Question

Find the duration of a 3% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 6.1%. What is the duration if the yield to maturity is 10.1%? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

YTM	Duration
6.1% YTM
10.1% YTM

Answer 1

YTM	Duration
6.1% YTM	2.9093
10.1% YTM	2.9038

Working:

Duration at YTM 6.1%

Period	Cash Flow	Discounting factor = 1/(1+R)^Y	PV of the cash flows = Cash flow x Df	Weighted cash flow = Period x Cash flow	Present value of weighted cash flow = Weighted Cash flow x Df
Y	CF	Df = 1/(1+6.1%)^Y	PV = CF x Df	WCF = CF x Y	WPV = WCF x Df
1	30	0.9425	28.2752	30	28.2752
2	30	0.8883	26.6496	60	53.2992
3	1030	0.8372	862.3649	3090	2587.0947
		Total = P =	917.2897	Total = WP =	2668.6691
		Duration = WP/P =	2.9093

Duration at YTM of 10.1%

Period	Cash Flow	Discounting factor = 1/(1+R)^Y	PV of the cash flows = Cash flow x Df	Weighted cash flow = Period x Cash flow	Present value of weighted cash flow = Weighted Cash flow x Df
Y	CF	Df = 1/(1+10.1%)^Y	PV = CF x Df	WCF = CF x Y	WPV = WCF x Df
1	30	0.9083	27.2480	30	27.2480
2	30	0.8249	24.7484	60	49.4967
3	1030	0.7493	771.7476	3090	2315.2427
		Total = P =	823.7439	Total = WP =	2391.9874
		Duration = WP/P =	2.9038