Question

What is the Macaulay Duration of a 4.4% annual coupon bond with 3 years to maturity, $1,000 face value, and yield to maturity of 4.4%? Round to three decimal places.

		a. 2.865
		b. 2.821
		c. 2.886
		d. 2.875
		e. 2.908

Answer 1

The formula to calculate the Macaulay Duration of a bond is

(ΣWx)/(ΣW)

Where W = Weights assigned to PV of bond CFs discounted at YTM

X = Period at which cash flows are recieved.

This can be better understood with the help of the below table.

Period	Cash Flows	Period * Cash flows	Present value factor	Present value of cash flows or bond price	Present value of weighted cash flows
(a)	(b)	(a) * (b) = (c)	(d)	(b) * (d)	(c) * (d) = (e)
1	44	44	0.9579	42.1456	42.1456
2	44	88	0.9175	40.3693	80.7387
3	1044	3132	0.8788	917.4851	2,752.4552
			Bond price	1,000.00
			Total Present value		2,875.34

Hence now the duration of bond will be 2875.3395/1000 = 2.8753