Present Value Calculator
What a future sum, a series of payments or a perpetuity is worth today at the discount rate you choose, with the discount factor.
Result
Present value: $37,688.95
At the discount rate you choose. A different rate gives a different present value, often by a lot.
- Total discount
- $62,311.05
- Discount factor
- 0.376889
- Face value
- $100,000.00
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Results are arithmetic on the returns, rates and horizons you enter, not a forecast and not investment, tax or retirement advice. The site supplies no expected return, inflation rate, contribution limit, tax rate or withdrawal rate. Real returns vary from year to year, and fees, taxes and the order of returns all change the outcome. Check anything that matters with a qualified adviser. Read the full disclaimer
How to use the Present Value Calculator
- Choose what to value, a single future amount, a series of payments, or payments that go on forever.
- Enter the amount, the discount rate, and for the first two the number of years and how often payments or compounding happen.
- Read what it is worth today, and the discount factor that turns one into the other.
The formulas
With a discount rate i per period and n periods:
single amount PV = FV ÷ (1 + i)^npayments PV = PMT × (1 − (1 + i)^−n) ÷ ipayments forever PV = PMT ÷ igrowing forever PV = PMT ÷ (i − g)The per-period rate is the annual rate divided by the number of periods in a year. Payments at the start of each period multiply the annuity value by (1 + i). At a 0% rate, a series of payments is worth simply their sum.
Discounting is compounding in reverse
Present value answers the question future value asks, from the other end. 100,000 in 20 years at 5% is worth 37,688.95 today, and 37,688.95 invested today at 5% grows back to 100,000 in 20 years. The discount factor, here 0.376890, is the share of a future amount that is worth having today.
Perpetuities
A perpetuity is the simplest possible stream: the same payment forever. It is what a preferred share, an endowment or a very long pension reduces to, and it shows what a discount rate means more directly than any other formula: the value is the payment divided by the rate.
With your numbers
- Present value = $37,688.95 for $100,000.00 received
- Discount factor = 0.376889
Quick reference
At the discount rate you choose. A different rate gives a different present value, often by a lot.
| Example | Present value |
|---|---|
| 100,000 in 20 years at 5% | $37,688.95 |
| 100,000 in 20 years at 8% | $21,454.82 |
| 10,000 a year for 20 years at 5% | $124,622.10 |
| Same at 0% | $200,000.00 |
| 10,000 a year forever at 5% | $200,000.00 |
| Growing 2% a year, at 5% | $333,333.33 |
| Growing 6% a year, at 5% |
Common questions about the Present Value Calculator
- What discount rate should I use?
- The return you could earn elsewhere on money of similar risk, or the rate you would have to pay to borrow it. The page supplies none, and the choice matters: 100,000 in 20 years is worth 37,688.95 today at 5% but only 21,454.82 at 8%.
- How can payments forever have a finite value?
- Because each payment further away is worth less today, and the values shrink fast enough that the total converges. 10,000 a year forever at 5% is worth exactly 200,000: invested at 5%, 200,000 pays 10,000 a year without ever being touched.
- Why can a growing perpetuity have no value?
- If the payments grow as fast as the discount rate or faster, each future payment is worth as much today as the one before it, or more, and the sum never stops rising. The formula would give a negative number, which looks like an answer and is not one, so the page says there is no finite value instead.
- How does this relate to NPV?
- Net present value discounts a whole list of cash flows, in and out, and adds them up. This page values one standard shape of cash flow. The NPV calculator handles uneven ones.