## Calculating SECA Offsets for Clergy

Update:  Apparently you have to adjust your compensation by a factor of 0.9235 before calculating the self-employment tax.  See comments at end.

Recently my pastor posed a problem to me: How to calculate his SECA offset?  The answer can be found using algebra or using infinite series.  (For the non-math inclined, skip to the bottom of this post for an answer.)

Background: Most of us who work for an organization in the United States are charged a 15.3% Social Security FICA tax.  (This is 15.3% of our salaries.)  Half (7.65%) of that tax is paid by our employers, and the other half is paid by us (in the form of a deduction from our paychecks).  However, clergy are considered self-employed for Social Security tax purposes, which means that they have to pay all 15.3% themselves.  To counteract this, many congregations pay their clergy an extra 7.65% of their compensation to cover the Social Security tax that is normally covered by employers.  This is called a SECA offset.  However, this extra bit is itself considered compensation, so it is also taxed by Social Security!  This means that the SECA offset payment, if it is calculated this way, is actually less than needed to cover the intended part of the clergy’s Social Security tax.  The congregation could then pay an extra part to make up that difference, but that extra part would also be taxed, which means they’re still underpaying… and so on forever, in a perpetual cycle.

Let’s take an example.  Suppose a pastor makes a nice, round $50,000 in compensation. On top of this, the congregation pays the pastor a SECA offset of 7.65%, which is$3825.  This means the pastor’s actual taxable income from the church is $53,825. The 7.65% Social Security tax on$53,825 is $4117.61, which means the congregation has actually underpaid by$4117.61 minus $3825, which is$292.61.  The congregation could then give the extra $292.61 to the pastor, but that would itself count as income and thus raise the pastor’s Social Security tax even further. Again, this process could continue forever. Fortunately, looking at this problem the right way mathematically can solve it for us. Let’s formulate the problem like this: How much should a congregation pay its clergy in SECA offset if it wants that payment to be exactly 7.65% of the clergy’s total compensation? (Infinite Series Solution.) Turning to math, let’s let A denote a pastor’s original compensation. The first-order attempt at covering the SECA offset is $0.0765A$. This, though, is taxable, so the congregation needs to include 7.65% of this amount, or $(0.0765)^2 A$. But then this extra is also taxable at 7.65%, so the congregation needs to include an additional $(0.0765)^3 A$, and so on. Continuing in this vein, we have what is known as an infinite series for the amount the congregation should pay the pastor in total compensation: $\displaystyle A + 0.0765 A + (0.0765)^2 A + (0.0765)^3 A + (0.0765)^4 A + (0.0765)^5 A + \cdots$. The shorthand way to write an infinite series like this one is with sigma notation: $\displaystyle \sum_{i=0}^{\infty} (0.0765)^i A = A \sum_{i=0}^{\infty} (0.0765)^i$. This infinite series is a special class of infinite series known as a geometric series, $\displaystyle \sum_{i=0}^{\infty} r^i$. In our example, $r = 0.0765$. Provided $-1 < r < 1$, geometric series satisfy the nice formula $\displaystyle \sum_{i=0}^{\infty} r^i = \frac{1}{1-r}$. This gives us our answer: The congregation should pay the pastor a total of $\displaystyle A \sum_{i=0}^{\infty} (0.0765)^i = \frac{A}{1-0.0765} = \frac{A}{0.9235} = 1.082837A$. Subtracting the original compensation of A from this, we’re left with $0.082837A$ for the SECA offset. This means the SECA offset should actually be 8.2837% of the original compensation if that payment is to be exactly 7.65% of the clergy’s total compensation. (According to the comment below, however, the Schedule SE adjustment of 0.9235 to the original compensation means that we should be using 0.9235(0.765), or 0.07064775, instead of 0.765 in all of these calculations. If so, then the calculations are the same but with the new number in place of the old. The result is that the SECA offset should actually be 7.6018% of the original compensation.) (Algebra Solution.) While the infinite series solution is the straightforward way of tackling the problem, the math is much easier if we set up an algebraic equation to solve the problem. Let’s let x denote the desired amount of SECA offset, with A the pastor’s original compensation. We want x to be exactly 7.65% of the pastor’s total compensation. The pastor’s total compensation, though, is $A+x$. That gives us the following equation: $x = 0.0765(A+x)$. Solving this for x, we get $x = 0.0765A + 0.0765x$, or $0.9235x = 0.0765A$, or $x = \frac{0.0765}{0.9235}A = 0.082837A$, the same answer as before – but with less work. (Of course, in practice there are other issues to consider, such as the fact that raising the pastor’s compensation by 8.2837% will raise his/her income tax and benefit payments as well. The answer to the problem as posed, though, which just focuses on the SECA offset, is 8.2837% of the original compensation amount.) Advertisements This entry was posted in applications, sequences and series. Bookmark the permalink. ### 5 Responses to Calculating SECA Offsets for Clergy 1. Jodee Paape says: SECA is not 15.3% of gross wages. There is an adjustment on Sch SE to reduce the base subject to the 15.3%. You have to take the gross wages for SECA purposes x 92.35% x 15.3% to arrive at the SECA tax. Your formula is not correct since we only want to pay for 1/2 of the SECA liability. In your example above, 1/2 of the SECA tax on$50,000 would not be $3,825 but rather would be$3,532.39. Instead of 7.65%, you should be using 7.064775%.

Jodee Paape, CPA/PFS and Church Treasurer

• Regina G says:

Jodee, Is the 7.064775% figured on housing allowance also, or just salary?

• Jodee Paape says:

It’s calculated on the portions of compensation subject to Self employment tax – most commonly salary plus housing allowance. In most situations the total compensation is determined and then the pastor requests how much of that be designated as housing allowance.

2. Pastor Terry says:

Would this “extra” simply be added to the overall pay package? It does not need to reported anywhere special on W-2, etc. as an offset?

3. I spent an hour trying to brute-force an answer with Excel before I realized we had both royally wasted our time. Your first commenter has a clue to the solution, but I don’t think any of us realized it was this simple. I’ll explain.

Given your initial example of the pastor who makes $50,000 and the church adds 7.65% of his salary to offset SECA, which is$3825, bringing his total income to $53,825, BUT as Jodee noted, he only pays SECA tax on 92.35% of his total income, which is$49,707.39. If you allow for the fuzzy math of income tax also being due on this, it should be about the same.

I’m not sure how it took me this long to notice, but 92.35% + 7.65% = 100%.

For this to work perfectly, you would be adding 7.60% to effective salary:
7.60% of 50,000 is $3,800.91.$53,891 x 92.35% x 7.65% = \$3,800.91.

But as it turns out, it’s easier to just add 7.65% to effective salary, which is probably why this site and others recommend the church just pay a FICA allowance of, you guessed it, 7.65%.

On the bright side, I got to mess around with Algebra again.