You have a choice between the following two identical homes: Home $A$ is priced at $$150,000$ with $80$ percent financing at a $10\mathrm{.}5$ percent interest rate for $20$ years. Home B is priced at $$160,000$ with an assumable mortgage of $$100,000$ at $9$ percent with $20$ years remaining. Monthly payments are $$899\mathrm{.}73.$ A second mortgage for $$20,000$ can be obtained at $13$ percent interest for $20$ years. At what opportunity rate of return $($IRR$)$ would the borrower be indifferent between Home A and Home B $($expressed in decimals, rounded to three digits$)?$

A