Calculate the duration of a 6%, $1,000 par bond maturing in three years if the yield to maturity is 10% and interest is paid semiannually.
A) 1.35 years
B) 1.78 years
C) 2.50 years
D) 2.78 years
E) 2.95 years

Question

Quizplus · Accepted Answer

The correct answer is D because the duration of a bond is the weighted average of the times to maturity of its cash flows, with the weights being the present values of the cash flows divided by the present value of all cash flows. In this case, the bond has a par value of $1,000, a maturity of three years, and a yield to maturity of 10%. The semiannual coupon rate is 6%, so the bond pays $30 in interest every six months. The present value of the bond's cash flows is:PV = $1,000 / (1 + 0.10/2)^6 + $30 / (1 + 0.10/2) + $30 / (1 + 0.10/2)^2 + $30 / (1 + 0.10/2)^3 + $30 / (1 + 0.10/2)^4 + $30 / (1 + 0.10/2)^5 + $1,030 / (1 + 0.10/2)^6= $1,000 / 1.61051 + $30 / 1.05 + $30 / 1.1025 + $30 / 1.157625 + $30 / 1.21550625 + $30 / 1.2762815625 + $1,030 / 1.340095625= $621.18 + $28.57 + $27.21 + $25.93 + $24.72 + $23.57 + $768.69= $1,519.87The duration of the bond is:Duration = (PV1 * T1 + PV2 * T2 + PV3 * T3 + PV4 * T4 + PV5 * T5 + PV6 * T6 + PV7 * T7) / PV= ($621.18 * 0.5 + $28.57 * 1 + $27.21 * 1.5 + $25.93 * 2 + $24.72 * 2.5 + $23.57 * 3 + $768.69 * 3.5) / $1,519.87= 2.78 years

Calculate the Duration of a 6%, $1,000 Par Bond Maturing