A $30-$year maturity bond has a $9\%$ coupon rate, paid annually. It sells today for $$897\mathrm{.}42.$ A $20-$year maturity bond has a $8\mathrm{.}5\%$ coupon rate, also paid annually. It sells today for $$909\mathrm{.}5.$ A bond market analyst forecasts that in five years, $25-$year maturity bonds will sell at yields to maturity of $10\%$ and that $15-$year maturity bonds will sell at yields of $9\mathrm{.}5\%.$ Because the yield curve is upward$-$sloping, the analyst believes that coupons will be invested in short$-$term securities at a rate of $8\%.$

Required:

a$.$ Calculate the expected rate of return of the $30-$year bond over the five$-$year period. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

b$.$ What is the expected return of the $20-$year bond over the five$-$year period? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$