Question

A bond pays annual interest. Its coupon rate is 8.3%. Its value at maturity is $1,000. It matures in 4 years. Its yield to maturity is currently 5.3%. The modified duration of this bond is ______ years.

3.19

4.00

3.41

3.59

Answer 1

Coupon rate	8.3%
YTM	5.3%
Par value of bond	1000
			Cash flow * PV factor
Year	Cash flow	PV factor	PV of cashflows	Year * PV of cash flows
1	83.0	0.950	78.82	78.82
2	83.0	0.902	74.86	149.71
3	83.0	0.856	71.09	213.26
4	83.0	0.813	67.51	270.04
4	1,000.0	0.813	813.37	3,253.47
	Total		1,105.64	3,965.30

Muculay's duration = 3,965.30 / 1,105.64 =  3.59

Modified duration = Muculay's duration / ( 1 + YTM )

Modified duration = 3.59 / ( 1 + 0.053 )

Modified duration = 3.59 / 1.053 = 3.41

Hence, third option 3.41, is the correct answer.