Approximating Bond Price Changes Using Duration and Convexity Rules

A 30-year maturity bond making annual coupon payments with a coupon rate of 16.0% has duration of 10.55 years and convexity of 161.7. The bond currently sells at a yield to maturity of 9%.

a. Find the exact price of the bond if its yield to maturity falls to 8%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price of the bond $

b. Assume that you need to make a quick approximation using the duration rule (instead of the exact calculation in part a above). What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Predicted price $

c. Assume that you need to make a quick approximation using the duration-with-convexity rule (instead of the exact calculation in part a above). What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Predicted price $

d-1. What is the percent error for each rule? [Hint: percent error is the deviation from the exact price, divided by the exact price. It indicates the extent to which the approximated price differs from the exact price. A smaller percent error indicates more precise approximation.] (Enter your answer 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.)

	Percent Error
YTM	Duration Rule	Duration-with- Convexity Rule
8%	%	%

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

	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 exact price of the bond if it's yield to maturity rises to 10%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price of the bond $

e-2. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Predicted price $

e-3. What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Predicted price $

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.)

	Percent Error
YTM	Duration Rule	Duration-with- Convexity Rule
10%	%	%

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