Present Value Calculator

What present value asks

Present value answers one question: what is a payment that arrives later worth right now? The formula runs compound interest backward. Instead of asking what $60,000 grows into, it asks what you would need to deposit today to end up with $60,000 later. That amount is PV = FV / (1 + r)^n, where FV is the future cash flow, r is the discount rate per year and n is the number of years until the money arrives.

The quantity 1 / (1 + r)^n is the discount factor, and it stays below 1 whenever r is positive. At 5 percent for 6 years the factor is 0.746215, so each future dollar is worth 74.6 cents today. At 12 percent it drops to 0.506631: each future dollar loses nearly half its value before it arrives. The longer the wait and the higher the rate, the smaller the factor.

The SEC's Investor.gov glossary entry on present value defines it as the current worth of a future sum of money given a specified rate of return (SEC, viewed 2026). The calculator above covers four cash flow shapes: one future amount, a fixed yearly payment for a set number of years, a payment that never ends, and a payment that never ends and grows each year. For each one it returns the PV, the effective annual rate behind your compounding choice, the discount factor for a single period, the total nominal amount and the total discount that time removes.

Four cash flow shapes, four formulas

Most PV problems fall into one of four shapes, and each has a closed form. All four assume the payment lands at the end of each period, the ordinary annuity convention:

The perpetuity formula looks too good to be true and is not. Park $100,000 at 5% and the balance earns exactly $5,000 a year, so paying out that amount leaves the principal untouched forever. The growing version subtracts g from r before dividing, which only makes sense when the rate and the growth rate are defined on the same basis: both nominal, both real, both yearly. The requirement r > g is not decoration; if growth outruns the discount rate the formula returns a meaningless number, because no finite price buys a stream that grows faster than it is discounted forever.

How to choose the discount rate

The discount rate is the one input with no formula, and it moves the answer more than the other two inputs combined. Three questions usually settle it.

A certain payment takes the government's own borrowing rate. The Treasury daily par yield curve publishes a rate for every trading day: the 10-year rate stood at 4.09% on December 1, 2025 (U.S. Treasury, 2025). For a payment arriving in 6 years, the 5-year or 7-year par yield is a closer match than the 10-year, because the discount rate should span the same wait as the cash flow.

A below-market family loan takes the IRS floor. The IRS publishes Applicable Federal Rates in a revenue ruling each month, and the AFR for the month of the loan is the minimum rate that keeps a cheap loan to a relative from being reclassified as a gift (IRS, 2026). The tables are split by term, so a 6-year loan uses the mid-term rate.

A risky payment takes your required return. Rent or business income might not show up, so discount at the return you would insist on to be compensated for that risk. This is why the same $60,000 due in 6 years is worth $44,772.92 at 5% but only $30,397.87 at 12%: the extra 7 points is the price of the doubt.

Inflation needs matching, not guesswork. Nominal (inflating) cash flows take a nominal rate; inflation-adjusted cash flows take a real rate. The exact real rate is (1 + nominal) / (1 + inflation) - 1, which at 5% nominal and 2.5% inflation works out to 2.439%, not the 2.5% a quick subtraction suggests.

Worked example 1: a down payment fund, step by step

Goal: $60,000 of house down payment money in 6 years. A mixed portfolio is expected to earn 5% a year, so 5% is the discount rate. Every intermediate value:

Step 1, the growth factor: (1.05)^6. 1.05^2 = 1.1025 and 1.05^3 = 1.157625, so 1.05^6 = 1.157625 × 1.157625 = 1.340096. Step 2, the discount factor: 1 / 1.340096 = 0.746215. Step 3, the present value: 60,000 × 0.746215 = $44,772.92. Invested at 5%, $44,772.92 compounds into exactly $60,000 in 6 years. The gap, $15,227.08, is the total discount: the part of the $60,000 that compounding is expected to produce on its own.

Discount the same promise with monthly compounding and the quoted 5% becomes an effective 5.1162% a year, giving $44,476.81. The more frequent compounding removes a further $296.12 of present value, because money discounted monthly shrinks slightly faster. That comparison is the calculator's last row.

Read the answer practically: if a guaranteed 5% for 6 years is available, setting aside $44,772.92 today finishes the job with no further deposits. Every dollar saved above that is cushion against the return coming in under 5%.

Worked example 2: what a pension promise is worth

Someone weighing a pension offer that pays $24,000 a year for 20 years of retirement, first payment one year from now, discount rate 5%. The annuity formula PV = PMT × [1 - (1 + r)^-n] / r prices the whole stream in one line:

Step 1: (1.05)^20 = 2.653298. Step 2: (1.05)^-20 = 1 / 2.653298 = 0.376889. Step 3: 1 - 0.376889 = 0.623111. Step 4: 0.623111 / 0.05 = 12.462211, the 20-year annuity factor. Step 5: 24,000 × 12.462211 = $299,093.05.

Two checks put that number in context. The payments add up to a nominal 20 x 24,000 = $480,000, so discounting removes $180,906.95, more than a third of the headline figure. And the factor 12.462211 has a life of its own: it is the price of $1 a year for 20 years at 5%, which is the number the PVIFA calculator tabulates across rates and terms.

The same offer priced as a perpetuity, $24,000 a year with no end date, would need 24,000 / 0.05 = $480,000 today, which is the whole nominal sum back as a single price. The 20-year cutoff is what saves $180,906.95 of present value: payments far in the future are worth so little now, and the year-50 payment carries a discount factor of just 0.0872.

Monthly versus annual compounding

A quoted annual rate is not a complete description until you know how often it compounds. The per-period rate is r / n, there are n x t periods in t years, and the effective annual rate is EAR = (1 + r / n)^n - 1. At a quoted 5%, here is what the same $60,000 due in 6 years is worth:

Two habits keep this straight. First, match rate to payment: monthly payments need a monthly rate, and counting years as whole periods while using a divided monthly rate is where the errors creep in. Second, check which rate a quote is: 5% nominal compounded monthly is 5.1162% effective, 11.6 basis points more than flat 5%, and on a $300,000 balance those basis points are worth about $348 a year.

How PV, NPV and IRR fit together

Net present value is PV with a price attached: add the present value of every cash flow, then subtract what you pay today. A rental expected to throw off $18,000 a year for 15 years at a 7% required return has an annuity factor of (1 - 1.07^-15) / 0.07 = 9.107914, so its PV is 18,000 × 9.107914 = $163,942.45. Offered at $150,000, the NPV is $13,942.45, which is the value the deal adds at a 7% hurdle. NPV above zero clears the hurdle, below zero it does not.

IRR runs the same machinery in reverse: it is the discount rate that makes the NPV exactly zero. For the rental, the rate that sets 18,000 x a(15, r) = 150,000 lands near 8.4%, the return the price implies. Use PV when the rate is given, NPV to judge one price, IRR to back a rate out of a price. All three share the same discounting engine, and the IRR calculator solves for the rate by iteration when cash flows are uneven.

Bond pricing, and the mistakes PV catches

A bond is two PV problems in one package: an annuity of coupons plus one future repayment of face value. Price a $10,000 bond with a 4% annual coupon and 5 years left, when the market now wants 5%:

Coupon stream: 400 × a(5, 5%) = 400 × 4.329477 = $1,731.79. Face repayment: 10,000 x (1.05)^-5 = 10,000 x 0.783526 = $7,835.26. Price = 1,731.79 + 7,835.26 = $9,567.05. The bond trades below face because its 4% coupon is short of the 5% the market demands, and the $432.95 discount is exactly the present value of that shortfall.

The recurring mistakes this calculator is built to catch: pairing a monthly rate with a year count (the discount factor comes out far too small), running nominal rates against inflation-adjusted cash flows, subtracting a growth rate from a rate defined on a different basis, and treating an annuity due as ordinary. An annuity due, with each payment at the start of the year, is worth (1 + r) times the ordinary figure: that $299,093.05 pension becomes $314,047.70 when every payment moves up by a year.

A last caution: PV is only as honest as its rate and its cash flow guesses. It assumes one flat rate for every year and treats the payments as known. It is the right tool for promises with numbers attached, and the wrong tool for guessing what a young business will earn in year 9.