Present Value of an Annuity Calculator
A Brief Introduction to Present Value of an Annuity
The term “present value of an annuity” is financial terminology. It means present value with a cash flow. The cash flow may represent an investment, a payment, savings contributions, or income received.
Solve present value (PV) for any cash flow.
- Set dates for penny perfect-accuracy
- Supports either ordinary annuity or annuity due.
- Supports 12 cash flow frequencies
- Calculate PV for legal settlements
Calculates the current value of a future stream of payments or investments.
The present value (PV) is the value of the cash flow today. Therefore, this present value of an annuity calculator determines today’s value of a future series of cash flows. The annuity may be either an ordinary annuity (also called an annuity-immediate) or an annuity-due (see below).
The PV will always be less than the future value—that is, the total of all future cash flows—except in the unusual case when interest rates are negative.
Why is this the case?
Compensation must be provided to the party who has to wait to receive the money. Consider the reverse situation: would you prefer $100 today, or $100 one year from now?
You would prefer $100 today. If you had to wait one year, there is the risk of not receiving the money. In addition, receiving the payment today allows you to invest it immediately and earn a return on the capital.
The present value of an annuity calculation incorporates these considerations and discounts the future cash flows. This type of calculation is also sometimes called a discounted cash flow calculator. More below…
The Calculator-Calculate Present Value Calculator for Recurring Payments
Information
What Is Present Value Used For?
There are two common scenarios where you may want to determine the present value of a cash flow.
- When an individual or an organization owes you money
- When you are considering an investment
For example, you may win a court settlement payable as an annuity, or you may win a state lottery and prefer to receive the proceeds as a single payment. How much should you expect to receive?
You can use this PV of an annuity calculator to determine the answer. Because an annuity is a regular, periodic cash flow, and because this calculator allows you to set a specific first payment date, it can calculate the current value of any future stream of payments or investments. 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 also be used to calculate the PV of an investment cash flow. For example, if you want to invest in a mortgage, you need to calculate the PV of the mortgage before you can make an offer or determine whether the offering price meets your investment objective. Similarly, if you are considering purchasing an equity investment (such as common stock), you can use this calculator to estimate the present value of the projected future earnings.
What Is the Correct Discount Rate?
The discount rate is a subjective number. There is no universally correct value that everyone should use.
When selecting a discount rate, you can take several approaches. For example, if you typically invest in the stock market and your average annual return is 8%, you can use 8% as your discount rate to compare the present value with what you normally earn from the market.
If you want to compare PV to a safer benchmark, you might use the U.S. Treasury 10-year yield, which is currently about 4.4% (WSJ July 2025).
Example
Buyers and sellers are very likely to use different discount rates. Consider a commercial building whose owner is selling the property, while a tenant has ten years remaining on the lease. What is the value of the lease contract to a potential buyer?
The buyer may view mutual funds and the lease as having comparable risks (mutual funds may lose value, and the tenant may default). In that case, the buyer could use their average mutual fund return, for example 7%, as the discount rate to calculate the PV of the lease. From the buyer’s perspective, they should not pay more for the contract if they can instead earn 7% in mutual funds. A buyer will generally want to use the highest discount rate they can justify, because a higher discount rate produces a lower PV—and therefore a lower purchase price. In other words, for the buyer, a higher discount rate is the more conservative approach.
The seller, however, may believe that the tenants are reliable and that the cash flow is safe. They may ask: why take on market risk and risk losing principal? In that case, the seller might prefer to invest the proceeds in a 2% certificate of deposit (CD), and therefore use 2% as their discount rate. A lower discount rate produces a higher PV. Thus, for the seller, a lower discount rate is the more conservative approach. They will want to be paid a higher price so they can reinvest the proceeds in a low-risk CD while reducing investment risk.
At first glance, this difference might suggest that no deal could ever be made: the buyer wants to pay too little, while the seller wants to receive too much.
However, transactions depend on each participant’s perspective. For example, the seller might believe they can reinvest the proceeds and earn not 2% but 20%. In that case, the seller could be willing to sell the lease at a 10% or 12% discount rate to access the funds and take advantage of a more profitable opportunity.
This demonstrates that the choice of discount rate is always a matter of individual perspective and financial objectives.
PV Calculator for Either Ordinary Annuity or Annuity Due
You may have encountered the terms “ordinary annuity” (also called “annuity-immediate”) and “annuity-due.” This calculator can calculate the present value for either type of annuity.
What is the difference between an ordinary annuity and an annuity-due?
These terms may sound like financial jargon, but they describe a simple concept.
- An ordinary annuity
- schedules its first cash flow for a future date. Payments are typically made at the end of each period.
- An annuity-due
- schedules its first cash flow on the as-of date—that is, the date on which the present value is calculated. Payments are typically made at the beginning of each period.
The present value formula must be slightly adjusted depending on the annuity type.
Because this calculator prompts the user for both the present value date (today’s date) and the first cash flow date, it works equally well for either type of annuity. If you set the dates to the same day, the calculator applies the annuity-due formula; otherwise, it applies the ordinary annuity formula.
Note: If you are calculating the present value for a contract that will close in the future, you should set today’s date to the closing date of the agreement.
Present Value Equations
This section documents the formulas used by this calculator and provides the steps for solving them. Use the links below to scroll directly to the equation of interest.
Present Value of an Ordinary Annuity
Fig. 2 – Step-by-step solution of the PV of an Ordinary Annuity equation.
Variables: R = 7.5%; f = 12; n = 48; PMT = 525.00.
Variable Definitions
- R
- Nominal annual interest rate.
- i
- Periodic interest rate.
- f
- Compounding frequency: the number of compounding periods per year.
- n
- Total number of periods.
- PMT
- Periodic cash flow amount (equal payments each period).
- k
- The period number of the cash flow, starting with 1.
Calculation Steps Explained – Fig. 2
- How do you calculate the present value of an ordinary annuity?
The present value of an ordinary annuity is calculated using a standard formula that assumes payments occur at the end of each period. Here is the calculation using the example values:
- Determine the periodic rate by dividing the nominal annual rate by the number of compounding periods per year:
i = 0.075 ÷ 12 = 0.00625. - Substitute the known values into the ordinary annuity formula:
PV = 525 × [1 − (1 + 0.00625)−48] ÷ 0.00625. - Evaluate the base of the exponent:
1 + 0.00625 = 1.00625, then raise it to the power of −48. - Calculate the power term:
(1.00625)−48 ≈ 0.74151018. Then compute the numerator:1 − 0.74151018 ≈ 0.25848982. - Divide the numerator by the periodic rate:
0.25848982 ÷ 0.00625 ≈ 41.35837114. - Multiply by the periodic payment amount:
525 × 41.35837114 ≈ 21,713.14484636…. - Round the result to two decimal places for currency reporting: PV ≈ $21,713.14.
This result represents the present value of receiving 48 monthly payments of $525, beginning one month from now, at a 7.5% annual interest rate compounded monthly.
- Determine the periodic rate by dividing the nominal annual rate by the number of compounding periods per year:
Step-by-step Solution – Fig. 2
- i = 0.075 ÷ 12 = 0.00625
- PV = 525 × [1 − (1 + 0.00625)−48] ÷ 0.00625
- = 525 × [1 − (1.00625)−48] ÷ 0.00625
- ≈ 525 × [1 − 0.74151018] ÷ 0.00625
- ≈ 525 × 0.25848982 ÷ 0.00625
- ≈ 525 × 41.35837114
- ≈ 21,713.14
Final Answer
The final answer (PV) is approximately $21,713.14.
Validate the calculator. Ordinary annuity for four years with monthly cash flows.
| Regular cash flow amount: | $525.00 |
|---|---|
| Number of cash flows: | 48 |
| Annual discount rate: | 7.5% |
| Valuation date: | |
| First cash flow date: | |
| Cash flow frequency: | Monthly |
| Compounding frequency: | Monthly |
| Present Value (PV): | = $21,713.14 |
Notes:
- This example uses the same calculation shown in Fig. 2.
- Displayed values are shortened for clarity.For readability, decimal values shown in each step are shortened. However, all calculations use high-precision values. When verifying results or calculating independently, use at least 12 decimal places for the periodic rate, and maintain full calculator or software precision for intermediate steps to ensure accuracy. (Do not round any intermediate results.)
PV of an Annuity-Due Equation
Fig. 4 – Step-by-step solution of the PV of an Annuity-Due equation.
Variables: R = 7.5%; f = 12; n = 48; PMT = 525.00.
Variable Definitions
- R
- Nominal annual interest rate.
- i
- Periodic interest rate.
- f
- Compounding frequency: the number of compounding periods per year.
- n
- Total number of periods.
- PMT
- Periodic cash flow amount (equal payments each period).
- k
- The period number of the cash flow, starting with 1.
Calculation Steps Explained – Fig. 4
- How do you calculate the present value of an annuity-due?
The present value of an annuity-due is calculated by adjusting the ordinary annuity formula to account for payments made at the beginning of each period. Here is the calculation using the example values:
- Calculate the periodic interest rate by dividing the nominal annual rate by the compounding frequency:
i = 0.075 ÷ 12 = 0.00625. - Substitute the values into the annuity-due present value formula:
PV = 525 × [1 − (1 + 0.00625)−48] ÷ 0.00625 × (1 + 0.00625). - Evaluate the base of the exponent:
1 + 0.00625 = 1.00625, and raise it to the power of −48. - Calculate the power term:
(1.00625)−48 ≈ 0.74151018. Then subtract from 1:1 − 0.74151018 ≈ 0.25848982. - Divide by the periodic rate:
0.25848982 ÷ 0.00625 ≈ 41.35837114. This is the ordinary annuity factor. - Multiply by
1.00625to adjust for annuity-due timing:41.35837114 × 1.00625 ≈ 41.61686096. - Multiply the factor by the periodic payment to determine the present value:
525 × 41.61686096 ≈ 21,848.85200165…. - Round to two decimal places for currency reporting: PV ≈ $21,848.85.
This result represents the present value of receiving 48 monthly payments of $525, starting immediately, at a 7.5% annual interest rate compounded monthly.
- Calculate the periodic interest rate by dividing the nominal annual rate by the compounding frequency:
Step-by-step Solution – Fig. 4
- i = 0.075 ÷ 12 = 0.00625
- PV = 525 × [1 − (1 + 0.00625)−48] ÷ 0.00625 × (1 + 0.00625)
- = 525 × [1 − (1.00625)−48] ÷ 0.00625 × 1.00625
- ≈ 525 × [1 − 0.74151018] ÷ 0.00625 × 1.00625
- ≈ 525 × 0.25848982 ÷ 0.00625 × 1.00625
- ≈ 525 × 41.35837114 × 1.00625
- ≈ 525 × 41.61686096
- ≈ 21,848.85
Final Answer
The final answer (PV) is approximately $21,848.85.
Validate the calculator. Annuity-due for four years with monthly cash flows.
| Regular cash flow amount: | $525.00 |
|---|---|
| Number of cash flows: | 48 |
| Annual discount rate: | 7.5% |
| Valuation date: | |
| First cash flow date: | |
| Cash flow frequency: | Monthly |
| Compounding frequency: | Monthly |
| Present Value (PV): | = $21,848.85 |
Notes:
- This example uses the same calculation shown in Fig. 4.
- Displayed values are shortened for clarity.For readability, decimal values shown in each step are shortened. However, all calculations use high-precision values. When verifying results or calculating independently, use at least 12 decimal places for the periodic rate, and maintain full calculator or software precision for intermediate steps to ensure accuracy. (Do not round any intermediate results.)
Present Value of an Annuity Help
An “annuity” is a fixed sum of money paid to someone each period, typically for the rest of their life. More generally, it refers to any regular stream of cash flows, which may or may not have a defined term. For example, if an annuity is scheduled to make 10 annual payments of $10,000 each, the total of the payments is $100,000. However, if instead of receiving 10 annual installments you preferred a single lump sum today, you would not receive $100,000. Why? Because receiving a single sum today eliminates the future risk of missed payments. Therefore, you would accept a smaller amount today in exchange for eliminating the possibility of not collecting all future payments.
If you are scheduled to receive a series of 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 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 2500 in the “Cash Flow Amount” field (do not type the currency symbol or commas). The cash flow frequency will be monthly. Enter 240 for the “Number of Cash Flows” (240 months equals 20 years). Assume monthly compounding. Because the first payment is due one month from now, set the “First Cash Flow Date” to one month after “Today’s Date.”
The PV is $363,431.62. Thus, you could accept $363,431.62 today instead of receiving $2,500 per month for 20 years. For you, the two amounts are financially equivalent.
A note about “Compounding Frequency.” The “Exact/Simple” option applies exact-day simple interest. When you select this option, the calculator applies no compounding and uses the exact number of days between cash flow dates. The “Daily” option also uses the exact number of days, but assumes daily compounding. If you are considering receiving a single lump sum instead of a stream of payments, the “Exact/Simple” option is the most conservative setting—it produces the highest present value.
The prior version of this calculator included a “Cash Flow Timing” option. Since you can now enter both “Today’s Date” and the “First Cash Flow Date,” that option is no longer necessary. The calculator will calculate the exact dates when each cash flow is due.
One additional point about “Today’s Date.” This input does not have to be the actual current date. Instead, set it to the date on which you want to know the present value. For example, if you are closing on the purchase of a mortgage and the closing is expected in one week, set “Today’s Date” to the closing date. That way, the calculator will show you the present value as of the transaction date.
David says:
What exactly is the definition of the
discount rate?
Karl says:
The discount rate is the rate used to find the present value.
The more important question perhaps is "What rate should I use for the discount rate?"
And that depends. If you want to know the present value of a future cash flow that would be derived from investing, then you want to use a rate you think you can earn if you were investing the money.
If you were to borrow the money then you should use the interest rate you would have to pay on a loan.
Does this help?
Jim Lequin says:
At 16% discount rate, what is the present value of Php 36,000 which is due at the end of 90 days? What is the discount?
Karl says:
This present value calculator is a better one to use for your particular need. It solves for the PV of a single future amount. (You’ll need to do the subtraction to learn the discount. I’ll add that calculation in the next update.
Rebecca says:
Do you have any suggestions for calculating PV when there’s a balloon at maturity?
Rebecca says:
Just found your ultimate financial calculator link which looks like may the solution for this.
Karl says:
Yes, I was just going to recommend that calculator.
Basically, you’ll create 3 rows. The 1st for an "Unknown" amount. This will be the PV.
The 2nd row will be for the amount and number of cash flows.
The 3rd row will be for the single balloon on the maturity date expected.
Scroll down the page and you see some tutorials that should be useful.
Brian Berg says:
I HAVE A CLIENT WHO IS 50 YEARS OLD AND IS RECEIVEING 700,000 IN 401K MONEY TODAY. SHE IS ASKING ME WHAT THAT WOULD BE WORTH IN CURRENT DOLLARS OR WHAT DISCOUNT RATE SHE SHOULD BE USING? PLEASE ADVISE
Karl says:
Hi Brian, If she is receiving a lump sum today of $700,000, then it’s value today in current dollars is $700,000. Or, is she starting to withdrawal the $700,000 today? Or is she receiving something less than the face value of $700,000 today? I’m not really clear what your question is.
As to what discount rate to use, please scroll down the page from the calculator and see the heading "What is the correct discount rate?." There are examples there. Check that out, and then if something isn’t clear, please ask.
Kelly Johnson says:
I have a friend who is trying to work out a fair lump sum payment for alimony in a divorce. The support obligation is $500/month and it will continue for 15 years (180 payments). The court is allowed to adjust for cost of living increases in the future. Is there any way to use your calculator to get a present value but that also takes into account a cost of living increase over time? Or can you suggest the fairest way to do that? Decrease the interest rate used in the calculation perhaps?
Karl says:
Good question.
I don’t have a calculator that has an inflation adjustment for a present value calculation (that I can think of :-), but what you suggest, reducing the rate would be the correct way to do it. So, if you are assuming say a 5% rate-of-return, and an inflation rate of 2%, use a 3% rate for your PV calculation.
Kelly Johnson says:
Thanks so much!
Sajid says:
Can you please help me with the following:
I have get the result from you calculator but troubling with back-end formula. What would be the formula, if there is monthly payment but compounding daily.
Thanks in advance.
Karl says:
Sorry, I don’t answer question about equations. I answer question about how to do a calculation (use a calculator) or questions dealing with what calculator to use.
The equations are involved, and if I started to answer those, it would take away from my time that I have to develop this site.
Pat says:
Hi, I am trying to determine the Present Value of a pension payment. The future annual payments $8674 or 722/monthly. I am 51 today and want the monthly payments to begin at age 65. Which tool would I use to calculate the current value of the payment? thanks
Karl says:
Hi, I’m not sure I understand your question. But if you are trying to calculate the present value of the first pension payment then use this present value of an amount calculator. That calculator will calculate today’s value of $722 or $8574.
If you want to know the PV of the entire stream of payments, then use this calculator. The "First Cash Flow Date" is the date you expect to start receiving payments when you are 65. You’ll have to estimate how long you expect to live to calculate the number of payments you’ll receive. If you expect to live to 95 (30 years), and you are going to use the monthly figure, then you’ll enter 360.
pat says:
Hi Karl, thanks for your response. So I am trying to figure out the present value of the annuity as of today. And if the monthly guarantee income is $722 then what is the current value of that entire annuity? If I use the Present Value of an Annuity Calculator I am not sure what the Annual Discount Rate should be ? Any ideas?
if this is not the calculator then where can I find the first cash flow date calculator on your site?
Thanks
Karl says:
Hi Pat, the annual discount rate is the rate-of-return that you expect to earn on your investments. There is no right or wrong number. Scroll down the page from the calculator and there’s a discussion about discount rate.
This is definitely the calculator to use.
joelle says:
how to determine the PV of a 10 years annuity of 3000$ with the first payment received 5 years from now and the rate is 8%?
what should i use as variable of FV, PMT, I/Y,N . ?
Karl says:
Please use this annuity calculator. And sorry,I don’t understand the second part of your question. But I think once you look at the recommend calculator, your questions will be answered. If not, please ask again.
Hadi says:
Hello Sir, could you help me with the followings:
After two years a $10,000 investment earning 8% APR compounded six monthly will accumulate to
a) $11,600
b) $11,664
c) $11,699
d) $12,597
An investor will receive an annuity of $4,500 a year for 12 years. The first payment is to be received four years from today. At a 12% discount rate, this annuity’s worth today is closest to:
a) $11,976
b) $19,840
c) $25,632
Mia places $25,000 in a term deposit with a fixed term and interest rate of 5 years and 8% APR respectively. If the interest is compounded on a weekly basis, what is the value of the investment at the end of the five years?
a) $27,081
b) $52,774
c) $37,284
d) $41,005
Karl says:
I’m not really following you. You have but one question that you raised. For that question, what is the value after 5 years, you should be using this future value of an annuity calculator.
CJ says:
Hi Karl,
Is it possible for you to share the formula for how you arrive at the difference in terms of the present value calculation when Today’s Date is different from the First Cash Flow Date? For instance, if today’s date is Jan 1st, but the cash flow date is Jan 31st?
Karl says:
It’s not a formula per se. It takes a few hundred lines of programming code, and I don’t enter into discussions about it because it becomes a bottomless pit and takes away from what little time I have to build this website. (I do this parttime.)