β³ Present Value Calculator
What future money is worth in today's dollars.
Present Value
Estimates for planning only, not financial advice.
What Is Present Value?
Present value is what a future amount of money is worth in today's dollars. Because money can earn interest, $100,000 arriving ten years from now is not worth $100,000 today. At a 7 percent discount rate, it is worth about $50,835, barely half its face amount. Discounting is compounding run in reverse: instead of growing money forward at an interest rate, you shrink future money backward at a discount rate. Every loan, bond price, pension offer, and lottery payout choice is a present value problem wearing different clothes.
How to Use This Calculator
Choose whether you are valuing a single future payment or a stream of equal payments, then enter the amount, the annual discount rate, the time horizon, and how many periods per year apply. The calculator discounts every future dollar back to today and shows both the present value and how much of the future total is "lost" to the time value of money.
Pick "A lump sum" for one future payment (an inheritance, a bond maturing) or "An annuity" for repeated equal payments (yearly withdrawals, lease income).
Enter the Future Value or the Payment Per Period, plus the annual Discount Rate. This rate is the return you could earn elsewhere, so be honest about it.
Set the Years and Periods Per Year. Monthly payments at a 7 percent annual rate use a monthly rate of 7/12 percent, which changes the answer versus annual payments.
For annuities, choose End or Beginning of period timing. Beginning-of-period payments are worth more because each one arrives a period sooner.
The Present Value Formulas
Discounting is compounding in reverse. Where compound interest multiplies by (1 + i)^n to move money forward, present value divides by the same factor to move it back. The annuity formula is the sum of n individual lump-sum discounts, collapsed into one expression by the geometric series. Notice the symmetry: the annuity present value factor (1 - (1+i)^-n)/i is the mirror image of the future value factor ((1+i)^n - 1)/i used when growing money forward.
One subtlety worth knowing: more frequent compounding at the same nominal rate discounts a little harder. $100,000 in 10 years at 7 percent is worth $50,834.93 with annual compounding but $49,759.63 with monthly compounding. The calculator lets you set the frequency so the answer matches how the money would actually compound.
Worked Example
You are promised $100,000 in 10 years and your discount rate is 7 percent compounded annually. PV = $100,000 / 1.07^10 = $100,000 / 1.9672 = $50,834.93. That lump sum is worth barely half its face amount today. Now value an annuity instead: $10,000 received at the end of each year for 20 years at 6 percent. PV = $10,000 x (1 - 1.06^-20) / 0.06 = $10,000 x 11.4699 = $114,699.21. The payments total $200,000, but the time value of money erases over $85,000 of that in today's dollars. Switch the timing to beginning-of-period and the value rises by a factor of 1.06 to $121,581.16.
How Sensitive the Answer Is to the Discount Rate
The discount rate is the single most important input, and small changes move the answer a lot. Here is $100,000 due in 10 years at four different rates:
| Discount rate | Present value | Share of face amount |
|---|---|---|
| 3% | $74,409.39 | 74.4% |
| 5% | $61,391.33 | 61.4% |
| 7% | $50,834.93 | 50.8% |
| 10% | $38,554.33 | 38.6% |
A seven-point swing in the rate cuts the present value nearly in half. This is why arguments about valuation are almost always arguments about the discount rate in disguise. When someone shows you a present value, ask what rate they used and whether it reflects your real opportunity cost. In my experience, most bad financial decisions come from using a discount rate that flatters the answer someone already wanted.
Present Value vs Net Present Value
Present value discounts one future amount, or one stream of payments, to today. Net present value goes one step further: it discounts ALL the cash flows of a project, money in and money out, and then subtracts the upfront investment. A positive NPV means the project beats your discount rate; a negative NPV means you would do better investing the money at that rate instead. Businesses live and die by NPV when choosing between projects. For personal decisions, PV is usually enough: comparing two offers, valuing a settlement, or deciding between a pension lump sum and monthly checks.
Lump Sum or Annuity Payments?
Lottery winners and retirees face this exact choice, and present value settles it fairly. Discount both offers at the same rate and compare. A $1 million annuity paying $50,000 a year for 20 years sounds like $1 million, but at a 6 percent discount rate its present value is only about $573,496, far less than a $700,000 lump sum. The catch is behavioral: the lump sum is only worth more if you actually invest it at the discount rate instead of spending it. If the money will sit in a checking account earning nothing, the annuity's forced discipline can beat the mathematically superior lump sum. Math sets the fair price; your habits decide the real one.
Where Present Value Gets Used
Present value is the engine of almost every financial decision. Bond prices are the present value of coupons plus principal. A mortgage balance is the present value of the remaining payments. Courts use it to value structured settlements and lottery winners choose between a lump sum and annuity payments by comparing present values. Businesses discount projected profits to decide whether a project beats its cost of capital. Whenever someone offers you money later instead of money now, discounting both offers at the same rate is the only fair way to compare them.
Related Tools
Keep going: our future value calculator grows money forward instead of backward, the compound interest calculator adds monthly deposits to the growth side, and the annuity calculator prices payment streams in both directions.
Estimates for planning only, not financial advice.
Frequently Asked Questions
What is present value?
Present value is what a future amount of money is worth in today's dollars. Because money can earn interest, $100,000 received ten years from now is worth less than $100,000 in your hand today. Discounting reverses compounding: instead of growing money forward at an interest rate, you shrink future money backward at a discount rate.
What is the present value formula?
For a lump sum it is PV = FV / (1 + r)^n, where FV is the future value, r is the discount rate per period, and n is the number of periods. For an annuity, a stream of equal payments, it is PV = PMT x (1 - (1 + r)^-n) / r. The lump sum formula is just the compound interest formula solved backwards.
What discount rate should I use?
Use the rate of return you could earn on the money instead, which is called the opportunity cost. For personal decisions, that might be your savings APY, your mortgage rate, or an expected investment return. A higher discount rate shrinks the present value, which is why risky projects with high required returns need bigger future payoffs to be worth doing.
What is the difference between PV of an annuity and a lump sum?
A lump sum is one payment at one future date, like a bond maturing in 10 years. An annuity is a series of equal payments, like $10,000 every year for 20 years. The annuity formula adds up the present value of each individual payment, which is why an annuity's PV is always less than the simple sum of its payments.
What does payment timing (beginning vs end of period) change?
An annuity-due pays at the beginning of each period, so every payment arrives one period earlier and is discounted one period less. Its present value is exactly (1 + r) times the value of an ordinary annuity that pays at period end. Rent is a classic annuity-due; a standard loan payment is an ordinary annuity.
Why is present value negative sometimes in spreadsheets?
Spreadsheet PV functions follow a cash flow sign convention: money you pay out is negative and money you receive is positive. If you enter a future value as a positive receipt, the PV comes out negative, meaning that is the investment (outflow) required today. It is bookkeeping, not a real negative value.
What is the difference between present value and net present value?
Present value discounts one future amount, or one stream of payments, to today. Net present value discounts all the cash flows of a project, inflows and outflows, and then subtracts the upfront investment. A positive NPV means the project beats your discount rate; a negative NPV means you would do better investing the money at that rate instead. Businesses use NPV to choose between projects.
Why does a higher discount rate lower the present value?
The discount rate is the return you could earn by investing the money instead. If you can earn 10 percent elsewhere, a future payment must be discounted aggressively, because waiting costs you that 10 percent. At 3 percent the same $100,000 due in 10 years is worth $74,409, but at 10 percent it is worth only $38,554. A higher rate means a higher opportunity cost, so future money is worth less today.
Does compounding frequency change the present value?
Yes, slightly. More frequent compounding at the same nominal rate grows money faster going forward, so it discounts harder going backward. $10,000 due in 5 years at 5 percent is worth $7,835.26 with annual compounding but $7,792.05 with monthly compounding. Set the periods per year in the calculator to match how the money would actually compound.
Should I take the lump sum or the annuity payments?
Discount both offers at the same rate and compare. A $1 million annuity paying $50,000 a year for 20 years sounds like $1 million, but at a 6 percent discount rate its present value is only about $573,496, far less than a $700,000 lump sum. The catch is behavioral: the lump sum wins only if you invest it at the discount rate. If it would sit in checking earning nothing, the annuity's forced discipline can beat the better math.
Can the discount rate be zero or negative?
Yes. At a 0 percent discount rate the present value equals the future value, because there is no time value of money. Zero is realistic for short-term, low-risk comparisons where the alternative earns nothing. Negative rates are rare but real: they model situations where holding cash costs you, such as some European bank deposits in past years, and they make the present value larger than the future amount.
Is present value the same as fair value?
Not exactly. Present value is a calculation from the discount rate you choose; fair value is what a willing buyer would actually pay, which also reflects market conditions, liquidity, taxes, and negotiation. Two people can compute different present values for the same cash flow by choosing different rates. PV is one input into a fair-value judgment, not the whole answer.