Siobh$$n is planning to purchase an Australian Treasury bond with a coupon rate $(2)$ of $4\mathrm{.}78\%$ p$.$a$.$ and face value of $$100.$ The maturity date of the bond is $15$ May $2033.$

If Siobhan purchased this bond on $4$ May $2018,$ what is her purchase price $($rounded to four decimal places? Assume a yield rate of $1\mathrm{.}35\%$ p$.$a$.$ compounded half$-$yearly. Siobh$$n needs to pay $24\mathrm{.}9\%$ of coupon payments and capital gains in tax payments. Assume that all tax payments are paid immediately.

$$ a$.$ $$140\mathrm{.}2493$

$$ b$.$ $$137\mathrm{.}9970$

$$ c$.$ $$148\mathrm{.}7430$

$$ d$.$ $$111\mathrm{.}721$