for education and planning. They are not financial, tax or legal advice.
Related Tools
Explore more tools on IntelCalculator Finance:
- Annuity Calculator for annuity payouts and balances
- Compound Interest Calculator for growth over time
- Interest Calculator and Interest Rate Calculator
- Retirement Calculator and Safe Withdrawal Rate Calculator
- Investment Calculator and Rate of Return Calculator
- Rent Calculator and Savings Calculator
- Bond Price Calculator and Dividend Growth Calculator
- Intrinsic Value Calculator and Glossary
Frequently Asked Questions
What is the present value of an annuity?
It is the amount today that equals a series of equal future payments, discounted at a chosen rate. It answers the question, “What is this payment stream worth right now?”
What is the formula for the present value of an annuity?
For an ordinary annuity, PV = PMT × [1 − (1 + i)^−n] ÷ i. For an annuity due, multiply that result by (1 + i). The calculator applies the right version based on your timing choice.
How do I calculate the present value of an annuity?
Convert your annual rate to a periodic rate, and convert the term to a number of payments. Compute the annuity factor, then multiply it by the payment. Or enter the values into the calculator above.
What is PVIFA?
PVIFA stands for present value interest factor of an annuity. It is the present value of $1 paid every period. Multiply it by your payment to get the present value. Card 4 generates PVIFA tables and a PVIFA lookup.
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period. An annuity due pays at the start. The due version is worth more by one period of interest.
Is present value of annuity the same as NPV?
Not exactly. Present value discounts only the inflows. Net present value subtracts the cost from the discounted inflows. NPV of an annuity is the PV of the payments minus the initial investment. Card 9 calculates it.
What discount rate should I use?
Use the rate that matches your risk and alternatives. That could be a loan rate, an expected safe return or a business hurdle rate. Test several rates, because the answer changes quickly.
How do I find the present value of a deferred annuity?
Find the value at the payout start date, then discount it back to today by the number of deferral periods. Card 7 does both steps and shows the cost of waiting.
How do I find the present value of a growing annuity?
Use PV = PMT₁ ÷ (i − g) × [1 − ((1 + g) ÷ (1 + i))^n]. Growth must be below the discount rate for this closed form to work. Card 5 also uses a payment-by-payment schedule for caps and step-ups.
How do I calculate a perpetuity’s present value?
Divide the payment by the yield: PV = PMT ÷ i. For growing perpetuities, divide the next payment by (i − g).
Should I take the lump sum or the annuity?
Compare the annuity’s present value to the lump sum. If the annuity’s PV is higher at a rate you trust, the annuity is worth more. Also weigh taxes, investment risk, inflation and how long you may live.
Can I calculate present value in Excel?
Yes. Use =PV(rate, nper, pmt, [fv], [type]). Enter the periodic rate, use a negative payment and set type to 1 for an annuity due.
How do I do this on a BA II Plus?
Set P/Y to match your payments per year, enter N, I/Y and PMT, set FV to 0, then compute PV. Use BGN mode for an annuity due.
What is the present value of a lease?
It is the discounted total of lease payments, using the rate implicit in the lease or the lessee’s incremental borrowing rate. It becomes the lease liability under IFRS 16 and ASC 842.
Does this calculator handle monthly, weekly and continuous compounding?
Yes. Payment frequency ranges from annual to daily. Compounding can match the payment frequency, be set separately or be continuous.
Why is my hand answer slightly different?
Printed tables round to four decimals, and calculators may be in the wrong timing mode. Card 12 shows the exact gap between methods.
Conclusion
The present value of an annuity tells you what a payment stream is worth today. The idea is simple: later money is worth less than money now, and the discount rate decides by how much.
This calculator covers the full topic. It handles ordinary and due annuities, deferred, growing and perpetual streams, NPV, factor tables, pensions, leases and lump-sum decisions. It also shows the steps and cross-checks every answer against Excel and BA II Plus methods.
Run your numbers, test a few discount rates and compare the results. Then use the answer as one input in a bigger decision, alongside tax, risk and your own goals. This article is for education, not financial or legal advice.