a$.$ An investor is in the $15$ percent federal tax bracket and pays a $6$ percent state tax rate and $3\mathrm{.}5$ percent in local income taxes. If this investor has the option to receive a $5\%$ municipal bond rate, how much should corporate bond rate be$,$ so the investor prefers investing on corporate bonds? $($show your work$)$

b$.$ Let's say you have the option to invest in municipal bonds that come with $3\%$ interest rate and corporate bonds that come with $4\mathrm{.}5\%$ interest rate. How much should tax rates be$,$ so you are indifferent between the two options? $($show your work$)$