All sub$-$questions a$)-$ i$)$ relate to the following information:

Consider the $3$ bonds below, with different maturities, yields to maturity $($YTM$)$ and coupon rates:

$\backslash$table$[[$Maturity$,$YTM$,$Coupon Rat

$],[1,4\%,0\%$

$1)$ what is the price of the $3$ year coupon bond?

$2)$what is the $2$ year spot rate?

$3)$ what is the $3$ year spot rate?

$4)$ based on the zero yield curve you have derived, what is the $2$ year forward rate commencing in $1$ year

$5)$ what is the duration of the $3$ year coupon bond?

$6)$ with regard to the $3$ year coupon bond, use the duration approximation to determine the approximate percentage chane in the bond price if bond ytm decreases by $0\mathrm{.}25\%$

$7)$ what is the durarion of the perpetuity?