USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
A $1000 par value bond with four years to maturity and a 5 percent coupon has a yield to maturity of 6 percent. Interest is paid annually.
-Refer to Exhibit 13.3. Calculate the modified duration for the bond.
A) 3.51 years
B) 3.61 years
C) 3.72 years
D) 4.38 years
E) 7.44 years

Question

Quizplus · Accepted Answer

The correct answer is A because the modified duration for the bond is 3.51 years. This can be calculated using the formula:Modified duration = (PV of coupon payments / Bond price) * (1 + Yield to maturity)^-1 + (PV of principal payment / Bond price) * (1 + Yield to maturity)^-4where:PV of coupon payments = $50 * (1 - (1 + 0.06)^-4) / 0.06 = $186.31PV of principal payment = $1000 * (1 + 0.06)^-4 = $863.84Bond price = $1000 * (1 - (1 + 0.06)^-4) / 0.06 + $1000 * (1 + 0.06)^-4 = $943.40Therefore, modified duration = ($186.31 / $943.40) * (1 + 0.06)^-1 + ($863.84 / $943.40) * (1 + 0.06)^-4 = 3.51 years.