Some 78 million baby boomers are poised to make one of their most important financial decisions of their lives, namely when to take Social Security benefits. Deciding is no picnic. As my recent column indicated, Social Security’s provisions are unbelievably complicated.

So, this morning, I said to myself, “Gee, I have a lot of knowledge about this issue based on helping to develop my company’s Social Security maximization software program (http://www.maximizemysocialsecurity.com/). Not everyone is going to want to shell out $40 (or $200 in the case of financial planners) to buy the program. Maybe it would help people if I just wrote down the formula for determining their total benefit.”

This is what I’ve done below. We don’t use this formula, per se, in our program, so this is the first time I or, I believe, anyone else has actually ever written down the formula.

I’ve focused on the benefit to married couples when both are alive. I’m leaving out child benefits and mother and father benefits. I’m assuming both spouses are alive between ages 62 and 70, so I’m ignoring survivor benefits. I’m also ignoring the extremely complex issue of how the particular days and months at which one starts collecting spousal and retirement benefits affect the benefit formula. Finally, I’m omitting the option that workers have to start collecting retirement benefits, suspend their retirement benefits at or after their full retirement age, and restart their benefits at a higher level at or before age 70.

Below you’ll see the formula for each spouse’s total (retiree plus spousal) benefit,

*B(a),*when she/her is age*a*.
After you’ve examined this formula — with its 10 functions, one of which is four dimensional, and the complicated restrictions on the arguments of some of the functions — and turned pale, ask yourself whether it makes sense for our basic saving system – Social Security, on which most retirees depend for virtually all or most of their old age income — to be so complicated that not one in a million Americans is able to correctly decipher it.

If, after perusing the formula, you agree we need to fix the system from the bottom up, at least for young people, please endorse The Purple Social Security Plan.

And whether or not you like my alternative system, please send a link to this column to your members of Congress and ask them: “Did you design this? Do you have any idea what you and former members of Congress have constructed here? Can you understand this formula? Is this something you expect me to master on my own? Isn’t it time to make Social Security not only financially sound (it’s 31 percent underfunded, i.e., desperately broke as described in my prior column) but also minimally user friendly?

**The “Simple” Social Security Benefits Formula**

There are two pieces to the formula, which I’ll reference as applying to Kate, whose spouse is Frank. The first piece refers to Kate’s retirement benefit, which is based on her own earnings record. The second piece refers to Kate’s spousal benefit based on Frank’s earnings record.

*B(a) = PIA(a) x (1 – e(n)) x (1 + d(n)) x Z(a)*

*+ max(.5 x PIA*(a) – PIA(a) x (1+d(n))) x E(a), 0) x (1- u(a,q,n,m)) x D(a)*
Here’s the notation:

*B(a)*is Kate’s benefit at age

*a*.

*PIA(a)*is Kate’s Primary Insurance Amount (her full retirement benefit) at age

*a*. Note,

*PIA(a)*can change as Kate ages due to the Re-Computation of Benefits if Kate works beyond age

*n*.

*n*is the age at which Kate starts collecting her retirement benefit. If

*q*is greater than or equal to

*m*and

*m*is less than

*n**,

*n*=

*q*.

*n**is Kate’s full retirement age, assumed to be 66.

*m*is Kate’s age when Frank first collects his retirement benefit or files for retirement benefits but suspends their collection.

*q*is the age that Kate applies for or is deemed to apply for spousal benefit.

*e(n)*is Kate’s Early Retirement Reduction factor. It ranges from .25 to 0 as n ranges from age 62 to 66 (Kate’s assumed full retirement age). For

*n*to be positive it must be less than

*n**.

*d(n)*is the Delayed Retirement Credit factor. It ranges from 1 to 1.32 as n ranges from 66 to

*70*.

*Z(a)*is a dummy variable, which equals 0 if Kate is not collecting her retirement benefit in year

*a*, i.e., if

*a*is less than

*n.*Its value is 1 if Kate is collecting her retirement benefit, i.e., if

*a*equals or exceeds

*n*.

*PIA*(a)*is Frank’s Primary Insurance Amount when Kate is age

*a*.

*D(a)*is a dummy variable, which equals 1 when Kate is age

*a*if Frank is either collecting his retirement benefit or has filed for his retirement benefit, but suspended its collection. Otherwise

*D(a)*equals

*0*.

*E(a)*is a dummy variable, which equals

*0*in year

*a*if Kate has, as of year

*a*, neither started collecting her retirement benefit nor filed for and suspended her retirement benefit’s collection. When

*D(a)*equals 1,

*E(a)*will equal 1. But

*E(a)*can also equal 1 when

*D(a)*is

*0*if Kate has filed for and suspended the receipt of her retirement benefit.

*u(a,q,n,m)*is the Spousal Benefit Reduction factor. It ranges from

*0*to

*.30*. If both

*m*and

*n are*less than or equal to

*n*, q = max(n,m).*For

*u(a,q,n,m)*to be positive,

*a*must equal or exceed

*q*.

The first part of the formula determining Kate’s own retirement benefit, is easier than the second. It says that Kate’s retirement benefit is anchored by her Primary Insurance Amount, which is itself determined by a formula based on the average of Kate’s 35 highest past covered earnings adjusted for economy-wide real wage growth. Kate’s PIA is then zapped or increased based on the early retirement and delayed retired factors,

*e(n)*and*d(n)*, respectively. But for Kate to receive a benefit, she has to apply for one. That’s governed by the*Z(a)*factor.
The second part of the formula refers to Kate’s spousal benefit. For Kate to be able to collect a spousal benefit on Frank’s account, Frank has to be either collecting his retirement benefit or have filed for it and suspended its collection, i.e., the final term on the right,

*D(a)*, must be*1*, not*0*. The spousal benefit reduction factor,*u(a,q,n,m)*, is, itself, a pretty complicated object. For example, if*q*is less than*m*, the factor equals zero. But if*n*equals or exceeds*m*and is less than*n**,*u(a,q,n,m)*exceeds zero.
The term

*E(a)*is important because Kate’s spousal benefit is not docked based on her own retirement benefit if she isn’t collecting a retirement benefit or hasn’t filed for her retirement benefit and suspended its collection. Finally, we have the*max*function, which takes the maximum value of*(.5 x PIA*(a) – PIA(a) x E(a)*and zero.