Present Day Value Calculator
What is money you will receive in the future worth right now? This calculator discounts a single future sum or a stream of equal payments back to today, with a choice of compounding frequency and a rate-sensitivity table that shows how the answer moves when the rate moves. It is the same present-value math behind bond prices, lottery cash options, and lease valuations, with every step of the arithmetic shown.
| Discount rate | Present value |
|---|
Single sum: PV = FV / (1 + r/m)(m × t). Annuity: PV = P × [1 – (1 + r/m)–(m × t)] / (r/m). r is the annual rate, m the compounding frequency, t the years. The annuity mode values an ordinary annuity, with payments at the end of each period.
Quick Answer
$10,000 arriving in 5 years is worth $7,835.26 today at a 5% annual discount rate. Discount it monthly instead of annually and the answer drops to $7,792.05, because more frequent compounding discounts harder. A stream of $2,000 a year for 10 years at 6% is worth $14,720.17 today. Enter your own numbers above for the full breakdown.
Key takeaways
- Present value is the discount factor 1/(1 + r)n applied to future money. The further away the cash and the higher the rate, the smaller the present value.
- Two calculators in one card: a single future sum, or an annuity of equal payments, ordinary or annuity-due.
- The discount rate choice moves the answer more than anything else, which is why the tool prints a sensitivity table at your rate plus and minus two points.
- Compounding frequency matters: at the same 5% nominal rate, $10,000 in 5 years is $7,835.26 annual, $7,792.05 monthly, and $7,788.14 daily.
- Quick Answer
- How to use the present day value calculator
- The present value formulas, and what each symbol means
- Worked example: $10,000 in 5 years, checked by hand
- Choosing a discount rate you can defend
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the present day value calculator
Pick a mode, fill in the fields, and click Calculate. The results stay hidden until you calculate, so the worked-example numbers pre-filled in the card are just a starting point.
- Choose single sum or annuity: use the single-sum mode for one future payment (a bond's face value, a lottery cash option, a future bill) and the annuity mode for equal payments each period (yearly pension payouts, lease instalments). The annuity mode values an annuity of equal payments. Ordinary timing means payments arrive at the end of each period; annuity-due timing moves every payment one period earlier, which raises the present value by one period of interest.
- Enter the amount, rate and years: the future value (or payment per period), the annual discount rate as a percent, and the number of years. The rate can be zero, which simply returns the undiscounted amount.
- Set the compounding frequency: annual, semi-annual, quarterly, monthly or daily. In annuity mode the payment is assumed to arrive once per compounding period, so monthly compounding means monthly payments.
- Read the three outputs: the big present-value number, the step-by-step arithmetic showing the discount factor, and the sensitivity table with your rate two points lower and higher. Copy or share the result text with the buttons beside it.
The present value formulas, and what each symbol means
Both modes discount future money by the growth that money could have earned. For a single future sum, PV = FV / (1 + r/m)(m × t), where FV is the future value, r the annual discount rate as a decimal, m the compounding frequency per year, and t the years. The divisor (1 + r/m)(m × t) is the discount factor. The walkthrough of the formula and its inverse, compounding, is set out in the Maths is Fun present value tutorial and in the time-value chapter of OpenStax Principles of Finance.
Ordinary annuity: PV = P × [1 – (1 + r/m)–(m × t)] ÷ (r/m)
r = annual rate as a decimal, m = compounding periods per year, t = years, P = payment per period. At a 0% rate the annuity formula reduces to P × m × t, the payments added up with no discounting.
For the annuity, the per-period rate is r/m and the number of periods is m × t. Each payment is discounted individually and the geometric series collapses to the closed form above. Because the ordinary formula assumes end-of-period payments, a stream that pays at the beginning of each period (an annuity due) is worth more by exactly one period of discounting; switch the payment timing above to annuity due and the tool applies that factor. the present value of growing annuity calculator handles the due case alongside growth for growing payments.
Worked example: $10,000 in 5 years, checked by hand
The card is pre-filled with this example. At 5% compounded annually: the per-period rate is 0.05/1 = 0.05, the discount factor is 1.055 = 1.27628, and PV = $10,000 / 1.27628 = $7,835.26. The total discount is $10,000 – $7,835.26 = $2,164.74, which is the interest the money would have earned.
The annuity mode with $2,000 a year for 10 years at 6%: periods = 1 × 10 = 10, per-period rate = 6%, PV = $2,000 × [1 – 1.06–10] / 0.06 = $14,720.17. Both results reproduce exactly when you run the card.
Now watch what the rate alone does to the same $10,000, five years out, annual compounding:
| Discount rate | Present value | What it means |
|---|---|---|
| 3% | $8,626.09 | A safe, low-return world. Future money keeps most of its value. |
| 5% | $7,835.26 | The worked example. Two extra points of rate erase $790.83. |
| 7% | $7,129.86 | A riskier cash flow. Worth 17% less than at 3%. |
| 10% | $6,209.21 | A demanding hurdle rate. Over a third of the future value is gone. |
A correction: an earlier version of this page said monthly compounding gave "about $7,788" for this example. That figure is the daily compounding answer ($7,788.14). Monthly compounding gives $7,792.05, as the calculator shows. The arithmetic above is verified against the tool.
Choosing a discount rate you can defend
There is no single correct rate; it depends on whose money it is and how certain the payment is. The rate should reflect the return the money could earn elsewhere at similar risk, which finance textbooks call the opportunity cost of capital.
Contractual and safe
Use a government bond yield. The daily Treasury par yield curve rates are the standard risk-free anchor for payments you are confident you will receive.
Your own savings goal
Use the return you expect your own money to earn, such as your portfolio's long-run return. Retirement planning usually lands between the Treasury yield and equity returns.
A business project
Use the project's hurdle rate or the company's weighted average cost of capital. Riskier cash flows get higher rates, which is exactly what the sensitivity table lets you test in seconds.
Common uses of the calculation: comparing investment projects whose cash flows arrive at different times, pricing a bond as the present value of its coupons plus face value (see FINRA's bond guide), working out the lump sum needed today to fund a future spending goal, discounting lease payments against a purchase price, and sizing up a lottery jackpot against its cash option (compare with the lotto annuity calculator). Discounting is also the inverse of compounding, so it pairs naturally with the compound interest factor calculator and the future value factor calculator.
What competing calculators miss
Most present-value tools do one narrow job, and each leaves something out:
- Single-mode tools (Calculator Doc's present day value page): one future sum, rate entered as a decimal, no compounding choice, no annuity mode. Ours handles both single sums and annuities with five compounding frequencies.
- Basic PV tools (CalculatorSoup's basic calculator): daily, monthly or yearly compounding, but a single sum only and no sense of how sensitive the answer is. Our sensitivity table shows the rate two points either side of yours on every run.
- Engineering-economics tools (AJDesigner's present worth page): strong on the P/F factor notation and worked examples, but built for a single payment and an engineering audience. Ours keeps the plain-language labels and the annuity mode for non-engineers.
- Tutorials without tools (Maths is Fun): excellent explanations of the time value of money, but no interactive calculator at all.
- The gap this page fills: two modes in one card, a visible discount factor and full step-by-step arithmetic instead of a bare number, a rate-sensitivity table on every calculation, and honest documentation of what changed when the old page's numbers were wrong.
Frequently asked questions
Present day value, usually just called present value (PV), is what a future sum of money is worth right now after discounting it at a chosen rate. Because money can earn a return over time, $10,000 received five years from now is worth less than $10,000 today.
Divide the future value by the discount factor: PV = FV / (1 + r/m)^(m x t), where r is the annual rate, m the compounding frequency per year, and t the years. For $10,000 in 5 years at 5% compounded annually, the discount factor is 1.05^5 = 1.27628, so PV = $7,835.26.
More frequent compounding at the same nominal rate discounts future money harder, because the money would grow faster. $10,000 in 5 years at 5% is worth $7,835.26 with annual compounding, $7,792.05 with monthly compounding, and $7,788.14 with daily compounding.
It is the lump sum today equivalent to receiving a fixed payment every period for a set time. Switch the calculator to annuity mode: $2,000 a year for 10 years at 6% is worth $14,720.17 today. The mode values an ordinary annuity, with payments at the end of each period.
Match the rate to the risk of the cash flow. Use a government bond yield such as the 10-year Treasury yield for safe contractual payments, your expected portfolio return for personal savings goals, and a hurdle rate or cost of capital for business projects. When unsure, run the calculation at two or three rates and compare.
The discount rate is the return you could earn by investing the money instead. If you can earn 10% elsewhere, a future payment must be discounted more aggressively than if you could only earn 3%. The rate is your opportunity cost, so a higher opportunity cost means the future money is worth less to you today.
Present value discounts one future amount, or one stream of payments, to today. Net present value discounts all of a project's cash flows, inflows and outflows, and subtracts the initial investment. A positive NPV means the project earns more than the discount rate.
Not exactly. Present value is a calculation from your chosen discount rate. Fair value is what a willing buyer would actually pay, which also reflects market conditions, liquidity, and negotiation. Present value is one input into a fair-value judgement, not the whole answer.
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References
- Maths is Fun. Present Value. Accessed October 23, 2026.
- Khan Academy. Present value. Accessed October 23, 2026.
- OpenStax, Rice University. Principles of Finance. Accessed October 23, 2026.
- U.S. Department of the Treasury. Interest Rate Statistics: Daily Treasury Par Yield Curve Rates. Accessed October 23, 2026.
- Board of Governors of the Federal Reserve System. H.15: Selected Interest Rates. Accessed October 23, 2026.
- Financial Industry Regulatory Authority (FINRA). Bonds. Accessed October 23, 2026.
- Consumer Financial Protection Bureau. Pension Lump-Sum Payouts and Your Retirement Security (PDF). Accessed October 23, 2026.
- U.S. Department of the Treasury. Daily Treasury Rate Archives. Accessed October 23, 2026.