A zero coupon bond has a Macaulay duration equal to its maturity, ie in this case 5 years. We can calculate modified duration from Macaulay duration by using the following relationship:
Modified duration = Macaulay duration/(1 + y) where y is the yield.
Therefore the correct answer is 5 / (1.05) = 4.76.
Or intuitively, all the other answers appear clearly incorrect: 5 and 5.25 are too high, and 4 is too low. Therefore the only reasonable choice is 4.76.
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