Your father-in-law would be responsible for whatever gain he realized from the sale of the house. His gain would be the difference between the sale price of $297,000 and whatever the fair market value of the house was at the time he inherited the home - NOT the original value of the home. His "basis" in the home is what the value was on the day it passed to him. The good news is that inherited property that is sold automatically qualifies for the long term capital gains tax rate which is currently capped at 15%, so no matter how long he held the property before selling it, he would owe no more than 15% on his gain.
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I am afraid there is no exemption on capital gains tax because of his age. There is a one-time exclusion allowed on the capital gains from the sale of your PRIMARY residence, but this is allowable for everyone and not just seniors. Sorry I didn't have better news.