Present Value of Annuity Calculator

The present value of an annuity is the amount that a series of equal payments due in the future are worth today. A dollar available now can be invested so a dollar to be paid out some years from now has less value. Therefore, each payment is discounted to its present value before they are added together.

This calculator supports both ordinary and annuity due annuities and allows you to increase the payment amounts annually, show the value of an annuity for life or calculate backwards for required payment amounts, interest rates or term lengths.

What is the present value of an annuity?

An annuity is a series of equal payments made at regular intervals such as retirement income, structured settlements, rent or lease payments, loan repayments, or regular deposits into a savings account. The present value of an annuity at a given discount rate is the amount that you would accept today instead of waiting for all the payments. In other words: it's the amount that you would have to invest now in order to generate those future payments with that investment, assuming the stated interest rate. This concept is based on the time value of money. Money available today has a higher value than the same amount of money received later because it can earn income in the meantime.

The difference between a regular pension and a retirement start

The timing affects the result. An ordinary annuity pays at the end of each time period, which is true for mortgages, car loans and most retirement plans. An annuity due pays at the beginning of each time period, which is true for rents, lease payments and many insurance premiums. Because an annuity due receives each payment one period sooner, its discount period is shorter, so it's always worth more than an ordinary annuity, assuming all other things are equal. The factor for that is the sum of the interest rate per period plus 1. You can compare the two options by switching the "timing" element.

Here's how to use this calculator.

Enter the payment amount, annual discount rate and number of years. Then select the frequency of payments and whether they are made at the end or beginning of each period. The present value will be displayed immediately. By activating "Increasing Payments" you can simulate a cash flow that increases annually by a certain percentage. By activating the "Sensitivity Analysis" section, you can check the lower and upper limits of the present value calculated based on the entered interest rate. This calculation tool also allows for conversion. If one of the fields (present value, payment amount, interest rate or number of years) is left blank and the other three are filled in, the empty field will be calculated.

Formula to calculate the present value of an annuity:

The present value of an ordinary annuity is calculated with this formula:

where PMT is the payment amount for each period, i is the annual discount rate and n is the number of periods. If the payment is made at the beginning of each period, multiply by the interest rate per period plus 1 to get the present value of the annuity due at the start of the period.

If the interest rate is stated as an annual rate but payments are more frequent than annually, divide the interest rate by the number of payments per year and multiply n by the number of years. For example, if m payments are made each year, then i is the annual interest rate divided by m and n is the number of years multiplied by m.

Consider an example as shown below:

The Present Value for this kind of an Annuity is calculated as follows:

How much will you recieve?

Consider a settlement that pays $2,500 at the end of every quarter for 8 years, discounted at 5 percent a year. The rate per period is 0.05 ÷ 4 = 0.0125, over 32 payments.

So $80,000 of nominal payments is worth about $65,603.19 today, and waiting for the money costs $14,396.81. Taking the same payments at the start of each quarter raises the present value to about $66,423.23. The table below shows the individual symbols and their example values.

Increasing pension and eternal pension

Not all cash flows are the same. In a growing annuity each payment is increased by a constant growth rate g. This is appropriate if the income from an annuity increases with cost of living or if rent is paid. The present value is:

If the payment stream never ends, it is a perpetuity. As the number of payments increases, the present value approaches a finite upper limit. This is because payments far into the future are heavily discounted and add little to the value.

A growing perpetuity converges only if the discount rate exceeds the growth rate. Otherwise it will grow to infinity. This calculator shows both the present value of a perpetuity and the results for a fixed period, so you can see how close the long term value is to that of an infinite stream of payments.

Factors that affect present value

There are three factors that affect the outcome. The most important factor is the discount rate. The higher the interest rate, the more future payments will be discounted, resulting in a lower present value. The lower the interest rate, the higher the present value. Discount rates used by companies offering structured settlements typically range from 9 to 18 percentage points, which explains why the lump sum payment is often well below the total amount of payments. The payout amount and number of payouts have opposite effects: The higher the payouts are and the more there are of them, the higher the present value will be. Timing also plays a role: An annuity that pays out earlier in life will generally have a higher present value than an annuity with the same payment terms.

Present value and future value of an annuity.

These are two different perspectives on the same cash flow. The present value discounts each payment to today's date and shows what the annuity is worth today. The future value compounds each payment amount with interest for the future, showing how much this stream of payments will be worth at the end of the period. The present value is useful when you are deciding whether to take a lump sum or an annuity, or determining how much to pay for a particular income stream. The future value is useful if you are saving for a specific goal. This calculator shows both values simultaneously so that you can see the same annuity from both perspectives.