Question $5[20$ points$].$ Suppose that zero interest rates with semiannual compounding are as follows:

$\backslash$table$[[$Maturity$($ years$),$Rate $(\%$ per annum$)],[0\mathrm{.}5,2],[1,2\mathrm{.}5],[1\mathrm{.}5,3],[2,3\mathrm{.}5]]$

a$.$ Calculate the forward rates with continuous compounding from $0\mathrm{.}5$ years to $1$ year and forward rate from $1$ year to $1\mathrm{.}5$ years.

b$.$ Value an FRA where you will pay $3\mathrm{.}2\%$ with semiannual compounding from $1$ year to $1\mathrm{.}5$ years on $$1$ million.