Consider Bond B with a face value of $300,000 to be repaid at maturity. The maturity of the security is 2 years. The coupon rate is 4% per annum and coupon payments are made semi annually. The current market rate is 4% p.a. What is the security’s duration (round your answer to two decimals)?Round your final answer to 2 decimal places.E.g. if the final answer is -3.59 years, type -3.59 in the answer box. If the final answer is 3.59 years, type 3.59 in the box .
Question
Consider Bond B with a face value of $300,000 to be repaid at maturity. The maturity of the security is 2 years. The coupon rate is 4% per annum and coupon payments are made semi annually. The current market rate is 4% p.a. What is the security’s duration (round your answer to two decimals)?Round your final answer to 2 decimal places.E.g. if the final answer is -3.59 years, type -3.59 in the answer box. If the final answer is 3.59 years, type 3.59 in the box .
Solution
The duration of a bond is a measure of the weighted average time until the bond's cash flows are received. It is calculated by multiplying each cash flow by the time at which it is received, and then summing these products.
For a bond with semi-annual coupon payments, the cash flows occur every six months. The bond's cash flows are the coupon payments and the face value at maturity.
The coupon payment is 4% of the face value divided by 2 (because the payments are semi-annual), which is 6,000.
The cash flows are:
- $6,000 at 6 months
- $6,000 at 12 months
- $6,000 at 18 months
- $306,000 at 24 months (the final coupon payment plus the face value)
The duration is calculated as:
(6/12 * 6,000 + 18/12 * 306,000) / $300,000 = 1.94 years
So, the duration of the bond is 1.94 years.
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