A $30-$year maturity bond making annual coupon payments with a coupon rate of $14\mathrm{.}5\%$ has duration of $11\mathrm{.}32$ years and convexity of $185\mathrm{.}2.$ The bond currently sells at a yield to maturity of $8\%.$

Required:

a$.$ Find the price of the bond if its yield to maturity falls to $7\%.($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Price of the bond

b$.$ What price would be predicted by the duration rule, if its yield to maturity falls to $7\%?($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Predicted price