Present Value of Money in 17 Minutes
Present value answers a simple question: what is money you will receive in the future worth today? You find it by discounting, which strips out the interest the money could have earned. It is the core of NPV, bond pricing and stock valuation.
Present value explained simply
Present value is what future money is worth today: PV = FV ÷ (1 + r)ⁿ. In the example, $1,000 received in 3 years at a 5% discount rate is worth about $863.84 today.
What this present value lesson covers
- What present value means and why future money is worth less today
- The present value formula for a single future amount
- What discounting and the discount factor are
- How present value feeds into NPV and valuation
Present value formula, explained
- PV
- present value, worth today
- FV
- future amount
- r
- discount rate per period
- n
- number of periods
- DF
- what $1 received in n periods is worth today
How to calculate present value step by step (worked example)
You will receive $1,000 in 3 years. If the discount rate is 5% a year, what is it worth today?
- Inputs: FV = $1,000, r = 0.05, n = 3.
- Growth factor: (1.05)³ = 1.157625.
- Divide: PV = $1,000 ÷ 1.157625 ≈ $863.84 (rounded to the cent).
Answer: About $863.84 today.
Present value vs future value
| Present value | Future value | |
|---|---|---|
| Question it answers | What is later money worth today? | What will today's money grow to? |
| Operation | Discounting (divide) | Compounding (multiply) |
| Formula | FV ÷ (1 + r)ⁿ | PV × (1 + r)ⁿ |
| $1,000, 5%, 3 years | $863.84 today | $1,157.63 later |
Is waiting always a cost? David's take
Present value rests on a simple idea: money later is worth less than money now, so waiting costs you. For money, that's true. For projects, it used to be true as well, because a shelved project just sat there. With AI agents, that's changing. The models get smarter, your skills improve from other work, and your instructions get sharper, so a project can come off the shelf in better shape than when it went on. I call it upcrastination. My test: name the specific thing that improved while it waited. If you can't, it's ordinary procrastination, and the textbook is right.
From David's concept: Upcrastination. This is David's opinion, alongside the standard textbook answer above.
Harder present value questions
How much does the discount rate change the answer?
For $1,000 in 3 years: about $889.00 at 4%, $863.84 at 5%, $839.62 at 6% and $751.31 at 10%. The higher the rate, the less future money is worth today.
How do you choose the discount rate?
Use the return you could earn elsewhere on something with similar risk: a savings rate for safe cash, a bond yield for debt, a cost of capital such as WACC for a company's projects.
Common present value questions
What is the present value formula?
For a single future amount, PV = FV ÷ (1 + r)ⁿ, where FV is the future amount, r is the discount rate per period and n is the number of periods. It is the future value formula rearranged.
How do you calculate present value step by step?
Turn the rate into a decimal, add 1, raise it to the number of periods, then divide the future amount by that number. For $1,000 in 3 years at 5%, divide $1,000 by 1.05³ to get about $863.84.
Why is present value less than future value?
Because money today can be invested to earn a return. To have $1,000 in three years at 5%, you only need about $863.84 today. The higher the rate or the longer the wait, the lower the present value.
What discount rate should I use for present value?
Use the return you could earn elsewhere on an investment of similar risk, often called the opportunity cost of capital. In exam questions the rate is usually given. For company projects it is often the WACC.