Consider a semi$-$annual coupon bond with a coupon rate of $6\%,$ par value $1000$ and $2$ years to maturity.

$($a$)$ What would be the price of this bond if the required return were $5\%$ per year?

$[10$ marks$]$

$($b$)$ If the required yield increased from $5\%$ to $6\%,$ by what percentage would the price of this bond change?

$[5$ marks$]$