What is the duration of a 3year 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 
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 3year bond is calculated as $2959.93 / $1078.73 = 2.75 years
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