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

1. 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?

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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:

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