Your bank is offering you an account that will pay $24\%$ interest $($an effective two$-$year rate$)$ in total for a two$-$year deposit. Determine the equivalent discount rate for the following periods:

a$.$ Six months

b$.$ One year

c$.$ One month

$($Note: Be careful not to round any intermediate steps less than six decimal places.$)$

a$.$ Six months

The equivalent discount rate for a period length of six months is $\%.($Round to two decimal places.$)$