# Social Security Wealth

Our custom reports, designed to find the best time for you to start collecting Social Security benefits, must consider a large number of alternatives. For each alternative, we compare what is gained by waiting to collect higher benefits versus what is lost by waiting. For example, single individuals who collect benefits at age 66 get 33 percent more each month than they would have gotten had they started at age 62. But, they must give up 4 years of benefits in order to get the bigger monthly check. So, we always have this trade-off to consider.

In order to make these comparisons manageable, we calculate for each alternative a measure-a single number--that we call "social security wealth." This type of calculation is used throughout the financial planning industry whenever comparisons involving time streams of benefits and costs are involved. Essentially, for each choice we convert the time stream of Social Security benefits and costs into a single number that represents the "present value equivalent" of that time stream. For a more detailed discussion, see an Investopedia article on Understanding The Time Value Of Money or search on the terms "discounting", "present value", or "time value of money".

## Some Examples

Financial analysts often refer to the "time value" of money. What they mean is that a $100 received today has greater value to you than $100 to be received, say, 5 years from now. If you get the $100 today, you could always deposit it in an interest bearing account. Suppose the account pays 3 percent per year. After 5 years, that $100 grows to about $116. So, taking the $100 today is clearly more valuable than waiting for that $100 5 years from now.

Here is another way to look at the above example. You are offered $100 today, which you plan to invest at 3 percent. As an alternative you are offered $X to be received 5 years from now? From a simple financial perspective, what value of $X makes it equivalent to the $100 today? The answer: $116. So, we can say that the *present value equivalent* of $116 to be received in 5 years, when the relevant interest rate is 3 percent, is $100.

Let's take another approach to this issue. If you invest $100 today at 3 percent in a 5-year CD, you will receive $116 when it matures. The formula for this compounding problem is:

And now with some real numbers:

We can rearrange this above formula to give us a present value equation:

Again with real numbers:

Let's look at an example involving the calculation of Social Security Wealth. John is unmarried and is about to turn 66, his full retirement age. If he starts benefits at age 66, he receives, say, $10,000 a year. If he waits until age 70 to start benefits, he gets $13,200 a year. (We can ignore inflation, since benefits are adjusted to keep pace with inflation.) Also, suppose John is in good health, but none of his ancestors have lived to age 85. So, John chooses to structure his finances to allow for the strong possibility that he might not live past age 85. (Keep in mind, that if John lives longer, he still gets his Social Security check.) We assume that John can afford to wait until age 70 to claim benefits, if that looks like the best choice.

Should John take benefits at age 66 or at age 70? A comparison that some people make is simply to add up the benefits that John would receive under the alternatives, without adjusting for the time value of money. Using this simple approach, if John takes benefits at age 66, he would receive $200,000 (= $10,000 × 20 years) by the time he reaches the end of his 85th year. By waiting until age 70 to start benefits, he would receive $211,200 (= $13,200 × 16 years) if he lives to the end of his 85th year. Based on this comparison, it appears that claiming benefits at age 70 is superior to claiming benefits at age 66. By waiting until age 70 to claim benefits, John can look forward to an extra $11,200 (= $211,200 - $200,000) if he lives through age 85.

But the above numbers do not take the time value of money into account. Using a 3 percent interest rate, the time stream of benefits associated with retiring at age 66 yields a measure of Social Security Wealth approximately equal to $153,200 in today's dollars. Retiring at age 70 generates Social Security Wealth approximately equal to $151,700 in today's dollars. Comparing these numbers shows that retiring at age 66 is the best choice, by a margin of $1,500 in today's dollars. So John should start receiving his Social Security checks sooner, because he gets more in today's dollars by claiming at age 66 rather than at age 70.