Present Value Calculator – What Future Money Is Worth Today
Present value (PV) answers one question: what is money you will receive or pay later worth in today's terms? Money you have now can be invested, so an amount that arrives in ten years is worth less than the same amount today. This present value calculator discounts a single future amount, a level series of payments such as a pension, lease or bond, and compares two or three offers to find the discount rate at which the better choice changes.
The present value formula, worked through
For an amount received t years from now, the discount factor is DF = 1 ÷ (1 + R/m)^(m·t), where R is the annual rate and m is the number of compounding periods per year. The present value is simply PV = amount × DF. Take 10,000 received in 10 years at 7% compounded annually: DF = 1 ÷ 1.07^10 = 0.508349, so PV = 5,083.49. Put another way, investing 5,083.49 today at 7% grows to exactly 10,000 in ten years. The 4,916.51 difference is the time cost of waiting. At 7%, a future amount's value today halves roughly every 10.24 years, which is why distant payments shrink so quickly.
What the discount rate means and how to pick one
The discount rate is your opportunity cost: the return you could realistically earn elsewhere on money of similar risk, or the interest you pay on debt the money could clear. A guaranteed payment from a strong government deserves a low rate; a promise from a shaky counterparty deserves a higher one. Because the answer depends heavily on the rate, the calculator draws the value at 2 points above and below your rate, and the comparison tab charts present value across every rate from 0% to 100%.
Match the rate to the amounts. Discount real (inflation-adjusted) amounts with a real rate and ordinary nominal amounts with a nominal rate; mixing the two double-counts or ignores inflation.
Compounding frequency and the effective annual rate
A rate of 7% compounded monthly is really 7.2290% a year once compounding is included, and 7% compounded continuously is 7.2508%. This effective annual rate (EAR) is (1 + R/m)^m − 1, or e^R − 1 for continuous compounding. A higher EAR means today's money grows faster, so the same 10,000 in ten years is worth a little less today: 4,975.96 with monthly compounding instead of 5,083.49. When payments arrive more or less often than interest compounds, the calculator converts the rate to a per-payment rate, (1 + R/m)^(m/p) − 1, the same way financial calculators handle different payment and compounding frequencies.
Ordinary annuity vs annuity due
A level stream of payments is an annuity. Its present value is PMT × (1 − (1 + i)^−N) ÷ i, where i is the rate per payment period. In an ordinary annuity each payment arrives at the end of its period, as with loan repayments and bond coupons. In an annuity due payments arrive at the start, as with rent, so each one is received a period sooner and the whole stream is worth (1 + i) times more. At 6% compounded monthly, 1,000 a month for five years is worth 51,725.56 paid at the end of each month and 51,984.19 paid at the start.
Lump sum or payments? The lottery example
Suppose you can take 1,000,000 today or 60,000 a year for 30 years, with the first payment today. The payments add up to 1,800,000, but that total ignores timing. Discounted at 3% they are worth 1,211,307.28 today, more than the lump sum; at 5% they are worth only 968,464.41. The break-even rate is about 4.70%. If you are confident of earning more than that on the cash, the lump sum wins; if not, the payments do. The Compare offers tab finds these crossover rates automatically.
Checking the result in a spreadsheet
Excel and Google Sheets calculate the same figure with =-PV(7%, 10, 0, 10000). The functions follow a cash-flow sign convention, treating money you would pay today to receive the future amount as negative, so the leading minus sign turns the answer positive. Each result in this tool includes the matching formula with your own numbers filled in.
What this calculator does not cover
It always solves for present value. To solve for a payment, rate or term, or to value growing annuities and perpetuities, use an annuity calculator. Uneven cash flows net of an upfront investment belong in the NPV calculator, flows on specific calendar dates in the SIP XIRR calculator, and odd-period simple interest and taxes are left out.