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Home loan purely from an income tax benefit point of view

I keep listening from people that “I am buying home with home loan to save tax”. While I agree that it is a good idea to buy home as an asset building agenda, I have a question from the income tax point of view. Let us say, I have one own home (no rent) and no plans to build asset (for the sake of argument), does it still make sense to take home loan for the sake of income tax benefit. My thinking is as follows…

If I am getting 10L anually, and assume I pay 30% tax on whole amount, I end up paying 3L as income tax and left with 10-3=7L in my pocket at the end of the year. If I take a home loan and pay 1.5 interest which is tax free, I have to pay 30% interest on 8.5L which will be ~2.5L. Though I am paying 0.5L less income tax, I have only 10 – (2.5+1.5) = 6L at the end of the year. Also let us assume that for 80C section, I invest other money in place of principle repayment benefit. My basic point is that the interest is going to bank’s pocket and not mine.

Is my understanding correct ?

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