First-Time Homebuyer Act of 2021 This bill modifies the first-time homebuyer tax credit. Specifically, it increases the allowable dollar amount of the credit from $8,000 to $15,000, revises the income formula for determining the maximum allowable credit amount, replaces the limitation on the credit based on purchase price (currently, $800,000) with a limitation based on area median purchase price, and revises rules relating to recapture of the credit and to members of the Armed Forces.