Present Value, Net Present Value, and the Time Value of Money
Present value (PV) is the worth, in today's dollars, of a sum that will exist later — the
difference between the two figures being the interest that sum would earn, compounded, in the
meantime. The operation is division where compounding was multiplication:
PV = FV ÷ (1 + r)N · $1,000 ÷ 1.0610 = $558.39
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For a stream of equal deposits the same discounting is applied payment by payment and summed:
PV = PMT × [1 − (1 + r)−N] ÷ r — $736.01 for ten deposits of $100 at 6%. Those deposits grow to
$1,318.08, and notice the cast of characters: the future value is mostly principal ($1,000, 76%) with
$318.08 of interest — while the present value is smaller than the principal alone, because even the
deposits themselves are future money being discounted.
PV vs NPV
Keep PV distinct from its famous relative. Net present value combines all of a project's
inflows and outflows — the purchase price, the running costs, the salvage — each discounted, into
one net figure; "net" is doing the same work it does in net income. PV values a sum or a stream;
NPV renders a verdict on a whole undertaking, and it anchors practical work from capital
expenditure appraisals to depreciation schedules. A positive NPV means the undertaking beats the
discount rate; negative, it falls short of it.
Why PV runs finance
PV is one of the five keys of the time value of money (PV, FV, I/Y, N, PMT) — the backbone of
finance. There could be no mortgages, auto loans, or credit cards without it: every loan is just a
present value (the amount advanced today) exchanged for a stream of future payments, priced so the
two sides are worth the same. Choosing the discount rate is choosing the price of time — which
is why a single percentage point, compounded over decades, moves valuations more than almost any
forecast of the cash flows themselves. To run the film forward instead, use the Future Value
Calculator; for the full five-key machine, the Finance Calculator.
FAQ
Can present value exceed future value?
Only with a negative interest rate — which has genuinely occurred for some government bonds. At any positive rate, PV is always the smaller number; the gap between them is exactly the interest.
What's a sensible discount rate for personal decisions?
Your opportunity cost: the return you'd expect from the realistic alternative use of the money — a savings yield for safety-first comparisons, a long-run portfolio return for investment choices, or the interest rate on debt you could pay off instead (a guaranteed return).
Disclaimer: This calculator provides estimates for educational purposes only and does not constitute financial advice.