Question

emiannual coupon bonds with the same risk (Aaa) and maturity (20 years) as your company's bonds have a nominal (not EAR) yield to maturity of 9%. Your company's treasurer is thinking of issuing, at par, some $1,000 par value, 20-year, quarterly payment bonds. She has asked you to determine what quarterly interest payment, in dollars, the company would have to set in order to provide the same effective annual rate (EAR) as those on the 20-year, semiannual payment bonds. What would the quarterly, dollar interest payment be

Answer 1

quarterly coupon payment = $22.25

Step-by-step explanation:

effective annual interest rate of current bonds = (1 + 9%/2)² - 1 = 9.2025%

if the new bonds will have quarterly payments, then the nominal interest rate should be:

1.092025 = (1 + r/4)⁴

⁴√1.092025 = ⁴√(1 + r/4)⁴

1.02225 = 1 + r/4

0.02225 = r/4

r = 8.9% annual

quarterly rate = 2.225%

quarterly coupon payment = $22.25