Your calculations and prorations (11/12 and 4/12) all appear correct. In Publication 936 see examples 1 and 2 in the Average Monthly balance section (here and extracted below) to see proration examples.
Example 1.
In 1986, Sharon took out a first mortgage of $1,400,000. The mortgage was a 7-year balloon note and the entire balance on the note was due in 1993. She refinanced the debt in 1993 with a new 30-year mortgage (grandfathered debt). On March 2, 2022, when the home had a fair market value of $1,700,000 and she owed $500,000 on the mortgage, Sharon took out a second mortgage for $200,000. She used $180,000 of the proceeds to make substantial improvements to her home (home acquisition debt) and the remaining $20,000 to buy a car (home equity debt). Under the loan agreement, Sharon must make principal payments of $1,000 at the end of each month. During 2022, her principal payments on the second mortgage totaled $10,000.
To complete Table 1, line 7, Sharon must figure a separate average balance for the part of her second mortgage that is home acquisition debt. The January and February balances were zero. The March through December balances were all $180,000 because none of her principal payments are applied to the home acquisition debt. (They are all applied to the home equity debt, reducing it to $10,000 [$20,000 − $10,000].) The monthly balances of the home acquisition debt total $1,800,000 ($180,000 × 10). Therefore, the average balance of the home acquisition debt for 2022 was $150,000 ($1,800,000 ÷ 12).
Example 2.
The facts are the same as in Example 1. In 2023, Sharon's January through October principal payments on her second mortgage are applied to the home equity debt, reducing it to zero. The balance of the home acquisition debt remains $180,000 for each of those months. Because her November and December principal payments are applied to the home acquisition debt, the November balance is $179,000 ($180,000 − $1,000) and the December balance is $178,000 ($180,000 − $2,000). The monthly balances total $2,157,000 [($180,000 × 10) + $179,000 + $178,000]. Therefore, the average balance of the home acquisition debt for 2023 is $179,750 ($2,157,000 ÷ 12).
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