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Complete guide for income from House property and HRA

I have tried to summarize the three most prevalent cases while claiming HRA and entering details under income from house property.
1. I own only one house and it is in city A, I stay in rented Accommodation in city B.
a) House in A is rented:
I can claim Principal and Interest of home loan (if any, taken for the construction of house in A). There is no cap on interest to be claimed u/s 24.
Principal cap- Subject to other 80C benefits claimed, to a maximum of 1 lakh.
I have to consider the Annual Value of my rented house in city A
Annual value= Rental income- Municipal Taxes
Income from house property= Annual value- 30% annual value- Housing Loan interest.
I can claim HRA for my stay in city B
b)House in A is vacant / my parents stay:
House in A is considered as Self-occupied and Annual value=0.
Cap on claiming interest on loan= 1.5 lakh
I can claim HRA for my stay in city B
2) I own only one house and it is in city B, I stay in rented Accommodation in city B (because my own house is far from workplace)
I can claim HRA for my stay in city B.
I can claim Principal and Interest of home loan.
a)if it is rented out:
I need to consider the rental income and compute Annual value while deciding the income from house property
b)if it is lying vacant/my parents stay:
I need to consider the Notional Rental Income and consider the property deemed to be let out (Even if I don’t receive income from it as rent) while deciding the income from house property.
This house is considered as self occupied property and i can claim max. 1.5 lakh interest on housing loan.

If so, how can I declare a property as self occupied and still show notional rental income. It isn’t logical right?

The basic underlying fact is if a house is said to be self occupied, There is a cap imposed on Interest on housing loan-1.5 lakh.
if it is rented out/ deemed to be let out(If the 2nd property is in same city as of the 1st property), there is no cap on interest on housing loan.
Please correct me if i am wrong in any of the above areas.
Let me pose a small situation as example.
My first house is in city A. There is no outstanding loan taken for this and it is acquired many years before. It is rented out.
I stay in city B.
My second house is in city C. I have taken a loan for this and construction is completed just now.
My parents are going to stay there and i will leave it vacant in future.
So, I can do the following:
Claim HRA for my stay in city B.
Show rental income and compute income from house property in city A according to things discussed above. Eg: Income from this property is 70000 this year
Show my house in city C as self-occupied. annual value=0 and claim interest for housing loan subject to max of 1.5 lakh. Eg: income from this property is -1.5 lakh this year
I can set off income from both the properties (70000-150000= -80000) and report a total loss of 80000 from these two house properties.
Please let me know if my calculation is right.

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