Question

You are considering a 15-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 7.03%, how much should you be willing to pay for the bond? Do not round intermediate steps. Round your answer to the nearest cent.

Answer 1

We want effective yield = 7.03%

For effective annual yield of 7.03%, let us first calculate the equivalent semi-annual rate, for which, we will use the following mathematical relation:

where EAR is effective annual rate, SAR is stated annual rate.

SAR/n is the periodic rate, which we want for semi-annual period, n = 2

SAR/n = 3.46% This is the effective semi-annual rate.

We will use this as YTM.

Price of a bond is mathematically calculated as:

where P is price of bond, C periodic coupon, i periodic YTM, M as face value and n periods to maturity.

For our question, we will use i = 3.46%, M = $1000, n = 30, C = 10% * $1000/2 = $50

P = $1,285.70 --> Price to pay for bond