Question

An Apple annual coupon bond has a coupon rate of 6.8%, face value of $1,000, and 4 years to maturity. If its yield to maturity is 6.8%, what is its Macaulay Duration? Answer in years, rounded to three decimal places.

Answer 1

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =4

Bond Price =∑ [(6.8*1000/100)/(1 + 6.8/100)^k]     +   1000/(1 + 6.8/100)^4

k=1

Bond Price = 1000

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,000.00)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	68.00	1.07	63.67	63.67
2	68.00	1.14	59.62	119.23
3	68.00	1.22	55.82	167.46
4	1,068.00	1.30	820.89	3,283.57
			Total	3,633.94

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=3633.94/(1000*1)

=3.634