Today is $1$ July $2021.$ Jacob has a portfolio which consists of two different types of financial instruments $($henceforth referred to as instrument A and instrument B$).$ Jacob purchased all instruments on $1$ July $2016$ to create this portfolio and this portfolio is composed of $272$ units of instrument A and $395$ 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$2=3\mathrm{.}29\%$ p$.$a$.$ and face value of $100.$ This bond matures at par. The maturity date is $1$ January $2024.$

$($a$)$ Calculate the current price of instrument A per $$100$ face value $($today$\text{'}$s value$).$ Round your answer to four decimal places. Assume the yield rate is j$2=4\mathrm{.}13\%$ p$.$a

a$.$

$57\mathrm{.}5871$

b$.$

$50\mathrm{.}2586$

c$.$

$70\mathrm{.}6470$

d$.$

$56\mathrm{.}4220$