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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.

28 thoughts on “present-value-of-an-annuity-calculator

  1. 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.

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

      • 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

    • 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.

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

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

    • 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.

    • 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

  2. 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.

  3. 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?

    • 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).

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

    • 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.

    • 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.

  5. 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?

    • 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?

  6. 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!

    • 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 value calculator 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.

      Regular Cash Flow Amount?: $1,486.00
      Number of Cash Flows? (#): 300 (25 years)
      Annual Discount Rate?: 5.5000% (pick what you want)
      Today’s Date?: 10/20/2017
      First Cash Flow Date?: 10/20/2027 (10 years, not 11.5)

      Here are the results I get:

      Present Value: $140,429.48
      Cash Flows Total: $445,800.00
      Last Cash Flow Date: 09/20/2052

      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!

  7. 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?

    • 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:

      Regular Cash Flow Amount?: $4,000.00
      Number of Cash Flows? (#): 300
      Annual Discount Rate?: 4.5000%
      Today’s Date?: 12/08/2017
      First Cash Flow Date?: 12/08/2017
      Cash Flow Frequency?: Monthly
      Compounding Frequency?: Monthly
      Present Value: $722,339.94
      Cash Flows Total: $1,200,000.00
      Last Cash Flow Date: 11/08/2042

      • 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!

        • 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.

  8. 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.

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