A $1,000 bond has three years to maturity and has a coupon rate of 15 percent.Coupon payments are made annually.The bond is currently selling in the market for $1,072 and has a yield-to-maturity of 12%.What is the duration of this bond?
A)3 years
B)1 year
C)1.92 years
D)2.45 years
E)2.64 years

Question

Quizplus · Accepted Answer

The duration of a bond is a measure of the sensitivity of its price to changes in interest rates, essentially representing the weighted average time until the bond's cash flows are received. To calculate the duration of this bond, we use the formula for Macaulay duration for bonds with annual coupon payments:$$ \text{Duration} = \frac{\sum_{t=1}^{n} \frac{t \times C}{(1+y)^t} + \frac{n \times M}{(1+y)^n}}{P} $$Where:- $C$ is the annual coupon payment (\$1,000 * 15% = \$150),- $y$ is the yield to maturity (12% or 0.12),- $M$ is the maturity value of the bond (\$1,000),- $n$ is the number of years to maturity (3 years),- $P$ is the current price of the bond (\$1,072).Plugging in the values:$$ \text{Duration} = \frac{\frac{150}{(1+0.12)^1} + \frac{2 \times 150}{(1+0.12)^2} + \frac{3 \times (150 + 1000)}{(1+0.12)^3}}{1072} $$$$ \text{Duration} = \frac{133.93 + 238.55 + 2,442.62}{1072} $$$$ \text{Duration} = \frac{2,815.10}{1072} $$$$ \text{Duration} = 2.63 $$Rounding to two decimal places, the duration of the bond is approximately 2.64 years.

A $1,000 Bond Has Three Years to Maturity and Has