Question

You are considering a 30-year, $1,000 par value bond. Its coupon rate is 9%, and interest is paid semiannually. If you require an "effective" annual interest rate (not a nominal rate) of 11.72%, 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 investor should be willing to pay $775.53

Step-by-step explanation:

A bonds effective interest rate is the investor's yield to maturity.

The price of a bond is equivalent to the present value of all the cash flows that are likely to accrue to an investor once the bond is bought. These cash-flows are the periodic coupon payments that are to be paid semi-annually and the par value of the bond that will be paid at the end of 30 years.

During the 30 years, there are 60 equal periodic coupon payments that will be made. Given a par value equal to $1,000, in each year, the total coupon paid will be
`1,000*0.09` =$90. This annual payment will be split into two equal payments equal to
`(90)/(2)=45` . This stream of cash-flows is an ordinary annuity.

The effective annual interest rate is 11.72% per annum which equates to 5.86% per semi annual period.

The PV of the cash-flows = PV of the coupon payments + PV of the par value of the bond

=45*PV Annuity Factor for 60 periods at 5.86%+ $1,000* PV Interest factor with i=5.86% and n =60

`= 45*([1-(1+0.0586)^-^6^0])/(0.0586)+ (1,000)/((1+0.0586)^6^0) =775.534`