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To answer your question about using your inheritance for capital improvements on your home, the answer is no, this will not lower any capital gains tax that you may owe on the sale of your mother's property. There is nothing in the IRS regulations that allows you to reduce your capital gains by virtue of using the inheritance money for a specific reason. If you have long term capital losses from loss on investments, you may use these losses to offset some or all of your gain on the sale of the home.
As a side note, you may want to check and be certain that you have correctly estimated the amount of capital gains tax that will be due as a result of selling your mother's home. If you and your brother inherited this home from your mother, then your basis in the home would have been "stepped up" to whatever the fair market value was of the home on the day your mother passed away. Your gain would then be the selling price less your basis. Since your mother only passed away 8 months ago, typically in a situation like that there is not normally a monumental difference in the selling price versus what the home was worth when she died. That being the case, you would not normally have much of a gain, if any at all. I am just giving you this information so you can double check the information you were given on how much capital gains tax you may be responsible for.
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