Sold and bought primary residence during the year, what exactly are the denominators?

[overcurious]

I have read a lot of questions on this topic here, but I am still not sure what the "Statements provided by your lender" average balance means. 

I had a primary residence with an outstanding mortgage since 2021. I sold that house on April 30, 2024.

I also bought another house on April 4, 2024, and I immediately made my primary residence, also backed by a mortgage. I think (correct me if I am wrong) I can consider the original property to be "second home" for the duration of April 2024 (slowly moving from one to the other and thus using both).

I know the "closing balance" as of each month on each of the mortgages. The question is however, do I add all the numbers and divide the sum by 12 or do I add the numbers relating to the first mortgage and divide by 4, then add all the closing balances for the second mortgage and divide them by 9 (April to December) and add those together?

The phrase from p936 "You can treat the balance as zero for any month the mortgage wasn't secured by your qualified home" as the indication that the first method (divide everything by 12) should be used. 

However, the phrase "and dividing that by the number of months the home secured by that mortgage was a qualified home during the year" seems to contradict that. 

I am sure this is a very common situation, so I would appreciate if someone who did it in the past can comment if I can safely use the first approach (which obviously, due to increased denominators) gives me better values (actually, makes all of my interest deductible) or if the latter approach must be used (which would only allow me to use approximately 2/3 or the total interest I paid during the year)

[Mike9241 · Accepted solution]

PUB 936 mentions average balance. however, there are many acceptable ways (most not in the PUB of computing average balance)

To calculate the average mortgage balance, you can use the following methods:
Monthly Balances Method: Add up all the monthly balances for the mortgage and divide by the number of months in the period you are considering.
*
First and Last Balance Method: Add the first balance and the last balance, then divide by 2.
*
Interest Paid Method: Divide the total interest paid during the period by the interest rate to estimate the average balance.
*
Daily Balance Method: Sum the outstanding balance of the mortgage for each day of the period and divide by the number of days in that period.
*

i seen some others - this was in some pro software some years back

balances at beginning and end of month divided by 2. Sum all 12 months and the divide by 12 

* for first home I suppose taking the monthly balances before the monthly payment (that's what you're paying interest on) and use the April balance before the payoff and divide by 4. do the same for the new home and divided by 9. add the two together.