$6\mathrm{.}11$ Sylvia has received a $\backslash (\backslash$$ $500,000\backslash )$ inheritance from her favorite, recently deceased aunt in Hawaii. Sylvia is planning to purchase a condo in Hawaii in the same area where her aunt lived all her life and to rent it to vacationers. She hopes to make $\backslash (8\backslash \%\backslash )$ per year on this purchase over an ownership period of $20$ years. The condo's total first cost is $\backslash (\backslash$$ $500,000\backslash ),$ and she conservatively expects to sell it for $\backslash (90\backslash \%\backslash )$ of the purchase price. No annual M$\backslash$&O costs are considered in the analysis. $($a$)$ What is the capital recovery amount? $($b$)$ If there is a real boom in rental real estate $10$ years in the future, what sales price $($as a percentage of original purchase price$)$ is necessary at that time $($year $10)$ to realize the same amount as the $\backslash (8\backslash \%\backslash )$ return expected over the $20-$year ownership period?