Capital gain is the profit realized from the sale of a capital asset, such as a principal residence. The calculation begins with the "Amount Realized," which is the property's selling price minus the costs of the sale (e.g., brokerage commissions, closing costs). From this amount, the "Adjusted Basis" is subtracted. The Adjusted Basis is the original purchase price of the home, plus the cost of any capital improvements made during ownership, minus any depreciation taken. The resulting figure represents the capital gain (if positive) or capital loss (if negative) for tax purposes.

B. Amount Realized + Adjusted Basis: This calculation adds the sale proceeds to the cost basis, which does not represent profit and has no financial meaning in this context.

C. Adjusted Basis / Amount Realized: This formula calculates a ratio of cost to sale price, not the monetary gain or loss from the transaction.

D. Adjusted Basis - Amount Realized: This formula inverts the correct calculation. It would calculate a capital loss as a positive number and a gain as a negative number.

1. North Carolina Real Estate Commission. (2023). North Carolina Real Estate Manual. Chapter 15, Real Estate Taxation, p. 478. The manual explicitly states, "The basic formula for determining the amount of gain is: Amount Realized – Adjusted Basis = Capital Gain."

2. Internal Revenue Service (IRS). (2023). Publication 523, Selling Your Home. p. 10, "Figuring Gain or Loss." The worksheet for calculating gain directs the user to subtract the adjusted basis (Line 3) from the amount realized (Line 2) to determine the gain or loss (Line 4).

3. Ling, D. C., & Archer, W. R. (2021). Real Estate Principles: A Value Approach (6th ed.). McGraw-Hill Education. Chapter 14, "Income and Property Taxation," Section 14.2. The text defines capital gain as the net sale proceeds minus the adjusted tax basis.