Now, in order to find the duration and convexity of a 8% coupon bond making semiannual coupon payments if it has three years until maturity and a yield to maturity of 10%, we conduct calculations in the following table.

As you can see in the table the bond price is $949.24, modified duration is 5.5880 years and the convexity is 8.5765.

(1) If the bond YTM increases 2% to 12%, what is the percent change in the bond price estimated based on the modified duration rule? (Refer to #9 in end-of-chapter problems and page 20 in the teaching note)

(2) If the bond YTM increases 2% to 12%, what is the percent change in the bond price estimated based on the convexity rule? (Refer to #26 in end-of-chapter problems and page 44 in the teaching note)

(3) Calculate the actual bond price with 8% semiannual coupon payments, YTM of 12%, and 3 year maturity. What is the actual percent change in the price?

Time until Period payment Payment 3.0 $1.040 Column Sums Payment discounted at PMT/(1 y/2) t 38.0952 36.2812 34.5535 32.9081 31.3410 776.0640 949.24 Timex Next Time X Time X weight weight weight (wt discounted 0.0401 0.0201 0.0201 0.0382 0.0382 0.0573 0.0546 0.1092 0.0364 0.0347 0.0693 0.1733 0.0330 0.0825 0.2476 2.4527 8.5844 0.8176 9.1920 2.7174 8.7542 Divide by 1 y/2 2.5880