The standard Treasury Bond futures contract has a face value of $$100,000,$ at least $15$ years to maturity and a coupon of $6\%,$ payable semi$-$annually. The quoted price of the futures contract is based on this standard bond. Instead of the standard bond, the short position chooses to deliver a treasury bond with a remaining maturity of $18$ years and a $4\%$ coupon, payable semi$-$annually. What conversion factor will be applied to the quoted price?

Question $5$ options:

$0\mathrm{.}796$

$1\mathrm{.}112$

$0\mathrm{.}769$

$0\mathrm{.}782$

$1\mathrm{.}106$