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 $2024.$

$($d$)$ Based on the price in part a and part b$,$ and the duration value in part c$,$ calculate the current duration of Joan's portfolio. Express your answer in terms of years and round your answer to

two decimal places.

a$.4\mathrm{.}83$

b$.6\mathrm{.}63$

c$.6\mathrm{.}02$

d$.4\mathrm{.}55$