Question

Consider a 5- year bond with a semi-annual 10% coupon and a yield to maturity(ytm) of 9.00%. what is the duration of this bond in years?

Answer 1

Macaulay duration = ∑[tC/(1+y)^t + nM/(1+y)ⁿ/P]

                                       t = 1 to n

t = Period in which coupon is received

C = Semiannual coupon payment = (10% x $ 1000)/2 = $ 50

y = Periodic yield to maturity = 9 % /2 = 4.5 %

n = Number of periods = 5 years x 2 = 10

M = Maturity value = $ 1,000 + $ 50 = $ 1,050

P = Market price of bond = $ 1,000 (Assumed)

Period	Cash Flow	Period x Cash Flow	PV of $1 @ 4.5 %	Present Value of Cash Flow
1	$50	$50	0.956937799	$47.85
2	$50	$100	0.915729951	$91.57
3	$50	$150	0.876296604	$131.44
4	$50	$200	0.838561344	$167.71
5	$50	$250	0.802451047	$200.61
6	$50	$300	0.767895738	$230.37
7	$50	$350	0.734828458	$257.19
8	$50	$400	0.703185127	$281.27
9	$50	$450	0.672904428	$302.81
10	$1,050	$10,500	0.643927682	$6,761.24
Total

Macaulay duration = $6,761.24 / $1,000 = 6.76 years