It is $2018$ and Charles is thinking about buying an Australian

Treasury bond with a coupon rate of j$2=3\mathrm{.}17\%$ p$.$a$.$ and a

face value of $$100.$ The maturity date of the bond is $15$ May

$2033.$

If Charles purchased this bond on $5$ May $2018,$ what was his purchase price $($rounded to four decimal places$)?$

Assume a purchase yield of j$2=4\mathrm{.}48\%$ p$.$a$.$

$$ a$.$ $$87\mathrm{.}62$

$$ b$.$ $$87\mathrm{.}2829$

$$ c$.$ $$85\mathrm{.}6981$ d$.$ $$87\mathrm{.}2812$