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Your gain is the sale price (less closing costs) in excess of your basis. Your basis is the purchase price plus the cost of any improvements you have made. There is no obligation to reinvest the proceeds from sale and your equity is not relevant to the calculation of profit. Your gain is figured as above and Section 121 of the Internal Revenue Code
allows you to exclude up to $250,000 of that gain ($500,000 if married) because it's your principal residence no matter what you do with the proceeds.
Section 121 provides as follows:
"26 U.S. Code § 121 - Exclusion of gain from sale of principal residence
(a) ExclusionGross income
shall not include gain from the sale or exchange of property if, during the 5-year period ending on the date of the sale or exchange, such property has been owned and used by the taxpayer as the taxpayer’s principal residence for periods aggregating 2 years or more.
(1) In general
The amount of gain excluded from gross income under subsection (a) with respect to any sale or exchange shall not exceed $250,000.
(2) Special rules
for joint returns
In the case of a husband and wife who make a joint return for the taxable year of the sale or exchange of the property—
(A) $500,000 Limitation for certain joint returns
Paragraph (1) shall be applied by substituting “$500,000” for “$250,000” if—
(i)either spouse meets the ownership requirements of subsection (a) with respect to such property;
(ii)both spouses meet the use requirements of subsection (a) with respect to such property; and
(iii)neither spouse is ineligible for the benefits
of subsection (a) with respect to such property by reason of paragraph (3)."
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