Present value: what future money is worth today
Present value is what a future amount of money is worth today. You find it by discounting: divide the future amount by (1 + r)^n, where r is the rate you could earn elsewhere and n is the number of years. At 5%, $10,000 due in 8 years is worth $6,768 today.
Updated October 20, 2026 · 8 min read · Plain math, no product pitches
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What is present value?
Present value (PV) is what money you will get in the future is worth to you today. It is smaller than the future amount, because money you have now can be invested and grow while you wait.
Finding it is called discounting: you shrink the future amount back to today using a discount rate, the yearly return you could earn on the money instead. It is the same math as compound growth, run in reverse. (For why a dollar today beats a dollar later, see the time value of money.)
Present value is how you compare money that arrives at different times: a lump sum against monthly payments, a payoff now against payments later, or a cost today against savings that trickle in for years.
One way to picture it: the present value is the amount you would need to deposit today, at the discount rate, to end up with exactly the future amount on the future date. If someone offers you less than that today, waiting is better; if they offer more, take it now.
How do you calculate present value?
Divide the future amount by one plus the rate, raised to the number of years.
- PV
- present value, what it is worth today
- FV
- the future amount
- r
- discount rate per period, as a decimal
- n
- number of periods until you get it
The further away the money and the higher the rate, the less it is worth now. Here is $10,000 received in the future:
| Discount rate | In 5 years | In 10 years | In 20 years | In 30 years |
|---|---|---|---|---|
| 3% | $8,626 | $7,441 | $5,537 | $4,120 |
| 5% | $7,835 | $6,139 | $3,769 | $2,314 |
| 7% | $7,130 | $5,083 | $2,584 | $1,314 |
| 10% | $6,209 | $3,855 | $1,486 | $573 |
What is the difference between present value and future value?
They are the same relationship seen from opposite ends. Future value asks what money today grows into; present value asks what money later is worth now. One multiplies by (1 + r)n and the other divides by it, so $6,768.39 today and $10,000 in 8 years are the same money at 5%, stated on two different dates.
That is the whole trick behind comparing offers. Two amounts on different dates cannot be compared directly, any more than prices in two currencies. Move both to the same date first, usually today, and the bigger number wins.
How do you find the present value of a stream of payments?
Discount each payment back to today and add them up. When the payments are equal and evenly spaced (an annuity), one formula does the adding for you:
- PMT
- the payment each period
- i
- discount rate per period (yearly rate ÷ 12 for monthly)
- n
- number of payments
When the payments differ, discount each one separately:
The calculator below does this for a common real choice: one amount today, or equal payments over time. Change the rate and watch what the payments are worth.
Present value calculator: lump sum or payments
What a stream of payments is worth today, and the rate where both options are equal.
Payments, added up
$750,000
Worth today at 5%
$422,818
Break-even rate
5.56%
Where both are equal
At 5%, the payments are worth $22,818 more than the lump sum today. If you could earn more than 5.6% a year on the lump sum, it wins; below that, the payments win.
Before taxes, and assuming every payment arrives in full. A payer that might not pay is worth less; use a higher rate for it.
How do you choose a discount rate?
Use the return you could realistically earn on the same money elsewhere, at a similar level of risk. The rate is the most important input, and the right one depends on how sure the future money is.
- A near-certain payment (a reliable payer, a fixed amount) compares with safe returns: savings accounts, certificates of deposit, high-quality bonds.
- An uncertain payment deserves a higher rate. Risk raises the discount rate, and a higher rate lowers the value today.
- Debt you would pay off instead is discounted at that debt’s interest rate, since paying it down earns exactly that.
A trap to avoid: discounting safe, guaranteed payments at a stock-market rate. Stocks have compounded about 10% a year since 1928, but with large swings and long losing stretches, and the future can be worse. For long-term planning we use 7% a year before inflation as a cautious figure, and even that is too high a bar for payments that are close to guaranteed.
Inflation: discount at the inflation rate alone to see buying power. $100,000 received in 20 years, with prices rising 3% a year, buys what about $55,000 buys today.
What rate of return is realistic? →What stocks, bonds and savings have actually earned, and what to plan with.What is net present value (NPV)?
Net present value is the present value of everything you get back, minus what you pay today. Positive means the decision earns more than your discount rate; negative means you would do better earning that rate elsewhere.
- C₀
- what you pay today
- C₁ … Cₙ
- what you get back at the end of each year
| Discount rate | 3% | 5% | 7% | 10% |
|---|---|---|---|---|
| NPV of the upgrade | $1,012 | $689 | $409 | $58 |
How is present value used to price a bond?
A bond’s price is the present value of what it will pay you: the interest payments (the coupons) plus the face value at the end, all discounted at the return buyers currently want from similar bonds.
How do you calculate present value in Excel or Google Sheets?
Use PV for equal payments or a single future amount, and NPV for uneven cash flows. Both work the same way in Excel and Google Sheets. Spreadsheets show money you would pay out as a negative number, which is why PV returns a minus sign.
| Formula | Result | What it finds |
|---|---|---|
| =PV(5%, 8, 0, 10000) | −6,768.39 | $10,000 due in 8 years |
| =PV(4%/12, 120, 500) | −49,385.09 | $500 a month for 10 years |
| =NPV(5%, B2:B11) − 2400 | 688.69 | The upgrade, with $400 in each of B2:B11 |
Is a lump sum or payments worth more?
Whichever has the higher present value at a rate you could actually earn. Pension buyouts, lottery prizes, legal settlements and some insurance payouts all offer this choice, and adding up the payments always makes them look bigger than they are.
Beyond the rate, weigh what the formula leaves out:
- How sure the payments are. A payer that might not pay in full is worth less; use a higher rate.
- Inflation. Payments that never rise lose buying power every year. At 3% inflation, a flat $1,100 pension check in 20 years buys what about $609 buys today.
- Taxes. A lump sum and a stream can be taxed differently; compare after-tax amounts.
- You. A lump sum only earns its rate if it stays invested and is not spent.
This is general math, not advice for your situation. To see what a lump sum could pay you each year if it stays invested, try the Freedom calculator.
How can you use present value in everyday money decisions?
You do not need a pension or a prize to use it. Two everyday questions it answers directly:
The same reasoning is why Bill Router’s tools assume you pay every card in full each month: the days between a charge and its due date are free time value, and a single month of card interest would wipe it out many times over.
Common present value mistakes
- Adding up future payments. $30,000 a year for 25 years is $750,000 on paper and about $423,000 today at 5%.
- Getting the timing wrong. Payments at the start of each year are worth more than at the end: the same $30,000 a year at 5% is worth about $444,000 if each one arrives a year sooner.
- Mixing periods. Monthly payments need a monthly rate (yearly ÷ 12) and a count of months.
- Picking a rate to get the answer you want. Choose the rate first, from what you could really earn at similar risk.
Questions people ask
Is a higher discount rate good or bad?
It depends which side you are on. A higher discount rate makes future money worth less today, so a future payment you are owed is worth less, and a future bill you owe costs you less in today's terms.
What is a discount factor?
It is 1 ÷ (1 + r)^n, the share of a future dollar that it is worth today. At 5% for 8 years the discount factor is 0.6768, so each future dollar is worth about 68 cents now.
What is the difference between present value and net present value?
Present value is what one future amount, or a stream of them, is worth today. Net present value subtracts what you pay today, so it tells you whether a decision adds value (positive) or loses it (negative) at your chosen rate.
Why is present value always less than future value?
Because money today can earn a return. As long as the discount rate is above zero, you need less than the future amount today to grow into it, so the present value is smaller. At a 0% rate they are equal.
What does a negative NPV mean?
It means the money you get back, valued today, is less than what you put in, at the rate you chose. You would do better earning that rate elsewhere. A higher rate makes NPVs smaller, so a project can flip from positive to negative as the rate rises.
What discount rate should I use for a pension lump sum?
Use a rate you could reliably earn on the lump sum at a similar level of risk. Pension payments are steady and predictable, so measuring them against an uncertain stock return makes the lump sum look better than it is. Try a range of rates and see where the break-even falls.
How do you account for inflation in present value?
Either discount at a real (after-inflation) rate to get the answer in today's purchasing power, or discount future dollars at a nominal rate. Do not mix them: use real amounts with a real rate, and nominal amounts with a nominal rate.
Do taxes change the present value?
Yes. Compare after-tax amounts on both sides. A lump sum and a series of payments can be taxed differently and at different times, which can change which option is worth more.