Present Value Calculator
Calculate what a future lump sum or a series of equal payments (annuity) is worth today, discounted at a given rate. See the PV formula and steps.
What is present value?
Present value (PV) answers the question: "if I'm going to receive money in the future (either a single amount, or a fixed amount every period), how much is that worth today?" It's the backward-looking half of the time-value-of-money pair — the other half, future value, answers the reverse question by projecting money forward instead of discounting it back.
This calculator covers two common cases: a lump sum received once in the future, and an annuity — equal payments received every period (like a pension or a structured settlement).
The formula: lump sum
- PV — present value (what the future amount is worth today)
- FV — future value (the amount to be received later)
- r — discount rate per period, as a decimal (rate ÷ 100)
- n — number of periods
Example: you'll receive $10,000 in 10 periods, discounted at 5% per period: PV = 10,000 / (1.05)^10 ≈ $6,139.13. The discount is FV − PV = $10,000 − $6,139.13 = $3,860.87 — that's the value lost to waiting.
The formula: annuity (equal payments)
- PMT — the payment received every period
- r, n — same meaning as above
Each payment is discounted back by a different number of periods (the first payment is discounted by one period, the last by n periods), and this formula sums all of them at once — the same geometric-series shortcut behind the loan-payment calculator, since a loan's payment schedule is really just an annuity whose present value equals the amount borrowed.
Example: you'll receive $100 every period at 0.5% per period, for 120 periods (10 years, monthly): PV = 100 × (1 − (1.005)^−120)/0.005 ≈ $9,007.35. Across 120 periods you'll receive $100 × 120 = $12,000 total, so the discount is $12,000 − $9,007.35 = $2,992.65.
Common mistakes
- Confusing FV (lump-sum) with PMT (annuity). These are different modes with different formulas — a single future amount discounted once isn't the same as recurring payments that each get discounted separately.
- Mismatching the rate and period units. A monthly rate must be paired with a count of months, not years — the discounting formula has no way to know your intent otherwise.
- Forgetting that a 0% rate is valid. It's not an error condition; it just means there's nothing to discount, so present value equals the total amount to be received.
- Mixing up present value with future value. Present value discounts money backward (divides by the growth factor); future value projects it forward (multiplies by the growth factor) — they're inverse operations, not the same calculation run twice.
Related calculators
For the reverse operation — projecting how much a deposit or a series of payments grows to after n periods — see the future value calculator. For a lump sum compounding at a stated annual rate with a chosen compounding frequency, the compound interest calculator covers the future-value side of that same case. If you're borrowing money and need to solve the annuity formula for the payment instead of the present value, the loan payment calculator uses the same discounting math in reverse — a loan amount is a present value, and the payment is solved so that the annuity's PV matches it.
Frequently asked questions
- What is the present value formula?
- For a single future lump sum, present value is PV = FV/(1 + r)^n, where FV is the amount received in the future, r is the discount rate per period as a decimal (rate ÷ 100), and n is the number of periods. For a series of equal payments (an annuity), it's PV = PMT × (1 − (1 + r)^−n)/r.
- How is present value different for a lump sum vs. an annuity?
- A lump sum is a single amount received once, n periods from now, discounted back to today in one step. An annuity is a series of equal payments received every period, each discounted back by a different number of periods — the annuity formula sums all of those individually-discounted payments in one closed-form expression.
- What happens if I enter a 0% rate for an annuity?
- A 0% rate is a valid input, not an error. The annuity formula would divide by zero at r = 0, so this calculator falls back to the simple PV = PMT × n — nothing is discounted, because there's no time value of money to account for.
- Why must the rate and periods use the same period unit?
- The rate here is per period, not per year — if payments arrive monthly, the rate must be the monthly rate and periods must be a count of months, not years. Mixing a monthly rate with a yearly period count (or vice versa) silently produces a wildly wrong answer.
- How is present value related to future value?
- Present value and future value are inverse operations built on the same compounding formula — present value divides by (1+r)^n to discount a future amount back to today, while future value multiplies by (1+r)^n to project a value forward in time. See our future value calculator for the reverse direction.
- Can present value ever equal the amount received in the future?
- Yes, but only when the rate is exactly 0% — with no discounting, PV equals the future amount (or the sum of the payments) exactly. With any positive rate, PV is always less than the amount received later, since money later is worth less than money today.
- What does the "discount" figure in the results mean?
- It's the difference between the total you'll receive and what that's worth today — total received minus present value. It quantifies how much value is lost purely to waiting, given the stated rate.