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Okay, I understand all your logic. However, I am slightly confused as to the information you provided in this summary:

 

"The two of you had Self-only coverage for 6 months and Family coverage for 6 months. So, using the formula for line 3 on page 4 of the 8889 Instructions, you have 6 months at $3,450 and 6 months at $6,900 (remember that this is for 2018). This totals to $67,500, which, when you divide by 12 months is $5,175 for the two of you to share."

 

 Under the Specific Instructions for Form 8889, it gives the following instructions for completing line 3 in the form:

 

"When figuring the amount to enter on line 3, apply the following rules.

...

4. If you were, or were considered, an eligible individual for the entire year and you changed your type of coverage during the year, enter on line 3 (see (6) in this list) the great of:

a. The limitation shown on the last line of the Line 3 Limitiation Chart and Worksheet (in these instructions), or

b. The maximum amount that can be contributed based on the type of HDHP coverage you had on the first day of the last month of your tax year.

TIP: If you had family coverage on the first day of the last month, you do not need to use the worksheet; enter $6,900 on line 3."

 

To me, these instructions apply directly to our situation. We were both considered eligible employees for the entire year and we changed coverage during the year. We had HDHP family coverage on the first of the month so our limit should be $6,900. The last-month rule does not apply because we were eligible all year.

 

Furthermore, I think the logic behind your calculations on the Limitation Chart and Worksheet are incorrect because you only consider eligible contributions for my self-coverage plan in the first 6 months (Jan-June) to be $3,450 each month. Shouldn't my wife's plan also give her a contribution limit to her separate self-coverage plan of $3,450 for the first 6 months? I think this is the reason for the caveat in the aforementioned instructions under topic (4) for line 3 instructions.