For an upvote full working must be shown, and each step of the calculation must be correct. Then the final answer must be correct to the decimal place.

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 $344$ units of instrument A and $426$ 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 $j_2=3\mathrm{.}26\%$ 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 $j_2=4\mathrm{.}19\%$ p$.$a$.$ and Joan has just received

the coupon payment.

a$.99\mathrm{.}4443$

b$.97\mathrm{.}8143$

c$.94\mathrm{.}0673$

d$.97\mathrm{.}4037$