Question $1(11$ marks$)$

On $1$ April $2024,$ you've just purchased a $10-$year bond issued by MTR Corporation to finance the future railway development. The bond has a face value of $$1,000$ and carries $8\%$ coupon, paid semi$-$annually. The yield of the bond is $($APR$)10\%,$ compounded semi$-$annually.

$($a$)$ How much did you pay to buy the bond on $1$ April $2024?$

$(4$ marks$)$

$($b$)$ Is the bond a par bond, discount bond or premium bond? Explain.

$(2$ marks$)$

$($c$)$ On $31$ March $2025,$ the bond becomes a par bond as its yield has decreased from $($APR$)10\%$ to $($APR$)x\%,$ compounded semi$-$annually.

$($i$)$ What is the value of $x?$ Explain.

$(2$ marks$)$

$($ii$)$ If you sell the bond immediately after receiving the $($second$)$ coupon, calculate the capital gain yield.

$(3$ marks$)$