Present and Future ValuePV
Present value is what a future amount is worth today; future value is what money today will grow to. Both rest on the time value of money: a dollar now is worth more than a dollar later because it can earn interest.
Would you rather have $1,000 today or $1,000 in five years? Today, because you could invest it. That simple idea — the time value of money — underlies bond prices, stock valuations, loans and retirement planning. This entry explains present and future value, the formulas and how investors use them.
- Category
- Fundamentals and Macroeconomics
- Reading time
- 3 min
- Also called
- Time value of money, Present value, Future value
- Updated
PV and FV in plain words
The time value of money holds that money now is worth more than the same amount received in the future.1
It is sometimes described in terms of the net present value of money.1
Compound interest means earning interest on your original money plus previously earned interest.2
How to calculate PV and FV, step by step
Pick a rate
Interest or required return. See Interest Rate.
Pick the periods
Years or months.
Future value
FV = PV × (1 + r)^n. See Compound Interest.
Present value
PV = FV ÷ (1 + r)^n.
Sum cash flows
Value each flow separately. See Discounted Cash Flow.
Compare options
Choose the higher present value.
Worked examples
Example 1 — Future value
≈ $8,954$5,000 invested at 6% for 10 years.
| FV | $5,000 × 1.06^10 ≈ $8,954 |
Money today can grow with compound interest over time.2
Example 2 — Present value
≈ $7,130 today$10,000 to be received in 5 years, discount rate 7%.
| PV | $10,000 ÷ 1.07^5 ≈ $7,130 |
A future sum is worth less today because of the time value of money.1
Example 3 — Choosing between offers
Take AOption A: $9,000 today. Option B: $12,000 in 4 years. Discount rate 8%.
| PV of B | $12,000 ÷ 1.08^4 ≈ $8,820 |
| Better choice | A ($9,000 today) |
Comparing present values shows which option is truly worth more.1
Present value vs future value
| Aspect | Present value | Future value |
|---|---|---|
| Question | What is it worth today? | What will it grow to? |
| Operation | Discounting | Compounding |
| Higher rate means | Lower PV | Higher FV |
| Used for | Valuation, bond prices | Savings goals |
Where PV and FV are used
Valuing stocks
DCF and dividend models. See Dividend Discount Model.
Bond pricing
Discounting coupons and par. See Yield to Maturity.
Retirement planning
How much savings will grow. See Rule of 72.
Loans
Payments and interest. See APR and APY.
Advantages and disadvantages
Advantages
- Puts money at different times on equal terms.
- Foundation of all valuation.
- Simple formulas.
Disadvantages
- Results depend heavily on the rate chosen.
- Assumes known future cash flows.
- Ignores risk unless the rate includes it.
Going deeper
Read as far as you need. Each level builds on the one before it.
Why money now is worth more
Beginner
Money available now can be invested to earn a return, so it's worth more than the same sum later.1
Net present value
Intermediate
Subtracting an investment's cost from the present value of its future cash flows gives NPV; positive NPV adds value. See Discounted Cash Flow.
Rates and risk
Advanced
Riskier cash flows get higher discount rates, often built from the risk-free rate plus a premium. See Capital Asset Pricing Model.
Common mistakes
Ignoring inflation
Use real or nominal rates consistently.
Mismatched periods
Monthly rates for monthly flows.
Too low a discount rate
Overstates value.
Forgetting compounding
Simple interest understates growth.
Check your understanding
Test yourself before moving on. Each answer comes with an explanation.
Key points to remember
- A dollar today is worth more than a dollar later.
- FV = PV × (1 + r)^n.
- PV = FV ÷ (1 + r)^n.
- The discount rate drives the result.
- It underpins all valuation.
Frequently asked questions
What discount rate should I use?
Is present value the same as NPV?
Why do higher rates lower stock prices?
Further learning
- Compound Interest
How money grows.
- Discounted Cash Flow
Valuing businesses with PV.
- Yield to Maturity
PV in bond pricing.
- Rule of 72
A quick FV shortcut.
Sources
This article is written in our own words. The sources below support the specific facts, rules and figures marked with a number in the text. Links open the original publisher’s page.
- Corporate Finance Institute. Time Value of Money (opens in a new tab) Checked .
- Investor.gov (SEC). What is compound interest? (opens in a new tab) Checked .
Educational content, not financial advice. Examples use hypothetical prices and simplified costs; actual fees, margin rules and regulations vary by broker, market and country. We are not affiliated with any publisher linked above. Last reviewed . Report an error or request a source credit.