Dana intends to invest $$78,000$ in either a Treasury bond or a corporate bond. The Treasury bond yields $5$ percent before tax, and the corporate bond yields $6$ percent before tax. Assume Dana's federal marginal rate is $24$ percent and she itemizes deductions.

Required:

a$-1.$ Assuming Dana's marginal state rate is $5$ percent, which of the two options should she choose?

a$-2.$ How much interest after$-$tax would Dana earn by investing in the corporate bond?

b$-1.$ If she were to move to another state where her marginal state rate would be $10$ percent, which of the two options should she choose?