Today is $1$ July, $2019.$ Camilla has a portfolio which consists of two different types of financial instruments $($henceforth referred to as instrument A and instrument B$).$ Camilla purchased all instruments on $1$ July $2011$ to create this portfolio, which is composed of $22$ units of instrument A and $22$ units of instrument $B.$

Instrument A is a zero$-$coupon bond with a face value of $$100.$ This bond matures at par. Its maturity date is $1$ January $2029.$

Instrument B is a Treasury bond with a coupon rate of $j_2=3\mathrm{.}46\%$ p$.$a$.$ and a face value of $$100.$ This bond matures at par. Its maturity date is $1$ January $2022.$

What is the duration of instrument $B?$ Express your answer in terms of years and round your answer to three decimal places. Assume a yield rate of $j_2=2\mathrm{.}99\%$ p$.$a$.$

a$.4\mathrm{.}834$ years

b$.2\mathrm{.}876$ years

c$.5\mathrm{.}753$ years

d$.2\mathrm{.}417$ years