# Present Value of an Annuity Calculator

Calculate the present value of an annuity by entering the payment, term, rate, and type of annuity in the calculator below.

Annuity
years

Payment
$Interest % ## Present Value:$
Learn how we calculated this below

## How to Calculate the Present Value of an Annuity

Annuities are financial assets that promise investors a guaranteed future return in exchange for making an investment today. Annuities are often used by people saving for retirement who want to create a future source of cash flow.

To determine how much an annuity is worth, a prospective investor will need to start by calculating its present value. The present value of an annuity is the amount of money an investor will need to invest today to secure annuity payments in the future.

Typically, the phrase “annuity” refers to any sort of payment arrangement that enables the payee (the person investing in the annuity) to secure a predictable source of cash flows in the future.

There are multiple types, including those that pay out at a standard rate in the future, along with those whose values might be affected by general changes in the market. They are often used to supplement 401(ks), IRAs, and other retirement savings vehicles.

Regardless, it is clear that an annuity investment—independent of your personal level of risk tolerance—can be a very lucrative investment. Annuities are a very common component of modern financial planning. However, there are things to consider when deciding whether an annuity investment will make financial sense for you.

In the sections below, we will discuss the most important things you need to know when evaluating the value of an annuity, including how to determine its present value as well as how to determine the value of the variations you might encounter. You can also try our annuity calculator or annuity payout calculator.

### What is Present Value?

The present value of an annuity is the amount of money you will need to pay in order to secure annuity payments in the future. Annuity payments come in many different forms, including annuities that issue a one-time payment, an annual payment, and many others.

By taking the time to calculate the present value of an annuity, you can decide whether or not investing in an annuity will be in your financial best interest. For example, once the time value of money (TVM) is accounted for, you can see whether it makes sense to allocate your money to a different type of financial asset or to annuities.

Other factors, such as your long-term financial goals, when you hope to retire, and your personal level of risk tolerance might also influence whether investing in an annuity is right for you.

### Types of Annuities

The term “annuity” can be used to describe a wide range of financial assets. According to most financial experts, the broad class of annuities typically falls into one of four categories. These include:

Immediate Annuities: The general goal of an immediate annuity is to ensure that investors can secure a direct lifetime payout. Once they make an initial investment (usually a lump sum payment), they will be able to secure a sustained level of cash flow that will last for the rest of their life, which will begin the year after the initial investment is made.

Deferred Annuities: Deferred annuities do not pay returns immediately, instead payments will begin at a predetermined point in the future. This type of annuity is also known as the “tax-deferred option” because payments can be deferred until it’s more advantageous for tax purposes. These annuities are ideal for people who want to make an investment now but don’t need to receive payments until a later date. Since the money is allowed to grow before any returns are paid to the investor, the payments may be larger than they would be for a similar immediate annuity investment.

Fixed Annuities: These annuities guarantee a fixed interest rate and the investor receives a predictable return over a predetermined length of time.

Variable Annuities: The value of variable annuities can fluctuate based on various market conditions and investment portfolios.

If you are considering investing in annuities, be sure to explore all the options available.

### Annuity Present Value Formulas

To calculate the present value of an annuity you can use one of several formulas, depending on the type of annuity.

#### Ordinary Annuity Present Value Formula

An ordinary annuity’s payments will be made at the beginning of each period, which is typically one year. Here is the formula used to calculate an ordinary annuity present value:

PV_{ORD} = PMT \times \left [ \frac{1 − (1 + i)^{−n}}{i} \right ]

Where:
PVORD = present value of an ordinary annuity
PMT = payment amount
i = interest rate
n = number of payments

These are generally considered to be the most common type of annuities, though the other variations are also available.

#### Annuity Due Present Value Formula

Contrary to ordinary annuities, annuities that are “due” will make their payments at the beginning of the time period (typically a year), which means when all variables are equal, their present value will be slightly higher. The formula is as follows:

PV_{DUE} = PMT \times \left [ \frac{1 − (1 + i)^{−n}}{i} \right ] \times (1 + i)
[formula may scroll beyond screen]

Where:
PVDUE = present value of an annuity due
PMT = payment amount
i = interest rate
n = number of payments

#### Present Value of Growing Annuities

In some cases, the value of an annuity will grow over time, meaning the rate of return will increase with each passing year. For these annuities, use the following formula:

PV_{GA} =\frac{PMT}{(i − g)} \times \left [ 1 − \left ( \frac{1 + g}{1 + i} \right )^{n} \right ]
[formula may scroll beyond screen]

Where:
PVGA = present value of a growing annuity
PMT = payment amount
g = growth rate
i = interest rate
n = number of payments

With these annuities, the longer you live, the more money you will make.

#### Continuously Compounding Interest Annuities

While most annuities will compound periodically, others will compound continuously. You can learn more about compound interest with our compound interest calculator.

When this is the case, you will need to use algorithmic calculations, including the following formula:

PV = PMT \times \left [ \frac{1 − e^{−in}}{e^{i} − 1} \right ]
[formula may scroll beyond screen]

Where:
PV = present value of an annuity
PMT = payment amount
i = interest rate
n = number of payments

These annuities can lead to even higher rates of return.

### Example

For example, let’s assume you will receive an annuity payment of $1,000 each year for 10 years at an annual interest rate of 5%. Assuming this is an ordinary annuity, the solution to find the present value is: PV = \$1,000 \times \left [ \frac{1 − (1 + 0.05)^{−10}}{0.05} \right ]
PV = \$1,000 \times \left [ \frac{1 − 1.05^{−10}}{0.05} \right ] PV = \$1,000 \times \left [ \frac{1 − 0.614}{0.05} \right ]
PV = \$1,000 \times \left [ \frac{0.386}{0.05} \right ] PV = \$1,000 \times 7.72173
PV = \$7,721.73 So, the present value of this annuity is equal to$7,721.73.

The formula figures the present value of each of the $1,000 payments and discounts them using the 5% interest rate. It then sums up all the present values to arrive at the present value amount. The table below shows the annual present values for each year of this annuity. While you would receive a total of$10,000, the present value is $7,721.73 because it is discounted each year using the 5% interest rate. You will notice that the$1,000 is worth less each year than the prior year. The farther out it is received, the less it will be worth today.

Table showing the present value of an annuity paying $1,000 per year over 10 years discounted at a 5% rate. Year Payment Present Value 1$1,000.00 $952.38 2$1,000.00 $907.03 3$1,000.00 $863.84 4$1,000.00 $822.70 5$1,000.00 $783.53 6$1,000.00 $746.22 7$1,000.00 $710.68 8$1,000.00 $676.84 9$1,000.00 $644.61 10$1,000.00 $613.91 Total$10,000.00 \$7,721.73

## Summing Up

Annuities can be a great asset for future retirement savings. If you are considering investing in annuities, you will want to explore the different options available and use the annuity calculators to try out different investment scenarios.