💰 Present Value Calculator
Present Value Calculator — PV, Annuity & NPV
Discount a future lump sum, annuity stream, or irregular cash flows to today's value. Includes PV sensitivity table, discount factor schedule, and PV decay chart.
PV = FV / (1+r)ⁿ
Lump Sum
PV = PMT × [1−(1+r)⁻ⁿ] / r
Annuity
NPV = Σ CFt / (1+r)ᵗ
Uneven Flows
💰 Lump Sum PV
📅 Annuity PV
📋 NPV (Uneven)
📊 Sensitivity Table
Present Value Calculator
PV = FV / (1+r)ⁿ · Annuity · Uneven Cash Flows
💰 Lump Sum
📅 Annuity
📋 Uneven Cash Flows
Single Future Amount
$
%
Annuity Payments
$
%
$
Uneven Cash Flows (NPV)
Enter the expected cash flow for each period. Period 0 is typically the initial investment (negative).
%
$0
Present Value
$0
Future Value
$0
Total Discounted
0.000
Discount Factor
📉 PV Decay — Today's Value vs Future Value Over Time
📊 PV Sensitivity — Different Discount Rates
How the present value changes at different discount rates (your rate highlighted)
| Discount Rate | Present Value | Discount Factor | % of FV |
|---|
📋 Period-by-Period Discount Schedule
| Period | Discount Factor | Cash Flow / FV | Present Value | Cumulative PV |
|---|
Present Value Formulas
- Lump Sum:
PV = FV / (1+r)ⁿ - Ordinary Annuity:
PV = PMT × [1 − (1+r)⁻ⁿ] / r - Annuity Due:
PV = PMT × [1 − (1+r)⁻ⁿ] / r × (1+r) - Uneven Cash Flows (NPV):
PV = Σ[CFt / (1+r)ᵗ]
How Discount Rate Affects Present Value
| Discount Rate | PV of $10,000 in 10 yrs | PV of $10,000 in 20 yrs | PV of $10,000 in 30 yrs |
|---|---|---|---|
| 2% | $8,203 | $6,730 | $5,521 |
| 5% | $6,139 | $3,769 | $2,314 |
| 8% | $4,632 | $2,145 | $994 |
| 10% | $3,855 | $1,486 | $573 |
| 15% | $2,472 | $611 | $151 |
| 20% | $1,615 | $261 | $42 |
Frequently Asked Questions
Present value (PV) is the current worth of a future amount of money, discounted at a given rate to reflect the time value of money. Money today is worth more than the same amount in the future because it can be invested to earn returns. PV lets you compare cash flows that occur at different points in time on a fair, equal-today basis — essential for investment decisions, loan comparisons, and business valuation.
For a single lump sum: PV = FV / (1+r)^n. For an ordinary annuity (payments at end of each period): PV = PMT × [1 − (1+r)^-n] / r. For an annuity due (payments at start): multiply ordinary PV by (1+r). For uneven cash flows: PV = Σ[CFt / (1+r)^t] — sum the discounted value of each individual cash flow.
An ordinary annuity pays at the END of each period (mortgages, car loans, bonds). An annuity due pays at the BEGINNING (leases, insurance premiums, some retirement accounts). Because annuity due payments arrive one period earlier, they're discounted one period less, making PV(annuity due) = PV(ordinary annuity) × (1+r) — always slightly higher.
The discount rate reflects the opportunity cost, risk, and inflation. Common choices: (1) Cost of capital or WACC for corporate projects. (2) Risk-free rate (Treasury rate) for low-risk government cash flows. (3) Your expected investment return (e.g., 7-10% for stocks) for personal finance decisions. (4) Inflation rate alone to find purchasing-power-equivalent present value. Higher discount rates = lower present values, reflecting greater risk or opportunity cost.
PV is the discounted value of a future cash flow or uniform series of payments. NPV (Net Present Value) is the SUM of all discounted cash flows for a project, including the initial investment as a negative outflow. NPV = Σ[CFt/(1+r)^t] − Initial Investment. A positive NPV means the project creates value; a negative NPV means it destroys value at the chosen discount rate. Use our Uneven Cash Flows tab to calculate NPV directly.