Question

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.

Answer 1

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

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