A present value calculator for lump sums, annuities and NPV
This present value calculator covers the three questions behind most time-value-of-money work: what will money be worth later (future value), what is a future amount worth today (present value), and is a series of cash flows worth its cost (net present value, NPV, and the internal rate of return, IRR). It handles lump sums and regular payments, with payments at the end of each period (an ordinary annuity) or at the start (an annuity due).
Money today is worth more than the same money later because it can earn interest. Discounting turns a future amount into today’s money; compounding does the reverse. Choose a mode, change the numbers, and the result, a breakdown and a table update as you type.
How to use the Present Value, Future Value & NPV Calculator
- Pick Future value, Present value or NPV & IRR.
- For future or present value, enter the amount, any payment each period, the yearly rate, how often it compounds and the years. Choose whether payments fall at the end or start of each period.
- For NPV, list the cash flows with period 0 first (the initial outlay as a negative number) and enter the discount rate per period.
- Read the headline result, the breakdown cards and the table. Use Copy the result to paste it elsewhere.
Present Value, Future Value & NPV Calculator features
Lump sums and annuities
Set the payment to zero for a lump sum, or add a regular payment for an annuity.
Ordinary or due
Annuity-due payments are multiplied by (1 + r), because each earns one extra period.
NPV with IRR
Discounted table per period, the profitability index and the IRR found by a root search; it says when no IRR exists.
Year-by-year growth
The future-value mode lists the balance after each year, up to 60.
The formulas
With periodic rate r (annual rate ÷ periods per year) and n periods: FV of a lump sum = PV × (1 + r)n; PV of a lump sum = FV ÷ (1 + r)n; FV of an ordinary annuity = PMT × ((1 + r)n − 1) ÷ r; PV of an ordinary annuity = PMT × (1 − (1 + r)−n) ÷ r. For an annuity due multiply the annuity result by (1 + r). If r = 0 the annuity factor is simply n. NPV = Σ CFt ÷ (1 + r)t, summed from t = 0, and the IRR is the rate that makes NPV zero.
Worked example: 50,000 due in 10 years at 6 % discounts to 50,000 ÷ 1.0610 = 27,919.74 today. Starting with 10,000 and adding 500 a month at 7 %, compounded monthly for 10 years, grows to about 106,639, of which 70,000 is money you put in.
Choosing the discount rate and reading NPV
- A positive NPV means the flows are worth more than the discount rate demands; a negative NPV means they fall short. NPV is in today’s money, so projects of different timing can be compared.
- The discount rate is your required return, an interest rate or an opportunity cost. A small change moves NPV a lot for long projects, so test a few values.
- Keep the period consistent: monthly flows need a monthly rate. To use a yearly rate with monthly flows, divide by 12 (or convert by compounding).
- IRR can be missing (all flows have the same sign) or ambiguous (flows change sign several times). Use NPV to decide in those cases.
- Flows on specific dates need the XIRR calculator; for retirement-style payouts see the annuity calculator; for growth with contributions see the compound interest calculator.
Present Value, Future Value & NPV Calculator FAQ
What is the difference between present value and future value?
Future value is what money grows to later; present value is what a future amount is worth today after discounting at a chosen rate.
How do I calculate NPV?
Discount each cash flow by (1 + r)^t and add them up, with the initial outlay as a negative number at period 0. This tool does it and shows every discounted flow.
What is an annuity due?
An annuity whose payments come at the start of each period, such as rent. It is worth (1 + r) times an ordinary annuity.
What does a negative NPV mean?
At that discount rate the project returns less than required. It does not mean a loss in accounting terms.
Why is there no IRR?
IRR needs both positive and negative flows. With a single sign there is no rate that gives zero NPV.
Is this financial advice?
No. It applies standard formulas to numbers you enter; actual returns, tax and inflation will differ.