$1\mathrm{.}2\mathrm{.}3$ a$.1)$ Given the below semi$-$annual rates, find the zero$-$prices for Z $(0,0\mathrm{.}5),$ Z $(0,1),$ Z $(0,$

$1\mathrm{.}5)$

Year Rate

$0\mathrm{.}55\mathrm{.}60\%$

$15\mathrm{.}40\%$

$1\mathrm{.}55\mathrm{.}25\%$

a$\mathrm{.}2)$ Find the continuously compounded rate for all the above given the Z $(0,0\mathrm{.}5),$ Z $(0,1),$ Z

$(0,1\mathrm{.}5)$

b$)$ Given the discount factor Z$(0,1)=0\mathrm{.}9091,$ find the interest rates

i$)$ annual compounding interest rate

ii$)($annualized$)$ semi$-$annual compounding interest rate

iii$)($annualized$)$ monthly compounding interest rate

iv$)($annualized$)$ continuously compounding interest rate