Consider two physically identical properties A and B$.$ Property A$\text{'}$s current asking price is $$570,000$ and Property B$\text{'}$s asking price is $$522,497.$ Property A$\text{'}$s current owner has a $25-$year remaining maturity assumable mortgage of $$473,100$ at a fixed mortgage rate of $11\mathrm{.}40\%.$ Property B$\text{'}$s current owner has a $25$ year remaining maturity non$-$assumable mortgage of $$473,100$ at a fixed mortgage rate. The current market mortgage rate for $25-$year maturity conventional $($not assumable$)$ mortgage is $13\mathrm{.}15\%.$ In either Case $($A or B$),$ the buyer would have the same amount $$473,100$ of $25-$year fixed rate mortgage financing. The Buyer's Alternative Investment Return is $14\mathrm{.}45\%.$

a$)$ given the current asking prices of the two properties, property A$\text{'}$s owner is trying to capture what $\%($rounded to $2$ decimals$)$ of the assumable mortgage's benefit $($of below market financing$)?$