Today is $1$ July $2021,$ Jacob plans to purchase a corporate bond with a coupon rate of j$2=4\mathrm{.}29\%$ p$.$a$.$ and face value of $100.$ This corporate bond matures at par. The maturity date is $1$ January $2024.$ The yield rate is assumed to be j$2=3\mathrm{.}75\%$ p$.$a$.$ Assume that this corporate bond has a $5\mathrm{.}7\%$ chance of default in any six$-$month period during the term of the bond. Assume also that, if default occurs, Jacob will receive no further payments at all. Calculate the purchase price for $1$ unit of this corporate bond. Round your answer to three decimal places.

a$.$

$72\mathrm{.}808$

b$.$

$76\mathrm{.}512$

c$.$

$100\mathrm{.}699$

d$.$

$101\mathrm{.}788$