A $30-$year maturity bond making annual coupon payments with a coupon rate of $14\mathrm{.}0\%$ has duration of $10\mathrm{.}04$ years and convexity of $147\mathrm{.}1.$ 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 to $2$ decimal places.$)$

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

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

d$-1.$ What is the percent error for each rule, if its yield to maturity falls to $9\%?($Enter your answers as a positive value. Do not round intermediate calculations. Round "Duration Rule" to $2$ decimal places and "Duration$-$with$-$Convexity Rule" to $3$ decimal places.$)$

d$-2.$ What do you conclude about the accuracy of the two rules?

multiple choice $1$

The duration rule provides more accurate approximations to the actual change in price.

The duration$-$with$-$convexity rule provides more accurate approximations to the actual change in price.

e$-1.$ Find the price of the bond if it's yield to maturity rises to $11\%.($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

e$-2.$ What price would be predicted by the duration rule, if it's yield to maturity rises to $11\%?($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

e$-3.$ What price would be predicted by the duration$-$with$-$convexity rule, if it's yield to maturity rises to $11\%?($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

e$-4.$ What is the percent error for each rule? $($Do not round intermediate calculations. Round "Duration Rule" to $2$ decimal places and "Duration$-$with$-$Convexity Rule" to $3$ decimal places.$)$

e$-5.$ Are your conclusions about the accuracy of the two rules consistent with parts $($a$)($d$)?$

multiple choice $2$

Yes

No