The face value of $4$ risk$-$free zero$-$coupon bonds below is $$1,000.$

$\backslash$table$[[$Bond$,$Time to Maturity,Price$],[$A$,3$ months,$980],[$B$,6$ months,$960],[$C$,9$ months,$930],[$D$,12$ months,$900]]$

$($a$)[2$ marks$]$ Construct the spot $($zero$)$ curve; ie$,$ calculate the $3-$month, $6-$month, $9-$month, $12$month spot rate $($quarterly APR$).$

$($b$)[2$ marks$]$ Based on the spot $($zero$)$ curve, construct the forward curve; ie$,$ calculate the forward rates $($quarterly APR$)f_{0\text{m}\text{o}\text{n}3\text{m}\text{o}\text{n}},f_{3\text{m}\text{o}\text{n}6\text{m}\text{o}\text{n}},f_{6\text{m}\text{o}\text{n}9\text{m}\text{o}\text{n}},f_{9\text{m}\text{o}\text{n}12\text{m}\text{o}\text{n}}.$

$($c$)[3$ marks$]$ A risk$-$free quarterly$-$coupon bond $E$ is in the same market. It has a face value of $$1000,10\%$ coupon rate and $1$ year to maturity. Price the coupon bond with the forward curve. What is the yield to maturity of bond E$?[$note: you may do a sanity check by pricing the bond with the spot curve.$]$