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 $222$ units of instrument A and $430$ 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$2=3\mathrm{.}14\%$ 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.

Question $8$Answer

a$.$

$4\mathrm{.}26$

b$.$

$4\mathrm{.}11$

c$.$

$6\mathrm{.}37$

d$.$

$5\mathrm{.}74$