Question

Find the duration of a 7.6% coupon bond making semiannually coupon payments if it has three years until maturity and has a yield to maturity of 6.0%. What is the duration if the yield to maturity is 12.0%? Note: The face value of the bond is $100. (Do not round intermediate)

Answer 1

Duration at YTM=6% is 2.7449 years

Duration at 12% Yield = 2.7203 years

Workings

Yield	6%
Bond	Period	1	2	3	4	5	6
	Cash-Flows	3.8	3.8	3.8	3.8	3.8	103.8
	PV of CFs	3.68932	3.581864	3.477538	3.376251	3.277913	86.93087
	Price	104.3338
	Weighted CFs	3.8	7.6	11.4	15.2	19	622.8
	PV of weighted CFs	3.68932	7.163729	10.43261	13.505	16.38957	521.5852
	Sum of weight. CFs	572.7654
	Duration	2.744871

Yield	12%
Bond A	Period	1	2	3	4	5	6
	Cash-Flows	3.8	3.8	3.8	3.8	3.8	103.8
	PV of CFs	3.584906	3.381986	3.190553	3.009956	2.839581	73.1749
	Price	89.18189
	Weighted CFs	3.8	7.6	11.4	15.2	19	622.8
	PV of weighted CFs	3.584906	6.763973	9.57166	12.03982	14.19791	439.0494
	Sum of weight. CFs	485.2077
	Duration	2.720326

Calculations are as below

Same formula is used with 12% yield.