Problem $5$: The term structure of the interest rate for the next $5$ years is found to be

$(s1,s2,s3,s4,s5)=(y\%,3\%,3\mathrm{.}5\%,(y+0\mathrm{.}5)\%,5\%)$

It is given that the forward rate $f_{2,4}=3\mathrm{.}8\%.$ Find, to $3$ signifcant fgures,

$($i$)$ the value of $y$

$($ii$)$ the price of a $4-$year zero$-$coupon bond with face value $$100,$ and

$($iii$)$ the yield of a $2-$year bond with face value $$100$ that pays $4\%$ coupons annually and can

be redeemed at a price of $$105.$