Compound interest problem

$($a$)$ A mortgage$-$backed security trades at a premium of $100$ basis points above the treasury interest rate of $5\%.$ What is the yield to maturity on the mortgage$-$backed

security?

$($b$)$ If the interest rate is $6\%,$ what is the price of a Treasury bill that matures one year

from today? Apply simple compounding.

$($c$)$ Suppose the five$-$year Treasury yield is $5\%$ and the corresponding municipal bond

yield is $4\%.$ What is the marginal tax rate embedded in the interest$-$rate spread?

$($d$)$ Suppose the one$-$year Treasury yield is $6\%$ and expected inflation rate is $5\%.$ What is the expected real rate of return?