Problem $16-20$ A $30-$year maturity bond has a $7\mathrm{.}2\%$ coupon rate,

paid annually. It sells today for $$873\mathrm{.}67.$ A $20-$year maturity bond

has a $6\mathrm{.}7\%$ coupon rate, also paid annually. It sells today for

$$886\mathrm{.}9.$ A bond market analyst forecasts that in five years, $25-$year

maturity bonds will sell at yields to maturity of $8\mathrm{.}2\%$ and $15-$year

maturity bonds will sell at yields of $7\mathrm{.}7\%.$ Because the yield curve

is upward sloping, the analyst believes that coupons will be

invested in short$-$term securities at a rate of $5\mathrm{.}1\%.$a$.$ Calculate the $($annualized$)$ expected rate of return of the

$30-$year bond over the $5-$year period. $($Round your answer to $2$

decimal places.$)$b$.$ What is the $($annualized$)$ expected return of the $20-$year bond?

$($Round your answer to $2$ decimal places.