# 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. In fact, sometimes this calculator is also known by the name **discounted cash flow calculator**. More below

### Information

## What is present value used for?

At a high level, there are at least 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 current value for 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 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. Or if you are considering the purchase of an equity (common stock) you can use this calculator to find the present value of their projected future earnings.

## 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 3.5% (April 2023).

### 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.

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.

## Shivangi says:

Hi Karl,

In a scenario, where let’s say we have a normal annuity where i’ll be receiving $100 on 12/31/2020 and I want to know the present value today i.e of 07/04/2020..If I wanted to calculate this manually, what would be the discounting factor I would take?

Just want to know how the discounting rate would be adjusted according to the period.

## Karl says:

Hi Shivangi, there are two types of questions I’m able to answer on this site. What calculator should I use to accomplish “X.” And how do I use a calculator’s feature? I don’t have the equations in my head and if I started to research them again, I would spend more time doing that than building the site.

## Lavelle Watts says:

Hi Karl,

I have a taxpayer receiving an annuity payment of $4,614 per month for 57 months. This is a total of $262,998.

The insurance company has offered to buy him out at $172,800.

Using your calculator I really think – just from a calculation side – that he is much better off keeping the payment stream rather than the lump sum.

## Karl says:

Hi Lavelle, I think you’re right if you are asking.

This is a useful calculator to use for such a question. I think there is also another interesting way to look at this scenario. Use the time to withdrawal calculator on this site. Fill in the inputs this way:

This will solve for the rate-of-return that your client would have to earn to make sure the 172,800 offer provides him with the $4,614 income for 57 months that he now has.

If you try it, you’ll see this taxpayer will have to earn in excess of 18% per year. Tough to do I think.

Take a look at the schedule and you’ll see that withdrawals will total 262,997.99.

## Jasmin says:

Can you help solve this 🙂

Calculate the PV of the following cashflows using a 7% discount rate.

a) 30 payments of 100 starting 5 years from today

b) you pay 10/yr for 3 years with the first payment being today, and then starting a yearfrom today you will receive $6/yr for 6 years

## Karl says:

Did you try this calculator? It will solve your first problem.

For the second problem, please use the Ultimate Financial Calculator. It will support calculating PV when there is both investment and withdrawal. Scroll down the page and see the link to the tutorials, or ask a specific question if something is not clear.

## Michael says:

Hi – which calculator should I use – FV is $53,928. Monthly withdrawal is $107 for 42 years. What would be the PCV calculator needed to ensure that the person get the full value of the $53,928 considering that amount is being reduced over time. Thank you!

## Karl says:

Hi, what are you trying to solve? 12 months x $107 x 42 years = $53,928. In other words, if you withdrawal $107 monthly for 42 years, the balance will be 0 and the return during the 42 years is 0%.

Also, I don’t think you mean that the FV is $53,928 since you say you want to make sure the person gets the full value of the $53,928. That statement means the PV is $53,928 and the FV would be 0.

## Michael says:

My apologies for using the wrong term. Yes, if she received $107 per month over 42 years it equals $53,928. A straight PCV at 5% over 42 years is about $6,948. However, the person needs to withdraw $107 each month to cover medical expenses. I am trying to figure out how much she should get today, the present cash value, taking into consideration the monthly withdrawals. I hope that makes it clearer. THanks.

## Karl says:

Does my 2nd answer, which I wrote before seeing this, help you answer the question?

## Karl says:

If you do mean that the FV is $53,928, then you can use this calculator in this manner. Enter $107 for the cash flow. Enter say 2% for the discount rate (the rate the person wants to earn on their money), 504 for the number of monthly cash flow (42 years), and set the dates one month apart for now at least. If you calculate, you’ll see that the FV is $53,928. The PV is $36,465. That means the party can take a single lump sum settlement of $36K today and have the equivalent of $53,928 42 years from now.