Today is $1$ July $2024,$ William plans to purchase a corporate bond with a coupon rate of j$2=3\mathrm{.}65\%$ p$.$a$.$ and face value of $100.$ This corporate bond matures at par. The maturity date is $1$ January $2029.$ The yield rate is assumed to be j$2=4\mathrm{.}5\%$ p$.$a$.$ Assume that this corporate bond has a $9\mathrm{.}6\%$ chance of default in any six$-$month period during the term of the bond. Assume also that, if default occurs, William 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$.39\mathrm{.}038$

b$.98\mathrm{.}297$

c$.95\mathrm{.}159$

d$.42\mathrm{.}330$