# Present Value of an Annuity Calculator

"Present value of an annuity" is finance jargon meaning **present value with a cash flow**. The cash flow may be an investment, payment or savings cash flow, or it may be an income cash flow.

The present value (PV) is what the cash flow is worth today. Thus this present value of an annuity calculator calculates today's value of a future cash flow. **The annuity may be either an ordinary annuity or an annuity due (see below).**

The PV will always be less than the future value, that is, the sum of the cash flows (except in the rare case when interest rates are negative).

Why?

Because there must be compensation made to the party who has to wait for the money. Think of it in reverse. Would you rather have $100 today, or $100 one year from now?

Of course, you would rather have $100 today since there is risk in not receiving the money if you wait, and further, if you receive the payment today, you can invest it today and earn a return on the capital.

The present value of an annuity calculation considers these things and discounts the cash flow. More below

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## What is present value used for?

At a high level, there are two scenarios when you may want to know the present value of a cash-flow.

- when someone or some entity owes you money
- when you want to make an investment

Perhaps you have won a court settlement payable as an annuity, or maybe you've been lucky enough to win a state lottery, and you want to receive the proceeds at once. How much should you expect?

Use this PV of an annuity calculator to tell you. Since an annuity is a regular, periodic cash-flow, and because this calculator allows you to set a specific first cash-flow date, it is capable of calculating the present value for any cash flow. The calculator is also particularly suitable for calculating the PV of a legal settlement, such as one involving alimony.

For the same reasons, this calculator can be used to calculate the PV of an investment cash-flow. Perhaps you want to invest in a mortgage? You'll need to calculate the PV of the said mortgage before you can make an offer or know if the offering price allows you to meet your investment objective.

## What is the correct discount rate?

A discount rate is a personal number. That is, there is no absolute right or wrong value one can use.

When determining the discount rate, you could use several approaches. If you invest in the stock market, and for you, you earn on average 8% per year, you can use 8% for the discount rate to compare the present value with the return you earn from the market.

If you want to compare PV to something safer, you might use the US Treasury ten-year rate, which currently is at about 2.5%.

### Example

Additionally, **buyers and sellers are very likely to use different discount rates**. For example, a commercial building's owner is selling the property, and a tenant has ten years remaining on the lease. What is the value of the contract to the prospective buyer?

The buyer may feel that mutual funds and the lease have similar risks (mutual funds loss of value and the lessee not paying). In that case, the buyer can use their average mutual fund return rate, say 7%, to calculate the PV of the lease. After all, why would they pay more to purchase the contract if they can earn 7% in mutual funds? The buyer will always want to use the highest discount rate they can justify because the higher the discount rate, the lower the PV – or the lower the cost of the asset. In other words, **for the buyer, using a higher discount rate is the more conservative approach**.

On the other hand, the seller may feel the tenants are reliable, and the cash flow is safe. They'll ask themselves why take a risk and put the money into the market where there is the risk of losing principal? In that case, the seller might want to park the money in a 2% CD, so they'll use 2% as their discount rate. Lower rates result in a higher PV. Thus, **for the seller, the lower rate is more conservative**. They'll need to be paid a higher price so they can put the proceeds from the sale in a lower yielding CD to reduce the investment risk.

With this example, it looks as if no deal would ever get done. The buyer will want to pay to little, and the seller will want to receive too much.

However, all deals depend on each participant's perspective. Perhaps the seller thinks that they have an opportunity to reinvest the money and earn not 2% but instead 20%. In that case, the seller might be willing to sell the lease at a 10% or 12% discount to have the funds available to take advantage of the more profitable opportunity.

See how what discount rate to use is a matter of personal choice and perspective?

## PV Calculator for Either Ordinary Annuity or Annuity Due

You may have heard of the terms "ordinary annuity" or "annuity due". This calculator will calculate the present value for either type of annuity.

First, what's the difference between an ordinary annuity and an annuity due? These two terms are a bit of financial jargon for an easy to understand financial concept.

**An ordinary annuity will have its first cash flow scheduled for a future date**. Textbooks frequently explain this concept by saying the cash flow gets paid at the end of the period.

**An annuity due will have its first cash flow scheduled on the as-of-date**, that is, the date for which the present value is calculated. Textbooks explain this concept by stating the cash flow gets paid at the beginning of the period.

The present value formula needs to be slightly modified depending on the annuity type.

Since this calculator prompts the user for the present value date (today's date) and the first cash flow date, it will work equally as well for either annuity type. **If you set the dates to the same day, then the calculator will use the annuity due formula; otherwise, it will use the ordinary annuity formula.**

Note, if you are calculating the present value for a deal that closes in the future, then you should set today's date to the day the contract is scheduled to close.

## Present Value of an Annuity Help

An "annuity" is a fixed sum of money paid someone each period, typically for the rest of their life. More loosely, it means any regular cash flow stream which may or may not have an explicit declared term. If an annuity is scheduled for 10 annual payments of $10,000 each, the sum of the payments is $100,000. However, if instead of being paid in 10 annual installments you wanted to receive a single sum, you would not receive $100,000. Why? Because if you receive a single sum today, there is no future risk of not receiving the amount due. Therefore, you would take less today to eliminate the risk of not collecting all payments.

If you are scheduled to receive a series of regular fixed payments of $2,500 for 20 years, what is today's cash value, 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 $2,500 in the "Cash Flow Amount" field (never type the currency symbol or commas). The cash flow frequency will be monthly. Enter 240 for the "Number of Cash Flows" (240 months is 20 years). Assume monthly compounding. Since the first payment isn't due until a month from now, set the "First Cash Flow Date" to one month from "Today's Date".

The PV is $363,431.62. Thus, you could accept $363,431.62 today in lieu of receiving $2,500 a month for twenty years. For you, the two are equal.

A note or two about "Compounding Frequency". The "Exact/Simple" option is actually exact day simple interest. When you make this selection, the calculator uses no compounding and the exact number of days between cash flow dates are used. The "Daily" option uses the exact number of days between dates, but daily compounding is assumed. If you are considering receiving a single amount in lieu of a cash flow stream, the "Exact/Simple" compounding option is the most conservative setting. That is, it will result in the highest present value calculation.

The prior version of this calculator provided you with an option to set the "Cash Flow Timing". Since you can enter "Today's Date" and the "First Cash Flow Date" this option is no longer necessary because the calculator will calculate the exact dates the cash flow is due.

One additional point about "Today's Date". This input does not have to be set to the current date. The date you use is the date you want to know the present value. If you were closing on a deal to buy a mortgage and the deal is expected to close in a week, then you would want to use the date of the closing for "Today's Date" so you'll know the present value on the closing date.

## John Luckart says:

Gentlemen:

I am thinking of buying a fixed indexed annuity. The premium is $1,000,000. I am 55 and under the contact I will receive $95,000.00 per year for life starting on 8-1-2026. I am trying to figure out the present value of the payments. An interest rate has never been provided to me. I tried to get the PV but was unable to do so. Any assistance you could provide would be greatly appreciated.

## John Luckart says:

Adding to the above my life expectancy at 65 would be 17.66 yrs

## Karl says:

By the way, if you are not happy with the compromise between 17 years and 18 years 🙂 you can use this time value of money calculator. It gives you finer control over the dates than this calculator. Scroll down the page and see tutorial nos. 20 & 22:

Present Value Calculation

How to discount a simple or complex cash flow to find its PV

Calculate Rate of Return (ROR) on Annuity

How to set up an annualized ROR calculation

## Karl says:

Thanks for using these calculators. There are 2 ways you can approach your analysis. The seller is stating that the annuity has a PV of 1,000,000 (the premium). If you want to see what the rate of return is on the premium, use the Internal Rate of Return Calculator. Enter the premium as the initial investment amount and the future payments in the years expected. The calculated IRR is the annualized rate of return you are earning on the premium.

The second way to approach this problem is to calculate the PV using the discount rate you want to earn. You can use this calculator for that. Enter today’s date and the date you expect to receive the first income (payment). I gather that will be about 10 years between the two dates. You can expect to receive 17 or 18 payments. Enter the rate you want. If the PV is more than $1,000,000, then you are earning less than the rate you want to earn.

Let me know if other questions come up. I would be interested to know how you make out with this.

## Sameera Irosh Perera says:

presen value =10000

monthly payment 172

number of payment 300

i want to know how monthly interest rate is calculated of this annuity

## Karl says:

If you want to calculate the interest rate, I would use this time value of money calculator. Scroll down that page and read this tutorial:

22. Calculate Rate of Return (ROR) on Annuity

How to set up an annualized ROR calculation

## Doug johnson says:

I calculated a present value of about $801,000. Using the following assumptions: discount rate 4.5%, life expectancy age 85 (240 monthly payments).

## Doug johnson says:

The imputed interest rate for a $1,000,000 over is about 3.3% assuming a mortality of 85 years.

## jerry says:

please be careful, before entering into this contract. I do not believe you will receive $95000 per year for life starting at age 65. the assumption that this indexed deferred annuity will grow substantially for this to happen is an assumption and not a guarantee. it sounds too good to be true. do not make a move without an independent, non-bias expert on these type of investments.

## russell says:

well your guess is as good as anyone else. take a guess and see the result.then change the interest rate and see the second result

## Lisa says:

Just wanted to say thanks. I use this almost every single day. It seems to do a fairly good job of estimating the present value of future pension payments.

## Brian says:

I am currently drawing a military pension and a second pension from service at the United Nations. Along with my social security and my wife’s social security it is a comfortable amount each month. How can I determine what amount of money I would need to have in an interest-generating investment to give me the pensions I am receiving right now? Is there a simple calculator somewhere on-line that would answer that question?

## Karl says:

You can use the Savings Withdrawal Calculator.

Like many calculators on this site, this calculator will solve for several unknowns. For your case, you’ll want to solve for “Savings on Hand (PV)” by entering a zero and then enter the “Regular Withdrawal Amount” to equal the monthly income (or whatever frequency you want).

## JeanAnn says:

When I select print it truncates the year on today’s date and the first cash flow date. How can I fix this?

## Karl says:

Oh my. That’s pretty bad. Sorry I missed it (there was a change to the calendar last weekend). I’ll have to fix it.

As a very temporary work around, you can select everything with your mouse and copy / paste to a word processor or notepad. You’ll have to also adjust the formatting, but you’ll get all the values.

## Karl says:

JeanAnn, the printing is fixed. If you try it again, and it does not work, you may have to do a hard refresh by press Ctrl-5 (on Windows, not sure about Mac) to make sure your browser has picked up the latest changes. If that still does not work, please let me know what browser you are using.

## JeanAnn says:

Thanks for your help! Prints fine now.

## Karl says:

NP. Good to know. Thanks for letting me know.

## Joseph Meszaros says:

Hi, I currently am receiving a pension of 77328 per year and would like to know how to value for a net worth calculation. I started receiving in 1/2014. I am currently 68 years old and know that there is a difference in using life expectancy and mortality tables. I just can not wrap my brain around this endeavor. Can you help?

## Karl says:

I’ll try. The "Regular Cash Flow Amount" is the 77,328 and you would set the cash flow frequency to annual. For "Number of Cash Flows" you can enter the difference between your life expectancy and your current age. That will give you, I feel, a reasonable present value of your pension.

Is that what you want to know?

## michael says:

Hi Karl,

I am being offered a lump sum payment of $148,000 now vs. receiving a guaranteed $1,486/month beginning in 11.5 years. I am trying to understand how the "discount rate" in your calculator functions vs an assumed rate of return I would need as a hurdle rate.

There is also the major question of final number of payments realized (longevity) which is an unknown.

Great tools! Thank you!

## Karl says:

Hi Michael,

First, the annual discount rate is your assumed rate of return.

I would think of the problem this way:

Longevity is certainly an unknown, but you have to make some assumption to do the calculation. Let’s assume the monthly cash flow will continue for 25 years. $1,486/month x 12 months x 25 years equals $445,800.

The question then becomes is $148,000 received today worth more or less than $445,800 which you won’t start to get for another 11.5 years and even then it will take 25 years to collect the full amount.

That’s exactly the question a

present valuecalculator is meant to answer, and because this calculator lets the user set the dates, this calculator will handle this scenario.I’ll fudge a little because I want to do everything in my head, but here’s how to set it up.

Here are the results I get:

Since the present value of the cash flow is less than the up-front amount of $148,000, it is probably best to take the up-front amount i.e. $148,000. This is particularly true when you consider that at PV calculation does not consider risk. There is some risk that the payor will not be able to pay the $1,486 each month over the entire term

Of course, your numbers (and conclusion) can vary.

Thank you for a very nice, real-life example!

## viko says:

hi. i can receive an amount of 850000$, or a monthly pension of 4000$.

i think that i can invest the money and receive 4.5% per year without taking a big risk. asuming a life period of 25 years, what is better for me?

## Karl says:

First, I would like to say that in general, I don’t give advice or make financial recommendations. I will discuss what calculator to use, and how to use them. I take this approach because everyone’s situation is different, and in your case, there may be other things such as taxes to consider.

On a present value basis, however, the $850,000 upfront is worth more than the $4,000 a month cash flow for 25 years.

Here is how I set up the present value calculation of the pension:

## viko says:

tank you, it was helpfull. i understand that tax issues are not considered in this calculation. another issue, as i understand, is the risk involved if the institution behind the pension will not survive and also that if i will not survive, my family may not receive the pension after me. is there any way to consider these 2 risks in the calculation some how to give it some risk evaluation?

again – thank you!

## Karl says:

You’re welcome Viko.

You’ve identified the two issues I was thinking about. As to taxes, if you want to see what their impact will be on the cash flow, you can use this investment calculator. Set the cash flow type to

."income"I can’t help you with evaluating the entity that is responsible for the pension. I think the best thing for that is to look at their credit rating or the rating on any bonds they may have issued.

## Russell Walker says:

I have studied engineering economics for over 50 years. You not making any recommendations regarding investment type and taxes is just smart. No one really can predict the future.

It’s not just ironic that I as an engineer have no pension except social security. Its the government types who never produced any wealth in their lives that have big pensions, unknown in private industry and they are receiving wealth for just playing politics and kissing ass all of their lives.

## NSmith says:

Hi Karl,

Any chance the three annuity calculators you have created will eventually make it to WP widget form? I have a blog dedicated to annuities and these are absolutely terrific. I would love to feature them alongside your retirement calculators. Thanks!

## Karl says:

The lack of a withdrawal/annuity plugin is certainly a gap in what I offer, and I do hope to rectify it. However, my list of "TODO’s" for this site is pretty long. I’m fairly certain there will be no new plugins in 2018.

I am interested in seeing your blog. Feel free to post a link to it here and you can even give yourself a plug if you wish!

## sunny says:

Mohsin had a note for Rs. 15000 with an interest rate of 6%. The note was dated January 12, 1983 and

the maturity date was 90 days after date. On January 27, 1983

he took the note to his bank which discounted it at a discount rate of 7%. How much did he receive?

## Karl says:

I don’t answer homework questions. 🙂

However, I will tell you what calculators you need to use. Use this Interest Calculator to calculate the 90 days of interest. And then use the Present Value Calculator to discount the amount by 7%.

## Charles says:

How do I calculate the present (today’s) Fair Market Value of a Single Premium Immediate Annuity?

It seems I would need to enter my single premium somewhere into the equation & the interest rate. Then deduct the amount & number of payments already made to me.

So far I cannot find any calculator that does that.

Any suggestions would be greatly appreciated.

Thank you.

## Karl says:

Charles, I’m not sure I understand all the details, particularly around the cash flow timing. Correct me where I’m wrong. If you want to answer the question, "Am I paying too much for an annuity?", then this is how I would do it. The below example says, the income is $2,000, starting today and I want to assume it will last for 10 years (120 months) and that I can earn 4.5% on my investments.

with those assumptions, we can see that the FMV or PV is $193 thousand.

If the single premium for this annuity is less than this, then the seller is giving the buyer a higher rate of return than the assumed 4.5%. And of course, if the premium is less, then the annuity isn’t earning 4.5% for the buyer. So, no, you would not enter the single premium into the calculation.

Does this help? If not, please ask. (If you want to calculate the rate of return on the annuity then you would use this internal rate of return calculator and it does require that you enter the initial premium.

## Charles says:

I have a Single Premium Immediate Annuity. Every January I get a letter stating the Fair Market Value of the Annuity from the past December. IOW in Jan 2017 I got notified of the FMV based on Dec. 31 2016.

What I’ve previously done in Jan is to call the insurance company to get the future FMV at the end of the current year. IOW in Jan 2017 I called to get the FMV based on Dec 31, 2017. Then I entered this into a spreadsheet. When I eventually received the official letter for the year end FMV it always matched, within a penny, the verbal quote I previously received. I’ve asked for the formula/equation but they won’t give it to me. It did take some time to get the FMV when I called because they said it had to be calculated for every month, not just for year end.

Years ago I tried 1 or 2 online calculators but they never matched the insurance company figures. Over the years it’s become more difficult to get through to someone at the insurance company who can provide this information. Therefore I’m trying again to find an online calculator.

I have a 20 guaranteed annuity & keep track of the FMV because if I die before the 20 years is up then someone will inherit the remaining balance. Even though I don’t have access to the FMV someone else may. Currently the FMV is over $100,000 therefore I like to keep track of it. I just need to know how the ins. co. calculates it.

## Karl says:

These details help. While my first answer to you provided an illustration that answered a different question that what you wanted to answer, I think the calculation is basically the same. That is, the FMV is the PV of the future cash flows.

You now want to know the FMV/PV of the annuity as of Dec. 31, 2018. In that case, set "Today’s Date" to Dec. 31, 2018 and set the "First Cash Flow Date" to the date of the first annuity payment due to you after 12/31/2018. For the "Number of Cash Flows" you’ll enter the number of cash flows remaining or due to you as of Dec. 31, 2018.

The "Annual Discount Rate" in essence, is the rate of return? Does the annuity contract stipulate a minimum annual rate of return that they guarantee? Or is it tied to a particular interest rate such as the prime rate or LIBOR? This I can’t answer, of course. But I’ve very confident unless there is something else that I don’t understand, once you know what rate to use, you’ll be able to calculate the FMV using this method.

(What’s been paid out in the past, or what you paid as the single premium, in my mind, is not relevant to the FMV calculation. The reason is, we want to know what the FMV is of what is owed to you in the future as of Dec. 31, 2018.)

## Karl says:

One more thing. You can easily confirm if what I am saying is correct. Follow the method that I outlined, do the calculation as of Dec. 31, 2017. Does the result match the letter that you received this year?

If it does, then you’re in great shape! If not, and if you want to provide the exact details, I’ll take a look again.

## Charles says:

Thank you – it works!

To confirm things I used Dec. 31, 2017 for today’s date, Jan 15, 2018 as the first annuity payment date, and 136 for “Number of Cash Flows” remaining. The contract states the Initial Interest Rate is 5.62% which is what I used & presumed it was compounded monthly. The calculation was hundreds of dollars too low.

The body of the contract mentions “…annual compound interest at the Commutation Rate of 5.62%.” So I changed the compounding frequency to Annually & the numbers fell into place.

For Dec. 31, 2017 the calculated value was $113,463.72 vs. the letter for $113,470.70. I checked several other years & got similar results.

Maybe the slight difference is due to some rounding off with the insurance company or the calculator. I have no idea but the figures are so close that it’s not an issue.

It used to be somewhat easy to get the FMV from the insurance company. But last year it was really a problem after being told they re-organized some depts. Your help & calculator will save me lots of time & grief.

Thank you again for all your help.

## Karl says:

Good to hear the calculator worked out and thanks for letting me know.

I think you are right about the relatively small difference being due to rounding. There are two possibilities. The contract may round the rate for presentation purposes (not so likely, I guess). That is, their computers may actually be using 3 or 4 digits of precision.

The more likely cause is the way it is calculated. The software can be programmed to round the return after each cash flow and post the result, or it can use an equation that doesn’t round until the final value is known.

And as I think about it, there may be one more cause for the difference, and I bet this is it. When entering dates for the calculators on this site the time is always assumed to be 12:00am or midnight. My guess is, the balance you are given is the end-of-day balance as of Dec. 31. If that is the case, you should use Jan. 1, as the "Today’s Date." The reason, of course, is their end of day, i.e. 11:59:59 is closer to Jan 1, 12:00:00am than it is to Dec. 31, 12:00:00am. If my guess is right, my initial suggestion is including one extra day.

If you care to test that, I would certainly be interested in the result.

## Charles says:

I used Jan. 1, as “Today’s Date “and kept Jan, 15 as “First Cash Flow Date”,

The new value was $113,481.16 compared to the official letter stating $113,470.70. Therefore it is $10.46 to high vs. the previous calculation of $113,463.72 which is $6.98 to low.

I compared previous insurance company statements to the calculator results while changing the dates. Changing either date forward or backward by 1 day typically changed the value $15-$20. Moving both of the dates in the same direction by 1 day does not change the value.

When I previously searched for calculators none of them seemed to do what I wanted because they did not have provisions to enter the single premium amount. Since you mentioned this wasn’t needed, I re-visited some of those calculators.

None used dates which made me wonder what they used. Some used number of years vs. “Number of Cash Flows” which makes it difficult or inaccurate to enter a partial year. And some used the monthly interest rate. I experimented with this one.

http://financeformulas.net/Present_Value_of_Annuity.html

I took exception with their method of computing monthly interest rate by simply dividing the annual rate by 12. I did try it (.468%) and got $112,428.18 which is quite a bit different compared to using your calculator as shown below. Therefore I’m presuming that dividing by 12 is not the proper method.

After some searching I found how to change my annual rate to .00456685972 monthly, which compounded does gives the 5.62%.

The above basic calculator only allows for 3 decimal place rate accuracy.

I used a .456% Rate & got $113,256.34.

Then tried a .457% Rate & got $113,187.00.

Changing that 3rd decimal place by just 1 unit changes the value by $69.

Using your calculator with 12/31/2017 for Today’s Date and 01/31/2018 for First Cash Flow Date comes up with $113,208.77 which is somewhere in the middle of the above two values.

I wondered why the other calculators (and the formula) did not use dates. I played with your calculator and it didn’t matter if both dates were beginning, middle or end of month, the FMV remained the same. But the date of the month had to be same. IOW Dec.1 and Jan.1, or Dec.15 and Jan.15.

To be continued –

## Charles says:

Part 2

I found this calculator which allowed an interest rate up to 5 decimal places.

https://www.investopedia.com/calculator/annuitypv.aspx

Using .45668% interest results in $113,209.18

Using .45669% interest results in $113,208.49

That’s only a $0.69 difference.

Your calculator using end on month dates comes up with $113,208.77 which again is somewhere in the middle.

Being curious I looked for a way to use more decimal places for higher accuracy which should match yours. Looking at several calculator examples the formula appears to be pretty simple, presuming you don’t need dates or need any rate conversion between months & years.

This formula I’ve seen several times, & goes with the calculator I used earlier.

http://financeformulas.net/Present_Value_of_Annuity.html

Initially I calculated my monthly interest rate to 8 decimal places & used that in the formula and got a value of $113,208.79003136.

Then I used my monthly interest rate to 12 decimal places & used it in the equation, rounding to 12 decimal places every step.

The value calculated was $113,208.769443898721.

Obviously your calculator is very accurate.

Having the adjustable dates helps in case “Today’s Date” and the “First Cash Flow Date” don’t match up as far as date of the month is concerned.

Again I thank you for your help, and I learned a few things along the way.

## Karl says:

That’s quite a study. Initially, you had said the first cash flow is Jan. 15th. I’m surprised that using Jan. 1 as "Today’s Date" and Jan 15 as "First Cash Flow" didn’t fix it. Perhaps different compounding and or different precision of the rate of return? Anyway, I guess you can be pretty confident that the insurance company’s calculated FMV is close enough. 🙂