Consider a security with a face value of $100 000, which is to be repaid at maturity.The security pays an annual coupon of 8% and has a maturity of three years.The current discount rate is 10%.What is the security's duration (round to two decimals)?
A)2.78 years
B)3 years
C)0.36 years
D)1.94 years

Question

Quizplus · Accepted Answer

Duration measures the sensitivity of a bond's price to changes in interest rates, essentially representing the weighted average time until a bond's cash flows are received. To calculate the duration of this security, we use the formula for Macaulay duration, which is the weighted average time to receive the bond's cash flows, discounted by the present value of those cash flows. The calculation involves discounting each of the cash flows (annual coupons and the final principal repayment) back to their present value, multiplying each by the time until the cash flow occurs, summing these values, and then dividing by the total present value of all cash flows. Given the information, the correct duration is approximately 2.78 years, indicating that this is the weighted average time until the investor receives the bond's cash flows.

Consider a Security with a Face Value of $100 000