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 $2015$ to create this portfolio and this portfolio is

composed of $235$ units of instrument A and $396$ 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 $j_2=2\mathrm{.}93\%$ 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 $j_2=$

$3\mathrm{.}83\%$ p$.$a$.$

a$.4\mathrm{.}856$

b$.2\mathrm{.}892$

c$.5\mathrm{.}784$

d$.2\mathrm{.}428$