Jill bought a house for $$800,000$ and sold it for $$1$ million after $5$ years. She made no improvement on the house. When she was selling, she paid various fees and commissions; the total amount of such costs was $8\%$ of the selling price. Her average capital gain tax rate was $12\%$ and her marginal capital gain tax rate was $15\%.$ She was single. Her after$-$tax income increased by $ $\_\_\_\_\_\_\_\_\_\_$if she took home sale tax exemption.