Gerald is planning to purchase an Australian Treasury bond with a coupon rate $($j$2)$ of $2\mathrm{.}12\%$ and face value of $$100.$ The maturity date of the bond is $15$ May $2033.$ Gerald's bond matures at par.

If Gerald purchased this bond on $5$ May $2018,$ what is his purchase price $($rounded to four decimal places$)?$ Assume a yield rate of $3\mathrm{.}62\%$ pa$.$ compounded half$-$yearly, allowing for taxation. Gerald needs to pay tax at rate $26\mathrm{.}1\%$ on coupon payments. Assume the tax on coupon is paid immediately on the coupon payment date.

a$.$ $$77\mathrm{.}6999$

b$.$ $$77\mathrm{.}1011$

c$.$ $$77\mathrm{.}1024$

d$.$ $$76\mathrm{.}3186$