Question

Find the duration of a 7.2% 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 10.0%? Note: The face value of the bond is $100. (Do not round Intermediate calculations. Round your answers to 4 decimal places.) 6% YTM 10% YTM

Answer 1

We need to find the macaulay duration , which is the weighted sum of the present values of the cash flows as shown in the table below,

year(Tf)	Cash flow	PV of Cash Flow @YTM =6% [ CF / (1+ YTM)^f]	(PV/Total)(Tf)	PV of Cah Flow @YTM =10% [ CF / (1+ YTM)^f]	(PV/Total)(Tf)
0.5	3.6	3.495145631	0.016925593	3.428571429	0.018454207
1	3.6	3.393345273	0.032865229	3.265306122	0.035150871
1.5	3.6	3.294509974	0.047861984	3.109815355	0.05021553
2	3.6	3.198553372	0.061957261	2.961728909	0.063765753
2.5	3.6	3.105391624	0.075190851	2.820694199	0.07591161
3	103.6	86.76336899	2.520961871	77.30791509	2.49664852
	Total	103.2503149	2.755762791	92.89403111	2.740146492

The duration for YTM @6% is 2.755 yrs

The duration for YTM @10% is 2.740 yrs