Problem $3.(2$ points$)$

Suppose that the term structure of interest rates is

A $30-$year Treasury bond was issued $28$ years ago and a $10-$year Treasury note was

issued $8$ years ago $($so that they have the same final maturity$).$ The $30-$year Treasury

bond pays a semi$-$annual coupon at a $10\mathrm{.}625\%$ annual rate. The $10-$year Treasury

note pays a semi$-$annual coupon at $4\mathrm{.}25\%$ annual rate. What is the spread between

the yield$-$to$-$maturity of the two bonds?

Suppose that $($in an instant$)$ the yield curve had steepened as follows

How does the spread in the yield$-$to$-$maturity of the two coupon bonds changes?