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 $2013$ to create this portfolio and this portfolio is composed of $351$ units of instrument A and $385$ 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 $j_2=3\mathrm{.}01\%$ 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$.$

a$.49\mathrm{.}8010$

b$.69\mathrm{.}8284$

c$.49\mathrm{.}1237$

d$.48\mathrm{.}7600$

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 $2013$ to create this portfolio and this portfolio is composed of $351$ units of instrument A and $385$ 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 $j_2=3\mathrm{.}01\%$ 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 $j_2=4\mathrm{.}27\%$ p$.$a$.$ and Joan has just received

the coupon payment.

a$.98\mathrm{.}5471$

b$.89\mathrm{.}4273$

c$.97\mathrm{.}0421$

d$.96\mathrm{.}4871$