Question

You are considering a 25-year, \$1,000 par value bond. Its coupon rate is 10%, and interest...

You are considering a 25-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 11.3280%, how much should you be willing to pay for the bond? Do not round intermediate calculations. Round your answer to the nearest cent.

Solution

First the nominal rate will be calculated

Effective annual rate=(1+Nominal rate/number of compounding periods in an year)^/number of compounding periods in an year-1

11.3280%=(1+Nominal rate/2)^2-1

Solving we get Nominal rate =11.0242%

Now the calculation for price of bond will be made

Price of bond=Present value of coupon payments+Present value of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

Face value =1000

n=number of periods to maturity=25*2=50

r-YTM-11.0242%/2=5.5121% semiannual

Semi annual Coupon payment=Coupon rate*face value/2=10%*1000/2=50

Putting values in formula

Price of bond=50*((1-(1/(1+.055121)^50))/.055121)+1000/(1+.055121)^50

Solving we get price of bond=913.45

Thus amount willing to pay =\$913.45