Question

You are considering a 30-year, $1,000 par value bond. Its coupon rate is 10%, and interest is paid semiannually. If you require an "effective" annual interest rate (not a nominal rate) of 7.3525%, how much should you be willing to pay for the bond? Do not round intermediate calculations. Round your answer to the nearest cent.

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Answer 1

Effective annual rate = (1 + nominal rate)/n)^n - 1

0.073525 = (1 + nominal rate / 2)^2 - 1

1.073525 = (1 + nominal rate / 2)^2

1.036111 = 1 + nominal rate/2

Nominal rate = 0.072221 or 7.2221%

Semi annual rate = 7.2221% / 2 = 3.61105%

Number of periods = 30 * 2 = 60

Semi annual coupon = [(10 / 100) * 1000] / 2 = 50

Price of bond = Coupon * [1 - 1 / (1 + rate)^time] / rate + Face value / (1 + rate)^time

Price of bond = 50 * [1 - 1 / (1 + 0.0361105)^60] / 0.0361105 + 1000 / (1 + 0.0361105)^60

Price of bond = 50 * [1 - 0.119024] / 0.0361105 + 119.024265

Price of bond = 50 * 24.396664 + 119.024265

Price of bond = $1,338.86