A $30-$year$-$maturity bond has a $7\%$ coupon rate, paid annually. It sells today for $$867\mathrm{.}42.$ A $20-$year$-$maturity bond has a $6\mathrm{.}5\%$ coupon

rate, also paid annually. It sells today for $$879\mathrm{.}50.$ A bond market analyst forecasts that in five years, $25-$year$-$maturity bonds will sell at

yields to maturity of $8\%$ and $15-$year$-$maturity bonds will sell at yields of $7\mathrm{.}5\%.$ Because the yield curve is upward$-$sloping, the analyst

believes that coupons will be invested in short$-$term securities at a rate of $6\%.$

Required:

a$.$ Calculate the $($annualized$)$ expected rate of return of the $30-$year bond over the $5-$year period.

Note: Do not round your intermediate calculations. Round your answer to $2$ decimal places.

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

Note: Do not round your intermediate calculations. Round your answer to $2$ decimal places.