# Social Security Benefits and the Time Value of Money: An Example

Occasionally, someone asks me for an explanation of the mechanics of discounting future values to get present value equivalents. In this post, I provide an illustration of those mechanics. You can find some additional discussion on our main website.

Suppose that Mary, a single female, is turning 62. She will receive \$25,000 a year if she claims at that age. Over a normal life span, up to age 86, she will receive a total of \$625,000 (ignoring any COLAs).

A serious problem with this total amount is that it assumes that the \$25,000 received 25 years from now has the same value to Mary today as the \$25,000 she will get over the next year. Clearly, these two amounts don’t have the same present value: \$25,000 25 years from now is worth a lot less than \$25,000 received over the next 12 months.

The conventional method for translating future values into present value equivalents is to discount those future values by a discount rate (or discount factor). For our calculations, we use a 3% real discount rate (that is, 3% over and above any inflation).

So, the present value of \$25,000 to be received next year would be calculated as: \$25,000/1.03 = \$24,272. In other words, at a 3% discount rate, \$25,000 received next year is worth \$24,272 to you today.

From an investment perspective, discounting is the twin of compounding. If you could invest \$24,272 today at 3% (above inflation), you would have \$25,000 in one year (= \$24,272*1.03).

The calculations for the entire 25 year period used in this example are shown below: The undiscounted annual benefits (\$25,000) are shown in the second column. The appropriate discount rate is shown in the third column. And the discounted amounts are shown in the last column.

Our measure of Social Security Wealth is the sum of the last column: \$448,389 in this instance. Compare that amount to the undiscounted amount of \$625,000. The discounted amount is about two-thirds of the undiscounted amount. (We have found this two-thirds relationship to be a fairly reliable rule of thumb in many instances.)

One useful way to think about the discounted total amount is as follows: \$448,389 invested at 3% above inflation will yield a time stream of annual payments of \$25,000, for a inflation-adjusted total of \$625,000 by year 25.

Now, you may wonder why we use a 3 percent discount rate. That is an issue for a future post.