An investor buys a 3.8% annual payment bond with 8 years to maturity. The bond is...

An investor buys a 3.8% annual payment bond with 8 years to maturity. The bond is priced at a yield-to-maturity of 5.6%. What is the bond’s Macaulay duration?

Expert Solution

Calculation of Macaulay duration of the bond

Maturity Period =	8 years
Face value (assumed) =	$1,000
Coupon Rate =	3.80%
Coupon payment at 3.8% of face value	$38.00
Yield-to-maturity	5.60%

Year (t)	Cash Flow from coupon payments and maturity amount (CF)	Present value (PV) discounted at 5.6% [=CF/(1+5.6%)^t]	PV *t
1	$38.00	$35.98	$35.98
2	$38.00	$34.08	$68.15
3	$38.00	$32.27	$96.81
4	$38.00	$30.56	$122.23
5	$38.00	$28.94	$144.69
6	$38.00	$27.40	$164.42
7	$38.00	$25.95	$181.65
8	$1,038.00	$671.25	$5,370.02
sum		$886.43	$6,183.96
		Bond's Price↑
	Macaulay duration = sum of (PV*t)/sum of PVs =	$6183.96/$886.43	6.98	Years

Macaulay duration of the bond is 6.98 years

Formulas used in excel calculation:

jeff jeffy answered 1 year ago

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