Question

A bond has a face value of $1000, fixed coupon rate of 8,3% and 3 years to maturity. The discount rate is 3,3%. What is the Macaulay Duration? State the answer as a number with 2 decimals (for example, 3.12).

Answer 1

Given that, Face value of bond = $1000

Coupon rate = 8.3%

Discount rate = 3.3%

Term = 3years

Coupon amount = face value × coupon rate

=$1000×8.3%

=$83

Computation of Macaulay duration of bond:

Year	cash flows	Discounted cash flows	year × discounted cash flows
1	$83	$80.35 (83/(1+3.3%)^1)	$80.35
2	$83	$77.79 ($83/(1+3.3%)^2)	$155.58
3	$83	$75.30 (83/(1+3.3%)^3)	$225.9
4	$1083	$951.10 (1083/(1+3.3%)^4)	$3804.4
		$1184.54	$4266.23

Macaulay duration = sum of (year× Discounted cash flows) /sum of (Discounted cash flows)

=$4266.23/$1184.54

=$3.60years