Today is $1$ July $2021.$ Joan has a portfolio which consists of two different types of financial instruments $($henceforth referred to as instrument A and instrument B$).$ Joan purchased all instruments on $1$ July $2016$ to create this portfolio and this portfolio is composed of $242$ units of instrument A and $455$ units of instrument B$.$

Instrument A is a zero$-$coupon bond with a face value of $100.$ This bond matures at par. The maturity date is $1$ January $2030.$

Instrument B is a Treasury bond with a coupon rate of j$2=3\mathrm{.}14\%$ p$.$a$.$ and face value of $100.$ This bond matures at par. The maturity date is $1$ January $2024.$

$($b$)$ Calculate the current price of instrument B per $$100$ face value $($today$\text{'}$s value$).$ Round your answer to four decimal places. Assume the yield rate is j$2=3\mathrm{.}93\%$ p$.$a$.$ and Joan has just received the coupon payment.

a$.94\mathrm{.}9112$

b$.97\mathrm{.}7848$

c$.98\mathrm{.}1363$

d$.99\mathrm{.}7063$