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It depends. If the amount of your inheritance includes a portion that is interest or capital gains you would be responsible for taxes for that portion. Usually there is a step up in basis at an individual's death. This means that if your grand parents owns assets the basis of the assets would be the fair market value of the asset at the time of death. So usually the capital gain on the sale of assets are minimum. The step up in basis is true if your grandparents individually owned the assets, or the assets were owned in a revocable trust. If the assets were owned in an irrevocable trust then there would be no step up in basis and the capital gain would be larger.