Question

You are considering a 10-year, $1,000 par value bond. Its coupon rate is 8%, and interest is paid semiannually. The data has been collected in the Microsoft Excel Online file below.

If you require an "effective" annual interest rate (not a nominal rate) of 10.16%, 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

Given about a bond,

Years to maturity = 10

Face value = $1000

coupon rate = 8% paid semiannually

effective annual rate required = 10.16%

So, 1st calculated nominal rate of interest for semiannual compounding

On excel, use formula =nominal(effective_rate,npery)

So, we get nominal rate = nominal(10.16%,2) = 9.91%

Number of payment of the bond = 2*10 = 20

Coupon payment semiannully = (8%/2) of 1000 = $40

So, Price of the bond calculated using formula

Price = PV(rate,nper,PMT,FV) = PV(9.91%/2,20,40,1000) = -880.29

So, fair price of the bond is $880.29