Question

You are considering a 25-year, $1,000 par value bond. Its coupon rate is 9%, and interest is paid semiannually. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below.

If you require an "effective" annual interest rate (not a nominal rate) of 9.3%, 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

Nominal rate of interest = ((1 + EAR)^(1/n) - 1) * n
= ((1 + 9.3%)^(1/2) - 1) * 2
= 9.09%

Rate = 9.09% / 2
Nper = 25 * 2 = 50
FV = 1000
PMT = 1000 * 9% / 2 = 45

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(9.09%/2,50,-45,-1000)
= $990.85

Price of the bond = $990.85