Present Value Calculator — PV, Annuity & NPV
Discount future money back to today's value. Calculate PV of a lump sum, annuity, perpetuity, or the Net Present Value (NPV) of custom cash flows.
PV = FV / (1+r)ⁿ
LUMP SUM
PV = PMT×[1-(1+r)⁻ⁿ]/r
ANNUITY
PV = PMT / r
PERPETUITY
NPV = Σ CFt/(1+r)ᵗ
NPV / CASH FLOWS
Present Value Calculator
Lump Sum · Annuity · Perpetuity · NPV
DISCOUNT A FUTURE SUM TO TODAY
Present Value
$5,584
$10,000
Future Value
6%
Discount Rate
$10,000 received in 10 years, discounted at 6%.
$5,584
Present Value
$4,416
Time-Value Discount
55.8%
% of Future Value
📊 PV Sensitivity — Different Discount Rates
How present value changes at different discount rates (your rate highlighted)
| Discount Rate | Present Value | Discount Amount | % of FV |
|---|---|---|---|
| 1% | $9,053 | $947 | 90.5% |
| 2% | $8,203 | $1,797 | 82.0% |
| 3% | $7,441 | $2,559 | 74.4% |
| 4% | $6,756 | $3,244 | 67.6% |
| 5% | $6,139 | $3,861 | 61.4% |
| 6% ★ | $5,584 | $4,416 | 55.8% |
| 7% | $5,083 | $4,917 | 50.8% |
| 8% | $4,632 | $5,368 | 46.3% |
| 9% | $4,224 | $5,776 | 42.2% |
| 10% | $3,855 | $6,145 | 38.6% |
| 12% | $3,220 | $6,780 | 32.2% |
| 15% | $2,472 | $7,528 | 24.7% |
| 20% | $1,615 | $8,385 | 16.2% |
📉 Present Value at Different Discount Rates
Present Value Formulas
- Lump Sum: a single future amount, discounted back by the number of compounding periods until it arrives.
- Ordinary Annuity: a series of equal payments, each discounted individually then summed.
- Perpetuity: an annuity that never ends — collapses to payment ÷ rate.
- NPV (Net Present Value): the sum of discounted cash inflows minus the upfront investment.
For the mirror-image calculation — growing money forward instead of discounting it back — see our future value calculator, or check the IRR calculator for the rate that makes NPV exactly zero.
| Discount Rate | Present Value | Discount Amount |
|---|---|---|
| 2% | $8,203 | $1,797 |
| 4% | $6,756 | $3,244 |
| 6% | $5,584 | $4,416 |
| 8% | $4,632 | $5,368 |
| 10% | $3,855 | $6,145 |
| 15% | $2,472 | $7,528 |
Illustrative: $10,000 received in 10 years, discounted at each rate.
How to Interpret NPV
| NPV Result | Interpretation | Decision |
|---|---|---|
| NPV > 0 | Investment returns more than the required rate | Accept the investment |
| NPV = 0 | Investment returns exactly the required rate | Indifferent — breakeven |
| NPV < 0 | Investment returns less than the required rate | Reject the investment |
— FAQ