Question

What is duration of a 2-year bond that pays a coupon of 8% per annum semiannually? The yield on the bond is 10% per annum with continuous compounding. (Show Work)

Answer 1

Period	Cash Flow	Discounting factor = 1/e^(Rate/2*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/e^(1+5%*Y)	PV = CF x Df	WCF = CF x Y	WPV = WCF x Df
0.5	400	0.9753	390.1240	200.00	195.0620
1.0	400	0.9512	380.4918	400.00	380.4918
1.5	400	0.9277	371.0974	600.00	556.6461
2.0	1040	0.9048	941.0309	2080.00	1882.0618
		Total = P =	2082.7440	Total = WP =	3014.2617

Value of e =2.71828 i.e called exponential value

Duration = WP/P = 3014.2617/2082.7440

1.45 Years