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 $2024.$

$($c$)$ What is the current duration of instrument $B?$ Express your answer in terms of years and round your answer to three decimal places. Assume the yield rate is $j_2=4\mathrm{.}19\%$ p$.$a$.$

a$.2\mathrm{.}420$

b$.2\mathrm{.}880$

c$.4\mathrm{.}840$

d$.5\mathrm{.}761$