$($i$)$

A $30-$year maturity bond making annual coupon payments with a coupon rate of $15\mathrm{.}3\%$ has duration of $9\mathrm{.}97$ years and conve $144\mathrm{.}9.$ The bond currently sells at a yield to maturity of $10\%.$

Required:

a$.$ Find the price of the bond if its yield to maturity falls to $9\%.($Do not round intermediate calculations. Round your answer decimal places.$)$

Price of the bond

b$.$ What price would be predicted by the duration rule, if its yield to maturity falls to $9\%?($Do not round intermediate calculat Round your answer to $2$ decimal places.$)$

Predicted price

c$.$ What price would be predicted by the duration$-$with$-$convexity rule, if its yield to maturity falls to $9\%?($Do not round interme calculations. Round your answer to $2$ decimal places.$)$

Predicted price