Present Value Calculator
A Brief Introduction to Present Value and the PV of an Amount Calculator
The Accurate Present Value Calculator answers the question, "What is today's value of an amount due at some date in the future, assuming "X" rate of return?"
- You select any start and end date.
- Accurate for legal settlements.
Would you prefer to receive $10,000 today, or would you prefer to wait one year to receive $10,000?
This is not a trick question. For illustration, most people would prefer to receive $10,000 today instead of waiting one year.
But what if you were offered $9,000 today or $10,000 in one year? How would you determine which choice is better?
That is the purpose of a present value (PV) calculator—it calculates today’s value of a future amount. You can then use that information to decide whether to accept (or offer) the amount today, or wait and accept (or offer) the future amount.
How does the calculator determine the present value (PV)?
The key to understanding the PV calculation is that there is no single “correct” present value. There is only an “accurate” present value based on the assumptions used.
What does that mean?
Read more below…
The Calculator-Calculate Present Value of an Amount
Information
PV and Discount Rate
The present value, also called the present discounted value, uses an input known as the “discount rate.” The discount rate is expressed as a percentage, and it is used to calculate the PV. Although the calculation is exact—even a difference of one day changes the result—the discount rate itself is a subjective number.
Why is that the case?
It depends on understanding the discount rate. You should select a discount rate equal to what you expect to earn if you invested the money. How you invest the money is your choice. For example, you might choose 10-year U.S. Treasury securities, which currently earn about 2.5% per year. Or you might invest in real estate and assume a rate of return greater than 10%.
In any case, the rate of return you expect to earn on your investments is the value you should use as the discount rate.
If you would like to test the PV result for accuracy, you can use this future value calculator. Enter the calculated present value, the discount rate as the annual interest rate, and set the other options to match the settings you used in this calculator. The calculated future value will equal the future value you entered here.
The FV result confirms the accuracy of the present value calculation. This confirmation should give you confidence that if you accept a present value settlement, you will achieve the expected future value result at your assumed rate of return.
Calculator’s Features
Suitable for Legal Work
This calculator allows the user to enter a PV date (Today’s Date) and an FV date. A change of even one day will change the result.
There is no need to describe the result as an “estimate,” as some websites do. This calculator is precise and suitable for use in arranging a legal settlement imposed by a court, or for any other business or investment purpose.
If you are calculating the PV for a contract that will be settled in the future (not today), you should enter as the PV date the date on which the agreement closes.
In addition to being highly accurate, the calculator also supports 13 compounding frequencies. If your discount rate assumes a particular compounding frequency, select from the list below the one that matches.
- Compounded Continuously
- Daily
- Weekly
- Biweekly
- Twice Monthly
- Every 4 Weeks
- Monthly
- Bimonthly
- Quarterly
- Every 4 Months
- Semiannually
- Annually
- Exact/Simple
Questions? Comments? How can I make this calculator (and page) more useful?
Please leave your remarks below.
Present Value Equation
- What is present value (PV)?
- Present value is the current worth of a future amount of money given a specified discount rate. For example, rather than wait five years for $1,000, you might accept $621 today. In that case, $621 is the present value of $1,000 receivable in five years.
Fig. 2 – Step-by-step solution of the Present Value equation.
Variables: C = 1,000; i = 10%; n = 5.
Variable Definitions
- C
- Future value to be discounted.
- n
- Number of compounding periods between the current date and the date when the sum is worth C.
- i
- Interest rate for one compounding period.
- PV
- Present value.
Calculation Steps
- Substitute the given inputs into the present value formula (see Fig. 1): PV = C ÷ (1 + i)n with C = 1,000; i = 10%; n = 5.
- Evaluate the base numerically and update the denominator: 1 + i = 1 + 0.10 = 1.10, so the denominator is (1.10)5.
- Compute the accumulation factor: (1.10)5 ≈ 1.61051…
- Divide the cash flow by the factor: 1,000 ÷ 1.61051… ≈ 620.921323…
- Round the result to two decimal places for currency reporting: PV ≈ $620.92.
Step-by-step Solution – Fig. 2
- PV = 1,000 ÷ (1 + 0.10)5
- ≈ 1,000 ÷ (1.10)5
- ≈ 1,000 ÷ 1.61051…
- ≈ 620.921323…
- ≈ 620.92
Final Answer
The final answer (PV) is approximately 620.92.
If you assume your discount rate compounds monthly, then you need to adjust the above calculation:
- PV = 1,000 ÷ (1 + (0.10 ÷ 12))(5 × 12)
- The new result is approximately: 607.79
Validate the calculator. Five years, annually compounded interest.
| Future Value (FV): | $1,000.00 |
|---|---|
| Days (–9,999 < # < 47,482): | <calculated> |
| Today’s Date: | |
| Future Value Date (year < 2100): | |
| Annual Discount Rate: | 10.0% |
| Compounding Frequency: | Annually |
| Days in Year: | 365 |
| Present Value (PV): | 620.92 |
Notes:
- This example uses the same calculation shown in Fig. 2.
- You can either enter two dates exactly five years apart (the calculator will determine the number of days), or—
- Enter a specific number of days, and the end date will be calculated.
- The “Days in Year” setting has no effect in this example, because the period spans exactly five years with no additional days.
- With annual compounding, you will get the same result for a two-year period whether or not one of the years includes a leap year. (The extra leap day has no impact on the calculation.)
Present Value Calculator Help
Present value is the opposite of future value (FV). For example, if you have $1,000 today, then one year from today it will be worth $1,000 plus the return on investment. That is the future value.
If you are scheduled to receive $10,000 one year from today, what is its value today, assuming a 5.5% annual discount rate? The “annual discount rate” is the rate of return that you expect to earn on your investments. This is a subjective number. There is no single “correct” answer, but you should use a realistic number based on your own investment history. The discount rate will vary from one individual to another.
Enter 10000 as the future value (do not type the currency symbol or commas). Set the start date and end date to one year apart, and set the discount rate to 5.5%. Assume monthly compounding and a 365-day year.
The PV is 9,466.04. You could accept 9,466.04 today instead of 10,000 in one year. The two amounts are financially equivalent.
Date Math: If you change either date, the number of days between the two dates will be calculated. If you enter a positive number of days, the future value date will be updated. If you enter a negative number of days, the present value date will be updated.
Mr. B. says:
A firm is evaluating two machines. The first costs $250,000.00 and will require annual maintenance of $30,000.00 per year for ten years. At the end of ten years, the salvage will be $75,000.00. The second machine costs $400,000.00, and will require maintenance of $2225,000.00 at the end of the fifth year. The salvage after 10 years will be $175,000.00. Which machine should the firm select if interest is 8.5% compounded annually?
For machine one, I got a NPV of -$413,669.04 and -$472,235.27 for machine two. That means none of the machines should be chosen.
Am I on the right track?
Karl says:
First, you mention NPV, and your comment appears on the present value calculator page. The two are not the same. (The site does have an NPV calculator as well.)
That aside though, I think you are missing a critical item – how much cash flow will the machine (help) create? In other words, if the machines create widgets and one machine can create enough widgets to produce $400,000 a year in sales and the other creates enough widgets to produce $350,000 a year in sales, then that cash flow needs to be considered.
On the other hand, if they are just going to sit there, then the return is negative, and the firm would be better off not buying either one. 🙂
Mr. B. says:
The second machine costs $225,000.00 not what I put originally. The only inflows for the two machines are from their salvage.
Karl says:
These machines are not used in the manufacturing process?
I’m not sure what your question is exactly.
Mr. B. says:
The terms of a lease agreement are $250 down and a monthly payment of $100 for 12 months, with an option to purchase for $300 at the end of the lease.
To find the present value for this situation, do you add or subtract the down payment?
Karl says:
The down payment is like any other payment.
You posted your question on the present value of a single amount calculator. Since you are asking about a series of payments, this would not be the appropriate calculator for the problem.
Since the amounts vary, you should use this calculator for pv of an irregular series.
If you try it, scroll down the page and see tutorial #20 about PV calculations.
Roger Sanders says:
I like your calculator. I’m trying to create something similar in vba but I can’t figure out how to calculate irregular periods. Such as, 35 days with monthly discounting or 370 days with annual discounting. Any help is appreciated.
Karl says:
Thank you.
I’m able to answer two categories of questions on this site. What calculator should I use? Or, how do I use a calculator?
I work fulltime (not on this site) and to answer questions about the equations get into the weeds too much. It would take away from development time.
I can say, however, that the feature you are asking about takes hundreds of lines of code, depending on how you need/want to implement it.
Charlotte says:
Hello,
Thank you very much for these great tools!
I wonder if anyone can provide some guidance on how to calculate the amortized cost at the beginning and end of each year, of a bond with a face value of 10,000; n=3 years; annual interest rate is 4% while market interest rate is 3%.
Karl says:
Hi, at this time, I don’t have a calculator on this site that directly does bond amortization calculations. I am working on a bond calculator, though I hadn’t thought of having amortized cost calculation as one of its features, but perhaps I’ll add it. (It won’t happen overnight though :-()
Charlotte says:
Thank you for your response, will check again at a future time!
Genghiz Erden says:
We have a rental agreement of $5400/month, still remaining 53 months.
Tenant wants to cancel the contract, and make one lump sum payment, how can we calculate the present value?
Karl says:
The calculator, as you discovered if for calculating the PV of a single future amount due.
Please use this PV of an Annuity (series) of cash flows calculator.
Paul says:
Using the annual rate of BANK interest on a monthly return since 1993 what is the present worth of $60,000?
Karl says:
I think you want to use the future value calculator which is here, and if you want to add to the starting amount, use the future value of an annuity calculator which is here.
Heizen says:
Which of the following would you select assuming 5% annual interest rate?
a)Receive SR 3000 now.
b)Receive SR 4000 five years from now.
c)Receive SR 5000 ten years from now.
Karl says:
It would be wrong for me to offer advice on this site. Mostly because I do not know your personal situation. Perhaps the 3 scenarios have different risks, for example.
I can help you to use the tools and interpret the results. Generally speaking, one would want to take the offer that has the highest present value.
David says:
Hi. If I’m trying to find the value of my defined benefit pension plan in order to settle on an amount to give to the ex, I would need the PV I guess but to find it I need the future value. How do I get the future value?
Thanks for your guidance.
Karl says:
You don’t need to know the future value. For what you want, you need to use a different calculator. Use this present value of an annuity calculator. An "annuity" is simply a series of payments – in your case the defined benefit. Once you check it out, if you have any questions, just ask.
David says:
Karl, thanks for your help. With assistance from the retirement system office, and their “factor” table that correlates to earliest age of retirement, I was able to get the same number using your calculator as the one listed as “value” on my statement.
Given that Im not yet eligible for retirement, I guess the unknowns are what QDRO calc method and any other variables might be used to determine the actual amount to be divided up?
How does the actual current value play a part in this?
Thanks again,
David
David says:
Sorry to bother you, I think I answered my own question: If one isn’t yet eligible for retirement, then there are no future streams of income. The “value”, or “cash flows total”, is just a figure based on the assumption that the status quo plays out until retirement. Therefore, the statement account balance is really the only number that could or should be used to base the division of pension upon.
Thanks again- I’ve learned a lot lately on the present value of future money if you will studying and using your calculators.
Best regards,
David
Karl says:
You’re right, it’s all how you want to think about it, and what assumptions you want to make. When you were asking about PV of a defined retirement plan, I was thinking that the defined benefit was say $2,200 a month starting in 10 years. Then if you wanted to assume a life expectancy of another 30 years, the calculator would calculate the PV of such a scenario. But to eliminate risk, if the plan will tell you today’s cash value, that’s the number to go with, I would say if the asset is to be divided today.
Please remember though, I do not give financial advice on this site. I will tell folks what calculator to use, and how to use a calculator. That’s really the limit of my support.
David says:
if i have a disability insurance policy that will pay out from 9/1/2019 – 9/1/2047 for 28 years and want to know the present day value of the policy to accept a lump sum payments, how much is it currently worth and can I take into account that I am already owed from 9/1/2019 to today?
Karl says:
First, since you are owed a series of payments, you’ll want to use this present value of an annuity calculator. (Annuity simply means a series of payments, paid over time, which fits your case.)
1. You’ll want to do the present value from today for the remaining payments due to you.
To answer your second question, about being owed since 9/2019, the answer is yes.
2. For that, you should use the future value of an annuity calculator. Calculate the future value for the only the back payments you are owed up until today.
To get the lump sum due to you, add #1 and #2 together.
Let me know if you have any questions.