Question

What is the duration of a bond with three years to maturity and a coupon of 7.5 percent paid annually if the bond sells at par?

Answer 1

Formula to calculate duration of bond
Duration of bond	Sum of (CF*Year)/Price of bond
CF represents present value of cash flow
Year represents time period when cash flow is received
Bond is selling at par and thus Yield to maturity which is discount rate would be equal to coupon rate of 7.5%
Assuming the face value of bond is $1,000.
Coupon amount	$75	1000*7.5%
Calculation of duration of bond
Year	Cash flow	Discount factor @ 7.5%	Present value	CF*Year
1	$75	0.930233	$69.77	$69.77	(69.77*1)
2	$75	0.865333	$64.90	$129.80	(64.90*2)
3	$1,075	0.804961	$865.33	$2,596.00	(865.33*3)
Total			$1,000.00	$2,795.57
Discount factor	1/(1.075^n)	n is number of years
At end of year 3, Bond would pay coupon amount plus face value of bond which is $1,000 and thus total cash flow would be $1,075 (1000+75)
Duration of bond	2795.57/1000
Duration of bond	2.80	years