Present Value Calculator
✦ Finance & MoneyUse this free present value calculator to find what a future sum or series of payments is worth in today's dollars — with any discount rate, adjustable compounding frequency, and a period-by-period breakdown.
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- ✓ Formula and sources shown
The formula
Present value — three modes
Lump sum: PV = FV / (1 + r)^n
Ordinary annuity: PV = PMT x [1 - (1 + r)^-n] / r
Annuity due: PV_due = PV_ordinary x (1 + r)
Growing annuity: PV = PMT₁ / (r - g) x [1 - ((1+g)/(1+r))^n] (r ≠ g)
PV = n x PMT₁ / (1 + r) (r = g)
Continuous: PV = FV x e^(-r x t)FV = future lump sum, PMT = payment per period, PMT₁ = first growing-annuity payment, r = periodic discount rate (annual rate / periods per year), n = total periods (up to 600), g = constant periodic growth rate of payments, t = years. r = g is handled as a special case to avoid division by zero. Full precision internally; rounded to 2 decimal places for display.
Calculating it by hand
- Choose your mode: single future sum, equal-payment annuity, or growing annuity.
- Enter the future value (lump sum) or the payment per period (annuity).
- Enter the annual discount rate — this is your required rate of return or opportunity cost.
- Set the number of periods (up to 600) and the period frequency (annual, quarterly, monthly, etc.).
- For an annuity, choose whether payments arrive at the end or beginning of each period.
- The calculator divides the annual rate by the frequency to get the periodic rate r, then applies the appropriate formula.
- Read the present value, the total discount amount, the per-period discount factor, and the cumulative-PV schedule.
Worked examples
$10,000 in 5 years at an 8% annual discount rate
Periodic rate r = 8% ÷ 1 = 0.08 (annual periods)Growth factor: (1.08)^5 = 1.469328PV = $10,000 ÷ 1.469328 = $6,805.83Total discount = $10,000 − $6,805.83 = $3,194.17Discount factor = 1 ÷ 1.469328 = 0.680583
Present value: $6,805.83 — the amount that, invested at 8% today, grows to exactly $10,000 in 5 years.
$1,000 a year for 5 years at 6% — ordinary annuity
r = 6% a year = 0.06; n = 5 periods1 − (1.06)^−5 = 1 − 0.747258 = 0.252742Annuity factor = 0.252742 ÷ 0.06 = 4.212364PV = $1,000 × 4.212364 = $4,212.36Annuity due: PV_due = $4,212.36 × 1.06 = $4,465.11
Present value (ordinary): $4,212.36; present value (annuity due): $4,465.11 — the $252.75 gap is each payment arriving one period sooner.
$500 first payment growing 3% a year, 7% discount rate, 10 years — growing annuity
r = 7% = 0.07; g = 3% = 0.03; n = 10 periodsRatio: (1 + g) ÷ (1 + r) = 1.03 ÷ 1.07 = 0.962617(0.962617)^10 = 0.6831791 − 0.683179 = 0.316821PV = ($500 ÷ (0.07 − 0.03)) × 0.316821 = $12,500 × 0.316821 = $3,960.26
Present value of the growing annuity: $3,960.26 — more than the $3,511.79 a flat $500 a year is worth at 7% over the same 10 years, because the payments keep rising.
Methodology
How discounting future money works
A dollar today is worth more than a dollar tomorrow — not just because of inflation, but because of what today's dollar could earn. The discount rate makes that opportunity cost exact.
Read sources and limitsHow does present value discounting work?
Present value is future value run backwards. If $1 invested today at 7% grows to $1.07 in a year, then $1.07 due in a year is worth exactly $1 today at that rate. Discounting divides a future amount by the growth factor (1 + r)^n, giving the sum that, invested now at the discount rate, would grow to that amount.
The discount rate is the key variable. Two people valuing the same future payment get different answers if they use different rates, and both can be right, because the right rate depends on each person's alternatives. A near-certain payment is discounted near the Treasury yield for its maturity; a risky one at a higher rate.
The period structure matters too. A 7% annual rate discounted monthly uses a periodic rate of 7% ÷ 12 and a different discount factor per period than annual discounting. The calculator shows the periodic rate beside the result so you can check which convention it applied.
How do you choose a discount rate for present value?
Use the return you could earn on an alternative of equivalent risk. For a government payment due in 10 years, that is close to the 10-year Treasury yield (published daily by the Treasury and in the Federal Reserve's H.15 release). Companies often use their weighted average cost of capital; individuals often use the return they expect from their own portfolio.
A higher rate gives a lower present value, and the effect grows with time. $100,000 due in 30 years is worth $13,136.71 today at 7% and $23,137.74 at 5% — 76% more from a 2-point change. Over 5 years the same change moves the value only from $71,298.62 to $78,352.62.
The calculator uses the rate you enter as-is and does not distinguish nominal from real rates. To value cash flows stated in today's purchasing power, use a real rate, (1 + nominal) ÷ (1 + inflation) − 1: a 7% nominal rate with 2.5% inflation is a 4.39% real rate.
How do you find the present value of an annuity?
An annuity is a series of equal payments at regular intervals, and its present value has a closed form that discounts every payment at once: PV = PMT × [1 − (1 + r)^−n] / r. The bracketed term is the annuity factor, the present value of $1 a period for n periods; multiply it by the payment.
Timing matters. An ordinary annuity pays at the end of each period, the standard loan and bond convention; an annuity due pays at the start, so each payment is discounted one period less and PV_due = PV_ordinary × (1 + r). $1,000 a year for 5 years at 6% is worth $4,212.36 as an ordinary annuity and $4,465.11 as an annuity due.
A growing annuity lets the payments rise at a constant rate g: PV = PMT₁ / (r − g) × [1 − ((1 + g)/(1 + r))^n]. It suits dividend streams, indexed pensions and rent escalation clauses. When r equals g the formula divides by zero, so n × PMT₁ / (1 + r) is used instead; the calculator handles that case automatically.
What is the difference between present value, future value and NPV?
Present value and future value are the same calculation in opposite directions: future value multiplies by (1 + r)^n, present value divides by it. With the same rate and periods they always agree — the present value of a future value is the original amount. Use the Future Value Calculator to project forwards and this page to work backwards.
Net present value (NPV) sums the present values of several cash flows and subtracts the up-front cost: NPV = −cost + PV(CF₁) + … + PV(CFₙ). A positive NPV means the investment returns more than the discount rate. This calculator does the discounting; for an NPV, add the period PVs from the schedule and subtract your initial investment.
The internal rate of return (IRR) is the discount rate at which NPV is zero — the implied return on a set of cash flows. This calculator takes the rate as given and does not solve for IRR.
What does this present value calculator not model?
The discount rate is held constant for every period. In practice the right rate can change as interest rates move or as the risk of a future payment changes. Run the calculator two or three times across a range of plausible rates to see how much the answer depends on that one input.
Taxes on the proceeds are not modelled: the present value is of the gross amount, before any tax due when it is received. An after-tax value needs your marginal rate and the tax treatment of that specific cash flow.
This calculator provides educational estimates based on the discount rate and timing assumptions you enter. It is not investment, tax, legal or financial advice. Investing involves risk, including possible loss of principal; actual results will differ from these estimates.
Present Value questions
What is present value?
Present value (PV) is what a future sum of money is worth today at a chosen discount rate. Because money available now can earn a return, a future dollar is worth less than a dollar today — how much less depends on the rate and how far away the payment is. $10,000 due in 10 years is worth $5,083.49 today at 7%.
What is the present value formula?
For a single future sum: PV = FV / (1 + r)^n, where FV is the future amount, r the periodic discount rate and n the number of periods. For equal payments (an ordinary annuity): PV = PMT × [1 − (1 + r)^−n] / r. For a growing annuity: PV = PMT₁ / (r − g) × [1 − ((1 + g)/(1 + r))^n], where g is the growth rate per period.
How do you calculate present value step by step?
For a lump sum: (1) divide the annual discount rate by the periods per year to get the periodic rate; (2) raise (1 + periodic rate) to the number of periods; (3) divide the future amount by the result. $10,000 due in 5 years at 8%: 1.08^5 = 1.469328, so PV = $10,000 ÷ 1.469328 = $6,805.83. The schedule shows the discount factor applied to each period.
What is a discount rate and how do I choose one?
The discount rate converts a future cash flow into today's equivalent and should reflect the return on an alternative of equivalent risk: the Treasury yield of matching maturity for a near-certain payment, a company's cost of capital for a project, or your expected portfolio return for personal planning. At long horizons the choice dominates: $100,000 due in 30 years is worth $23,137.74 at 5% but $13,136.71 at 7%.
What is the present value of an annuity?
It is the value today of a series of equal future payments discounted at a constant rate: PV = PMT × [1 − (1 + r)^−n] / r. $1,000 a year for 5 years at 6% is worth $4,212.36 today, meaning $4,212.36 invested now at 6% would fund exactly five year-end withdrawals of $1,000 and leave nothing.
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 beginning, so each payment is discounted one period less and is worth slightly more: PV_due = PV_ordinary × (1 + r). $1,000 a year for 5 years at 6% is worth $4,212.36 as an ordinary annuity and $4,465.11 as an annuity due. Loans and bonds use the ordinary convention; leases and rent often use annuity due.
What is a growing annuity and when do you use it?
A growing annuity is a series of payments rising at a constant rate g each period, used to value growing dividends, indexed pensions or rent escalation. PV = PMT₁ / (r − g) × [1 − ((1 + g)/(1 + r))^n]. A $500 first payment growing 3% a year for 10 years at 7% is worth $3,960.26 — more than the $3,511.79 a flat $500 a year is worth. When r equals g, PV = n × PMT₁ / (1 + r).
What is the present value of a perpetuity?
A perpetuity pays a fixed amount forever, and its present value is PMT ÷ r: $1,000 a year at 5% is worth $1,000 ÷ 0.05 = $20,000. A perpetuity growing at rate g is worth PMT₁ ÷ (r − g), with r greater than g — the Gordon growth model for valuing a dividend stream. This calculator models finite periods; 200 annual periods at 5% gives $19,998.84, already within $2 of the perpetuity.
How does the discount rate affect present value?
Inversely, and more strongly the further away the payment is. $100,000 due in 30 years is worth $23,137.74 at 5%, $13,136.71 at 7% (43% less) and $5,730.86 at 10%. Over 5 years the same 5%-to-7% change moves the value only from $78,352.62 to $71,298.62, a 9% drop. That is why long-dated cash flows such as pensions and infrastructure are so sensitive to the rate assumed.
How do I use present value to compare a pension lump sum with monthly payments?
Discount the monthly payments at the return you could realistically earn on the lump sum, then compare. $2,000 a month for 25 years (300 monthly periods) has a present value of $342,120 at 5% and $282,974 at 7%. If the lump sum offered is higher than the PV at a rate you are comfortable assuming, it is worth more on paper. Plans compute their own lump sums with IRS minimum present value segment rates, and lifetime payments, survivor benefits and taxes all matter.
What is the present value of $1 million received in 20 years?
It depends on the discount rate: $1,000,000 ÷ 1.03^20 is $553,675.75 at 3%, $376,889.48 at 5% and $258,419.00 at 7%. The same future sum is worth less than half as much today when the rate rises from 3% to 7%, so set the rate to match the alternative use of the money — a safe savings rate for a guaranteed payment, a higher one for an uncertain payment.
How do I calculate present value in Excel?
Use =PV(rate, nper, pmt, [fv], [type]). For a single future sum, leave pmt at 0: =PV(5%, 10, 0, -20000) returns $12,278.27, the value today of $20,000 due in 10 years at 5%. For payments, =PV(5%/12, 240, -1000) values $1,000 a month for 20 years at 5% at $151,525.31. Enter cash you will receive as negative so the result is positive, and set type to 1 for an annuity due.
Source notes
Method, sources & limitations
Every figure on this page comes from the formula above applied to the values you enter. Nothing is estimated from market data, and no result is a forecast. These are the sources behind the method and any fixed figures it uses:
- Board of Governors of the Federal Reserve System — Selected Interest Rates (H.15)
- U.S. Department of the Treasury — Interest rate statistics (daily Treasury yield curve)
- IRS — Minimum present value segment rates (pension lump sums, IRC §417(e))
- U.S. Securities and Exchange Commission (Investor.gov) — Compound interest calculator (methodology reference)
Educational information only. Results are estimates produced from the assumptions you enter, and are not financial, tax, legal or medical advice. Check anything that matters against a qualified professional and the cited sources.