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An Apple annual coupon bond has a coupon rate of 6.9%, face value of $1,000, and...

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Finance

An Apple annual coupon bond has a coupon rate of 6.9%, facevalue of $1,000, and 4 years to maturity. If its yield to maturityis 6.9%, what is its Modified Duration? Answer in years, rounded tothree decimal places.

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4.1 Ratings (814 Votes)

Modified Duration = Duration / (1+YTM)

Duration = Sum [ Weight * Year ]

Year CF PVF @6.9% Disc CF Weight Duration
1 $      69.00     0.9355 $   64.55     0.0645          0.06
2 $      69.00     0.8751 $   60.38     0.0604          0.12
3 $      69.00     0.8186 $   56.48     0.0565          0.17
4 $      69.00     0.7658 $   52.84     0.0528          0.21
4 $ 1,000.00     0.7658 $ 765.75     0.7658          3.06
Duration          3.63

Modfied duration = Duration / ( 1+YTM)

= 3.63 / ( 1 + 0.069)

= 3.63 / 1.069

= 3.40%

Modified duartion is 3.40%
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