Answer to Question #301211 in Finance for Mary

Question

You intend to purchase a 10-year, $1,000 face value bond that pays interest of $60 every 6 months. If your nominal annual required rate of return is 10 percent with semiannual compounding, how much should you be willing to pay for this bond?

Answer 1

If your nominal annual required rate of return is 10 percent with semiannual compounding, how much should you be willing to pay for this bond?

The number of semiannual compounding periods in 10 years is 20 periods since interest is paid every 6 months.

We will apply the annuity formula to get the current price of the bond to be paid. The present value of the interest payment and the present value of the repayment of the face value of the bond at the end of 10 years is calculated.

Bond price = $\frac{A(1-(1+r)^{-n}}{r} + \frac{F}{(1-r)^{n}}$

Where:

A is the periodic interest payment which is $60

r is the periodic rate of return which is 10%/2 = 5%

n is the total number of periods = 20

F is the face value of the bond = $1000

Bond price = $\frac{60(1-(1+0.05)^{-20}}{0.05} + \frac{1000}{(1-0.05)^{20}}$

Bond price = 747.73 + 376.89

Bond price = $ 1124.62