Key takeaways
- PV = FV ÷ (1 + r)ⁿ, where r is entered as a percentage (8 for 8%), not a decimal.
- PV is the mirror image of future value: it discounts backward instead of projecting forward.
- A higher discount rate makes a future amount worth less today.
- This idea is called the time value of money.
In this guide
What is present value?
A dollar today is generally worth more than the same dollar received years from now, because money today can be invested and grow. Present value (PV) answers the reverse question of future value: given an amount you'll receive in the future, what is it actually worth right now?
Why does present value matter?
Present value lets you compare a future payment against a present one on equal footing. Without discounting, it's tempting to assume $2,000 later is worth the same as $2,000 now — but it isn't.
$2,000 promised 5 years from now, discounted at 8% per year, is worth only about $1,361.17 today — nearly a third less than its face value.
The formula
| Symbol | What it means | Example |
|---|---|---|
| FV | Future value — amount received later | $2,000 |
| r | Annual discount rate as a percentage | 8 |
| n (years) | Years until the future amount is received | 5 |
| PV | What that future amount is worth today | $1,361.17 |
How to calculate present value step by step
- 1Divide the annual rate by 100 and add 1. This gives the yearly discount factor.
- 2Raise that factor to the power of the number of years. This spreads the discount across every year.
- 3Divide the future value FV by that result. The result is the present value, PV.
- 4Compare PV to any amount offered today. This tells you which option is actually worth more right now.
Enter your own future value, discount rate, and time in the calculator below.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Entering the rate as a decimal. Like future value, enter 8 for 8%, not 0.08.
- Using the wrong discount rate. A higher assumed rate makes a future amount worth less today, because it implies you could have earned more elsewhere.
- Forgetting present value is an estimate. The discount rate is an assumption, so the result changes if that assumption changes.
Tips and tricks
- It's the mirror image of the future value calculator, which projects an amount forward instead of discounting it back.
- The same discounting idea underlies the compound interest calculator, just applied in reverse.
- Comparing a loan payoff instead of an investment payout? The EMI calculator applies a related idea to monthly loan payments.
Where you'll use it in real life
- Comparing payout options: deciding between a lump sum now or a larger amount paid out later.
- Bond and investment analysis: estimating what a future payment is worth in today's terms.
- Negotiating deferred payments: understanding the real value behind an offer paid over time.
- Business valuation basics: projecting the value of expected future cash in today's money.
Quick summary
Present value is PV = FV ÷ (1 + r)ⁿ: add 1 to the discount rate, raise it to the power of the years, then divide the future amount by that result. A higher discount rate or more years both shrink the present value. Use the calculator above to check your own numbers.
Worked example
You've been offered $2,000 five years from now, and you want to know what that's worth today assuming a discount rate of 8% per year.
- 01PV = FV / (1 + r)ⁿ
- 02PV = $2,000 / (1 + 0.08)^5
- 03PV = 2000 / 1.4693
- 04PV = $1,361.17
These numbers are pre-filled in the calculator above.
Frequently asked questions
Why is a future amount worth less today?
Because money available now could be invested and grow, a future payment has to be discounted back to reflect what it's really worth if received today instead — this is called the time value of money.
What's the difference between present value and future value?
Future value takes an amount today and projects it forward; present value takes an amount in the future and discounts it back to today. They use the same formula, just solved in opposite directions.
How does the discount rate affect present value?
A higher discount rate makes the present value smaller, because it assumes money today could grow faster elsewhere, making the future amount comparatively less valuable now.
Is the rate entered as a whole number or a decimal?
As a whole number percentage — enter 8 for an 8% rate, not 0.08.
