Exhibit 19.8
Use the Information Below for the Following Problem(S)
Consider two bonds, both pay annual interest. Bond C has a coupon of 6% per year, maturity of 5 years, yield to maturity of 6% per year, and a face value of $1000. Bond D has a coupon of 8% per year, maturity of 15 years, yield to maturity of 6% per year, and a face value of $1000.
-Refer to Exhibit 19.8.Calculate the modified duration for Bond D.

Question

Quizplus · Accepted Answer

The price of the bond = $1194.24 =
 $80 \left( \frac { 1 - \frac { 1 } { 1.06 ^ { 15 } } } { .06 } \right) + \frac { 1000 } { 1.06 ^ { 15 } }$ 
The present value of the weighted cash flows = $11640.32 =
80/(1.06)+ 160/(1.06)² + 240/(1.06)³ + 320/(1.06)⁴ + 400/(1.06)⁵ + 480/(1.06)⁶
+ 560/(1.06)⁷ + 640/(1.06)⁸ + 720/(1.06)⁹ + 800/(1.06)¹⁰ + 880/(1.06)¹¹
+ 960/(1.06)¹² + 1040/(1.06)¹³ + 1120/(1.06)¹⁴ + 16200/(1.06)¹⁵
Macaulay duration = 11640.32/1194.24 = 9.75
Or 9.8 years
Modified duration = 9.8/(1 + .06)= 9.2 years.

Exhibit 19.8 Use the Information Below for the Following Problem(S)