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 9.22%, 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

the following is the calculation of amount to be paid for the bond.

=> present value of annuity factor *[semi annual interest] + present value factor *[face value of bond]

here,

present value of annuity factor = [1 - (1+r)^(-n)]/r

here.,

r = 9.22% per annum => 4.61% for semi annual period =>0.0461.

n = 15 years=>30 semi annual periods.

[1-(1.0461)^(-30)]/0.0461

=> 0.7412955/0.0461.

=>16.0801627.

coupon payments = $1,000 par value * 10% coupon rate *6/12 months =>$50 per 6 months.

present value factor = 1/ (1+r)^n

=>1 /(1.0461)^30

=>0.25870447

face value =$1000.

now

price to be paid = [16.0801627*$50] + [0.25870447*$1000]

=>804.008135+258.70447

=>1,062.71..........(rounded to neares cent)

price to be paid for the bond = $1,062.71