Question

What is the duration of a 3-year bond with $1,000 par value, 10% coupon and 7% YTM?

Question 12 options:

	3.44 years
	2.34 years
	2.93 years
	2.75 years

Answer 1

Solution: Correct answer is 2.75 years.  Explanation below:

Formula for bond duration is as follows:

Bond Duration=Current bond price(∑t=1n​(1+y)tt∗C​+(1+y)nn∗M​)​

where:C=periodic coupon paymenty=periodic yieldM=the bond’s maturity valuen=duration of bond in periods​

Time Period	Cash Flow	PV of Cash Flow	PV of time weighted Cash Flow
1	Coupon Payment = $100	$100/(1+7%) = $93.46	$93.46 x 1 = $93.46
2	Coupon Payment = $100	$100/(1+7%)^2 = $87.34	$86.34 x 2 = $172.68
3	Coupon + Face Value = $1100	$1100/(1+7%)^3 = $897.93	$897.93 x 3 = $2693.79
		Sum = $1078.73	Sum= $2959.93

The Macaulay duration for the 3-year bond is calculated as $2959.93 / $1078.73 = 2.75 years