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 $2019$ to create this portfolio and this portfolio is composed of $279$ units of instrument A and $452$ 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$2=3\mathrm{.}39\%$ 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$2=4\mathrm{.}27\%$ p$.$a$.$

Answers

a$.$

$49\mathrm{.}1237$

b$.$

$64\mathrm{.}1702$

c$.$

$69\mathrm{.}8284$

d$.$

$62\mathrm{.}8288$