Present Value (PV) Calculator
A sum due in the future is worth less today — that is its present value (PV). Enter the future amount, an annual discount rate, the horizon and the compounding frequency (annual, monthly, continuous, etc.) and the calculator applies the standard time-value-of-money formula PV = FV ÷ (1 + r/m)^(m·n) to give the present value, the discount factor and the effective annual rate. Foundational for retirement planning, bond pricing, capital budgeting and any DCF model.
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Present value (PV)
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Discount factor
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Total discount (FV − PV)
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Effective annual rate (EAR)
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Formula: PV = FV ÷ (1 + r/m)^(m·n); for continuous compounding, PV = FV·e^(−r·n). The discount rate is typically a risk-free rate (e.g. 10-yr government bond) or the investor’s required return.
Formula
PV = FV ÷ (1 + r/m)^(m·n) Continuous compounding: PV = FV · e^(−r·n) Discount factor = PV / FV | EAR = (1 + r/m)^m − 1
- · Time value of money: a dollar today is worth more than the same dollar in the future, because today’s dollar can be invested immediately to earn interest.
- · The discount rate (r) reflects opportunity cost — retail users typically plug in a risk-free rate (10-yr US Treasury, HKMA Exchange Fund Bills); corporates use weighted-average cost of capital (WACC); personal retirement planning uses a long-run expected return.
- · The higher the compounding frequency (m), the higher the effective annual rate (EAR) and the lower the present value. 5 % nominal compounded monthly gives an EAR ≈ 5.1162 %; continuous compounding gives e^0.05 − 1 ≈ 5.1271 %.
- · Continuous compounding is the m → ∞ limit, with PV = FV·e^(−r·n) — common in Black–Scholes and other derivative-pricing models.
- · The discount factor is PV ÷ FV — between 0 and 1 for positive rates. It lets you bring cash flows at different dates onto the same timeline before summing them (the foundation of NPV).
- · This tool prices a single lump-sum future amount. For a stream of equal periodic payments, use the annuity present-value formula PV_A = C · [1 − (1 + r)^(−n)] / r instead.
- · Reference: standard finance-mathematics textbooks (Brealey, Myers & Allen, "Principles of Corporate Finance"; Bodie, Kane & Marcus, "Investments").
Frequently asked
Why should I bother computing present value?
Any decision that pits "future" against "today" needs it: should you take a lump-sum pension or a monthly annuity? A business project pays $1 m in 5 years — what is it worth today? A maturity-value $5 m policy — what should you pay for it now? Discounting future amounts back to today puts everything on the same timeline so you can compare or sum them (the basis of NPV).
What discount rate should I plug in?
There is no single right answer — it depends on the use case. General guidance: (1) For risk-free cash flows, use a government bond yield matching the horizon (10-yr US Treasury ≈ 4–5 %; HKMA Exchange Fund Bills slightly lower). (2) For corporate projects, use the firm’s weighted-average cost of capital (WACC). (3) For personal retirement / long-run estimates, use an expected long-run return (4–5 % conservative, 7–8 % aggressive). Always document the rate you chose — small changes move PV materially.
Does the compounding frequency really matter that much?
Less than your intuition suggests, but not negligible. For 5 % over 10 years on a $100,000 future amount: annual compounding PV $61,391; monthly $60,716; daily $60,654; continuous $60,653. The same nominal rate goes from EAR 5 % (annual) to ≈ 5.12 % (monthly), dropping PV by about 1.1 %. Going from monthly to continuous barely changes anything. In practice: bank deposits and mortgages compound monthly, bonds compound semi-annually, textbook derivative-pricing models use continuous compounding.
How is this different from the Compound Interest and CAGR calculators?
Three angles on the same equation: (1) Compound Interest — given today’s principal, find the future value (FV = PV·(1+r)^n, forward). (2) CAGR — given both today’s and the future value, solve for the annualised rate. (3) Present Value (this tool) — given a future value, discount it back to today. All three are applications of time value of money; pick the one matching what you know and what you want.
Can I use this for bond pricing?
For zero-coupon bonds, yes — plug the face value as FV and the yield to maturity (YTM) as the discount rate; the resulting PV is the theoretical price. For coupon bonds you need to discount each coupon plus the final principal separately, then sum — this tool handles one cash flow at a time, so apply it repeatedly. For production bond pricing use a Bloomberg / Refinitiv terminal or Excel’s PRICE / PV functions.
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