Question

An Apple annual coupon bond has a coupon rate of 5.1%, face value of $1,000, and 4 years to maturity. If its yield to maturity is 5.1%, what is its Macaulay Duration? Answer in years, rounded to three decimal places.

Answer 1

Basic Data

Coupon rate -5.1%;(c=5.1%)

Face Value- $1000;(y=5.1%)

Maturity-4 years;(n=4)

Yield to maturity-5.1%

To find

Macaulay Duration?

Answer

Coupon rate is 5.1%,Cashflow for every year will be $51 &

At the end of 4th year Maturity value of $1000 along with coupon amount of $ 51 will be received.

Yield to maturity is the discounting factor

Duration can be found using the following table:-

A	B	C	D	E	F
Year	Cashflow	Discount Factor @5.1%	Discounted Cashflow (B*C)	Weight (D/Total discounted cashflow)	Duration weight (A*E)
1	51	0.9515	48.52	4.852%	0.04852
2	51	0.9053	46.17	4.617%	0.09234
3	51	0.8613	43.93	4.393%	0.13179
4	1051	0.8195	861.30	86.13%	3.4452
		Total	1000		3.717years

Alternative method:-

The same problem can also be found by using the following formula-Kindly see the image attached

C = 5.1% n = 4 Formula: Duration (1+0.051 (1+0.051 + 4(0.051 -0.051) 0.0 0.051 +0.051 2 20.607 - 1.051 +O 0.051 (1-2201 -1) + 0.051 20.607 - 1.051 0.0622 20.607 - 16.897 3.71 years