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Present Value Calculator

Find what money you'll get in the future is worth today. Works for a single future amount, a series of equal payments, or both, at a rate you choose.

Level: Grades 11–12

  • Common Core standard HSA.SSE.B.4Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
Printable worksheet

Present Value Calculator

Know the answer you need? Pick an input to work backward.

Inputs

The single sum you will receive (or need) at the end. Use 0 to value payments only.

Optional. The same payment made once per compounding period, such as an annuity or lease payment.

Result

Present value

$6,139.13

At 5% a year, $10,000.00 received over 10 years is worth $6,139.13 today.

Total received, undiscounted
$10,000.00
Discount (time value of money)
$3,860.87

See the step-by-step solution ↓

Step-by-step solution

  1. Find the rate for each year (i): divide the yearly rate by 1, because it's applied 1 time a year

    i=0.051=0.05

  2. Count the periods (N): 1 a year for 10 years

    N=1×10=10

  3. Work the future amount back to today by undoing one period of growth for every period you wait

    $10,000.00(1+0.05)10=$6,139.13

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

Please note: Results are estimates for planning and comparison. Lenders, banks, and tax authorities may round differently or include fees not modeled here, so confirm figures with your provider before deciding.

How to solve this on a calculator

The keys to press to get this page's worked-example answer on an ordinary calculator, with what the display should show after each step. A named-model tab follows that calculator's official guidebook.

What a future sum is worth today, with CPT PV

Problem
You will receive $10,000 in 10 years, and the discount rate is 5% compounded annually. What is it worth today?
Formula
PV from N = 10, I/Y = 5, PMT = 0, FV = 10,000
Example values
N = 10 (years); I/Y = 5 (annual discount rate, percent); FV = 10,000 (amount received later). These are the fixed values from the worked example on this page, so the keys stay the same whatever you type into the calculator above.
Why a financial calculator
Discounting is CPT PV: the calculator runs the growth formula backwards for you.
The whole sequence
CLR TVM1P/YEND10N5I/Y0PMT10000FVCPTPV

Step by step

  1. CLR TVM

    Press CLR TVM so nothing left over from an earlier problem (such as an old FV) changes the answer.

    Display: TVM cleared

  2. 1P/Y

    Type 1 and press P/Y: one period a year, since the rate compounds annually and N is in years. C/Y (compounding per year) is set to the same value.

    Display: P/Y=1

  3. END

    Press END: each payment is made at the end of its period.

    Display: END

  4. 10N

    10 N: ten yearly periods.

    Display: N=10

  5. 5I/Y

    5 I/Y: the discount rate.

    Display: I/Y=5

  6. 0PMT

    0 PMT: there are no payments in between.

    Display: PMT=0

  7. 10000FV

    10000 FV: you receive it at the end, so it is positive.

    Display: FV=10,000

  8. CPTPV

    CPT PV: about −$6,139.13. Negative because it is what you would pay today to receive $10,000 in 10 years.

    Display: PV=-6,139.13253541

If your answer looks wrong

  • Sign convention: money you receive is positive and money you pay out is negative. FV is what you receive (positive), so PV comes out negative: the price you would pay today. Its size, $6,139.13, is the present value.
  • P/Y and C/Y: here P/Y must be 1 because the rate compounds once a year. With P/Y = 12 and N = 10, CPT PV shows -9,592.72493111 (only 10 months of discounting); with P/Y = 12 and N = 120 it shows -6,071.61040299 (monthly compounding). This site's keypad starts with P/Y = C/Y = 1, and setting P/Y also sets C/Y; on a calculator where C/Y doesn't follow P/Y, set C/Y to the same value too, or the monthly rate is worked out from a different compounding.
  • If PMT still holds a payment from an earlier problem, the answer includes it: enter 0 PMT or press CLR TVM first.

How this is checked: an automated test presses these keys on this site's financial calculator, checks every display along the way, and confirms the answer matches the calculator on this page (last checked 2026-10-19). It has not been checked on any particular brand or model, and real calculators label some keys differently.

What this calculator does

Find out what money you'll receive later is worth to you today. A dollar promised in the future is worth less than a dollar in your hand. That's because money you have now can be invested and grow. Present value puts a number on that idea. It's the amount you'd need to invest today, at a given rate, to end up with the future amount.

Working back from a future amount to today is called discounting, and the rate you use is the discount rate. The calculator discounts a single future sum back to today. The money might instead come as a series of equal payments, such as an annuity, a lease or a structured settlement. In that case, add the payment and choose whether each one arrives at the start or end of its period. The calculator then adds the present value of the payments to the present value of the lump sum.

Where it's used

Why this math matters outside the classroom:

  • Future sums today. Receiving $10,000 in 5 years is worth about $8,219.27 today at a 4% yearly discount rate.
  • Settlement offers. People compare a lump sum now with a series of future payments by converting the payments to present value.
  • Business projects. Companies discount a project's expected future cash flows to compare them with its cost today.
  • Finance classes. Students see that a higher discount rate or a longer wait makes the same future amount worth less today.

Grade level and standards: Grades 11–12; Common Core State Standards for Mathematics HSA.SSE.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Enter the future amount you expect to receive. Enter 0 if you only want to value a series of payments.
  2. Enter the yearly discount rate, the number of years, and how many times a year the rate compounds (is applied).
  3. If you like, enter a payment made once per compounding period. Then choose whether payments come at the start or end of each period.
  4. Read the present value, the plain total before discounting, and the gap between them, called the discount.

What the inputs mean

Future amount
The single sum you will receive (or need) at the end. Use 0 to value payments only.
Annual discount rate
The return you could earn elsewhere with similar risk, or the rate you've been told to use. A higher rate gives a lower present value.
Compounding periods per year
How often the discount rate is applied each year. If you enter payments, the calculator assumes one payment per compounding period.
Payment each period
The same amount received every period. With payments, the years must work out to a whole number of periods.
Payments are made at the
End of period is called an ordinary annuity. Start of period is called an annuity due. It's worth more, because each payment arrives one period sooner.

Formula and method

i = r ÷ n;  N = n × years
PV (lump sum) = FV ÷ (1 + i)^N
PV (payments at end) = PMT × (1 − (1 + i)^(−N)) ÷ i
PV (payments at start) = PMT × (1 − (1 + i)^(−N)) ÷ i × (1 + i)
at 0%: PV = FV + PMT × N

In the formulas, FV is the future amount and PV is the present value. r is the yearly discount rate as a decimal, and n is the number of compounding periods per year. i is the rate for each period, and N is the total number of periods. PMT is the size of each payment.

Money grows by (1 + i) each period, so dividing by (1 + i)^N undoes N periods of that growth. The payment formula discounts each payment by its own number of periods and adds them up. Payments at the start of a period are discounted one period less. That's why that version is multiplied by (1 + i).

Worked example

You will receive $10,000 in 10 years, and the discount rate is 5% compounded annually.

  1. Rate per year: 0.05 ÷ 1 = 0.05. Number of periods: 1 × 10 = 10.
  2. Discount the $10,000: $10,000 ÷ 1.05^10 ≈ $6,139.13.
  3. The discount, or the gap, is $10,000 − $6,139.13 ≈ $3,860.87.
  4. If you also receive $1,000 at the end of each year: $1,000 × (1 − 1.05^(−10)) ÷ 0.05 ≈ $7,721.73.

Result: The $10,000 is worth about $6,139.13 today. With the ten $1,000 payments added, the total present value is about $13,860.87.

Understanding the result

Say someone offers you a sum today instead. If it's more than the present value, taking it now is the better deal at your discount rate. If it's less, waiting is better.

Present value changes a lot with the discount rate and the number of years. Try a few rates to see how much your answer depends on that choice.

Assumptions and limitations

  • The discount rate stays the same the whole time and is applied n times a year.
  • Any payments are all the same size and happen once per compounding period.
  • You're sure to receive the money. The only way risk shows up is through the rate you choose.
  • No rounding is applied in the calculation.
  • It doesn't handle uneven amounts, payments that grow, or net present value (an investment's worth after its upfront cost).
  • Taxes and inflation aren't handled separately. For an answer in today's buying power, use a real rate, meaning one with inflation already taken out.
  • Discount rates can only be zero or positive in this calculator.

Frequently asked questions

How do I choose a discount rate?

Use the return you could reasonably earn on an investment with similar risk. You could also use what it costs you to borrow, or a rate set by whoever asked for the calculation. The higher the rate, the less a future amount is worth today.

What is the difference between an ordinary annuity and an annuity due?

An ordinary annuity pays at the end of each period, like most loan payments. An annuity due pays at the start, like rent. Each payment arrives a period sooner, so an annuity due has a higher present value.

Is present value the same as net present value?

No. Present value discounts future money back to today. Net present value then subtracts what you pay up front. That tells you whether an investment adds value at the rate you require.

Why does compounding frequency change the result?

When the rate is applied more often, money grows faster. So you need less money today to reach the same future amount. At 5% over 10 years, $10,000 is worth about $6,139.13 with yearly compounding. With monthly compounding, it's worth about $6,071.61.

How this calculator is checked

Method: Standard time-value-of-money formulas: PV = FV/(1 + i)^N and the present value of an ordinary annuity and annuity due. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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