Article — Present Value (PV) Calculator
The Present Value Calculator, for lump sums and payments
Present value (PV) is what a future amount is worth today, discounted at a chosen rate. PV = FV ÷ (1 + r/n)^(n × t), where FV is the future amount, r is the annual rate (decimal), n is compounding periods per year, and t is time in years. For continuous compounding, PV = FV × e^(−r × t). The same formula prices bonds, values pensions, and ranks investment projects with net present value (NPV).
The CFA Institute curriculum treats present value as the bedrock of valuation. The SEC requires public companies to discount pension and lease liabilities at appropriate rates. Every discounted-cash-flow model in equity research starts here.
What is present value?
Money has a time value: a dollar today is worth more than a dollar a year from now, because today's dollar can earn interest before the year is up. Present value reverses that growth. Take a future amount, divide by the growth factor, and you get the equivalent amount today.
Three forces make a dollar today more valuable. Opportunity cost — you could invest. Inflation — tomorrow's dollar buys less. Risk — tomorrow's payment might not arrive. The discount rate combines all three into one number. Higher rate, lower present value. The longer the wait, the more the discount compounds.
The U.S. Treasury issues TIPS (Treasury Inflation-Protected Securities) that adjust their principal for inflation. The implied real (after-inflation) discount rate on 10-year TIPS hovered around 2% in 2024 according to the Federal Reserve's H.15 release. That figure is the closest thing in markets to a pure time-value-of-money rate, free of inflation and credit risk.
The present value formula
Lump sum PV = FV ÷ (1 + r/n)^(n·t)Continuous PV = FV × e^(−r · t)Annuity PV = PMT × [1 − (1+r/n)^−N] ÷ (r/n)Perpetuity PV = PMT ÷ rWorked example. You will receive $10,000 in 5 years. Discount rate 6%, monthly compounding. PV = 10,000 ÷ (1 + 0.06/12)^(12 × 5) = 10,000 ÷ 1.348 = $7,413. The same future amount discounted at 8% gives $6,712, at 10% gives $6,070. Doubling the rate cuts the present value by about 18%.
Present value vs future value
Present value and future value are mirror operations on the time-value-of-money line. PV moves money backward through time; FV moves it forward. They use the same growth factor; one divides, the other multiplies.
At 7% compounded annually for 10 years, $1.00 today grows to $1.97 (future value). Going the other way, $1.00 in 10 years is worth $0.51 today (present value). The two numbers always multiply back to 1 at the same rate and horizon: 1.97 × 0.51 = 1.00. The SEC's investor.gov tools use both perspectives in their compound-interest and savings calculators.
Present value of an annuity
An annuity is a series of equal payments at regular intervals: a pension, a mortgage, a bond coupon stream, a court settlement paid over years. The present value of an annuity is what you would accept today as a lump sum in exchange for that stream.
For an ordinary annuity (payment at the end of each period): PV = PMT × [1 − (1 + r/n)^(−N)] ÷ (r/n). For an annuity due (payment at the beginning), multiply by (1 + r/n). Beginning-of-period payments are worth slightly more because each one is discounted across one fewer period.
A perpetuity is an annuity that never ends. Its present value collapses to PMT ÷ r. A perpetuity paying $100 per year discounted at 5% is worth $2,000 today. U.K. consol bonds (now retired) and modern preferred stock both behave as perpetuities for valuation purposes.
Choosing the discount rate
The right discount rate is the opportunity cost of capital — what the money could earn in the next-best alternative of comparable risk. For a risk-free Treasury cash flow, use the matching Treasury yield. For a corporate cash flow, use a rate that includes a credit spread. For an equity investment, use the cost of equity or weighted-average cost of capital (WACC).
For personal finance, common choices are the after-tax return on a high-yield savings account (low-risk lump sums), the expected return on a diversified portfolio (long-horizon investment decisions), or the after-tax cost of debt (decisions about paying down a loan vs investing). The Federal Reserve's Survey of Consumer Finances reports household-level discount rate implied by savings and borrowing behavior.
Always check whether your discount rate is nominal (includes inflation) or real (after inflation), and match it to your cash flows. Use a nominal rate for nominal future cash flows; use a real rate for inflation-adjusted cash flows. Mixing the two is the single most common source of present-value error in corporate models.
Present value in bond pricing and DCF
A bond is the simplest application of PV. Its price equals the present value of every coupon plus the present value of the face value at maturity, all discounted at the yield to maturity. The CFA Institute's fixed-income curriculum builds an entire toolkit on this single mechanic. Move the yield up and prices fall; move yield down and prices rise — entirely through the PV math.
Equity valuation uses discounted cash flow (DCF), the same mechanic applied to future free cash flows or dividends. A company's intrinsic value is the present value of all cash it will generate, from now to forever, discounted at its cost of capital. Net present value (NPV) extends the idea to projects: sum the PV of every cash flow (including the initial outlay), and accept the project if NPV is positive.
Common present value mistakes
The first mistake is mismatching the period of the rate and the periods. A 6% annual rate is not 6% per month. Convert: 6% annual = 0.5% per month for simple monthly periods. Spreadsheet PV functions expect rate and number-of-periods on the same basis — pass annual rate with annual periods, or monthly rate with monthly periods, never one of each.
The second is ignoring inflation on long horizons. A nominal $1,000,000 in 30 years sounds rich, but at 3% inflation it has the buying power of about $412,000 today. For retirement, pension, and insurance planning, discount with a real return rate (nominal − inflation, more precisely (1 + nominal) ÷ (1 + inflation) − 1) so you see today-dollar purchasing power.
The third is using too low a discount rate for risky cash flows. A 3% Treasury rate is fine for a Treasury bond, not for a startup's projected earnings. The Britannica Money entry on present value points out that adding a risk premium to the rate is mathematically equivalent to expecting a lower probability of payment — either way, the PV of risky cash flows is below the PV of safe cash flows of the same nominal size.