# Present Value Calculator

Would you prefer receiving $10,000 today or wait a year to receive $10,000?

This is not a trick question, and hopefully, for at least the sake of illustration, you would rather receive $10,000 today rather than wait a year.

But what if, I offered you $9,000 today or $10,000 in a year. How do you know which opportunity you should pursue?

That's the point of a present value calculator - it will calculate today's value of a future amount that you can then use to decide whether to accept (or offer) the value as of today or to wait and accept (or offer) the future value amount.

How does the calculator calculate the present value (PV)?

The key to understanding the PV calculation is to realize that there is no "right" present value amount; there is only an "accurate" present value.

What?

More below

### Information

## PV and Discount Rate

The present value, also known as the present discounted value uses an input known as the "discount rate." We express the discount rate as a percentage, and it is used to calculate the PV. And while the calculation is exact (a change of one day changes the calculated result), the present value itself is a personal number.

Why is that?

It boils down to understanding the discount rate. You should select a discount rate equal to what you would expect to earn if you invested the money. How you invest the money is up to you. You might choose 10-year treasuries, currently earning about 2.5% a year or you might select real estate, and then you might assume a rate-of-return exceeding 10%.

In any event, the rate-of-return you earn on your investments is the value you should use for 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 how you set this calculator. The calculated future value will match the future value you entered here.

The FV result confirms the accuracy of the present value calculation, and it should, in turn, give you confidence that if you accept a present value settlement that you'll achieve the expected future value result at your assumed rate-of-return.

## Calculator's Features

As you can see, this calculator gives the user the ability to enter a PV date (Today's Date) and an FV date. Notice that a change by one day changes the result.

I don't need to use any weasel words like "estimate" like you might find some sites using. This calculator is perfectly suitable to use for arranging a legal settlement imposed by a court, or for any other business or investment need.

If you are calculating the PV for a contract that is settling later, (i.e. not "today") you should enter for the PV date, the date the agreement closes.

In addition to the calculator being very accurate, it also supports 13 compounding frequencies. If your discount rate assumes a particularly compounding frequency, then you'll want to pick from the below list the one that matches.

- Compounded Continuous
- Daily
- Weekly
- BiWeekly
- Twice Monthly
- Every 4 Weeks
- Monthly
- BiMonthly
- Quarterly
- Every 4 Months
- Semiannually
- Annually
- Exact/Simple

Questions? Comment? How can I make this calculator (and page) more useful?

Please leave your remarks below.

Present value is the opposite of future value (FV). Given $1,000 today, it will be worth $1,000 plus the return on investment a year from today. That's future value.

If you are schedule to receive $10,0000 a 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 receive on your investments. This is a personal number. There is no "right" answer, though you want to use a realistic number based on your investment history. The discount rate will vary from individual to individual.

Enter $10,000 as the future value (never type the currency symbol or commas), set the start date and end date for one year's duration 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 in lieu of $10,000 in a year. The two amounts are equal.

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.