 # How Do Discount Rates Affect the Present Value of an Annuity?

An annuity is an insurance product that promises to give you regular payments in the future in exchange for an upfront premium. Since you could theoretically create annuity income on your own via investing, calculating the present value of an annuity can help you make the best decisions about your money. The present value refers to the amount of money you would need to invest today in order to receive the annuity's promised income stream in the future.

The discount rate is one factor that can affect the present value of an annuity. This rate, which may also be referred to as the interest rate, has an inverse effect on your present value — the higher the discount rate, the lower the present value.

## The Present Value Formula

Even if you prefer to use an online calculator to do the math, you should know the formula for calculating the present value of an annuity:

Present value = PMT x ((1 − (1 / (1 + r)n )) / r)

Let's define each of these factors:

• PMT = Dollar amount of each annuity payment
• r = Discount rate (or interest rate)
• n = Number of periods (or years) in which you can expect payments

For an example, let's say you expect an annual payment of \$50,000 (PMT) per year for 10 years (n) with a discount rate of 4% (r). You would calculate your present value like this:

Present value = \$50,000 x ((1 − (1 / (1 + .04)10 )) / .04)

Present value = \$405,544.79

Now let's take a look at how changing the discount rate in this formula affects the present value.

## A Higher Discount Rate Equals a Lower Present Value

The placement of the discount rate in the formula can help you understand its effect on the present value. The placement of the discount rate (r) is known as the denominator in a fraction. The higher a denominator is, the lower the total value. (Think of the difference between 1/2 and 1/20.)

For example, if the same annuity from above had an annual payment of \$50,000 (PMT) for 10 years (n), but the discount rate was adjusted up to 6%, the present value would go down significantly:

Present value = \$50,000 x ((1 − (1 / (1 + .06)10 )) / .06)

Present value = \$368,004.35

On the other hand, if the discount rate were adjusted down to 2.5%, here's how it would affect the present value:

Present value = \$50,000 x ((1 − (1 / (1 + .025)10 )) / .025)

Present value = \$437,603.20

There is a good reason why annuities often use the terms "discount rate" and "interest rate" interchangeably. The interest the money will earn is used to discount the present value of an annuity. The power of compounding interest over time means that you need less of today's dollars to create your future annuity payments. The higher the discount rate (i.e., the higher the interest rate), the less money you need to reach the future value of the annuity.

## Why Calculate the Present Value of an Annuity?

Understanding the present value of your annuity can help you make the best decisions for your money, particularly if you have the option of taking your annuity proceeds as a lump sum rather than via equal payments over time.

For instance, let's say the annuity with an annual payment of \$50,000 over 10 years with a fixed discount rate of 4% offered you a lump sum of \$400,000 now. When you calculate the present value of this annuity at \$405,544.79, you know that you'd be getting less money by taking the lump sum.

That said, present value calculations may not always be quite so easy. If you have a variable rate annuity or a lifetime annuity (with no defined term), then it is much more difficult to accurately determine the present value. Even in these situations, however, it can be useful to calculate potential present values based on your best estimation of the rate or term.

## Making the Best Annuity Decisions

The inverse relationship between the discount rate and the present value gives you a handy rule of thumb: When the discount rate goes up, the present value goes down. Understanding how this works can help you make better decisions about your annuity income. 