Which of the following amounts is closest to the value of a bond that pays $75 semiannually and has an effective semiannual interest rate of 7%? The face value is $1,000 and the bond matures in 7 years.There are exactly six months before the first interest payment.

Question

Quizplus · Accepted Answer

The first step is to calculate the present value of the bond using the formula:

Present Value = (Coupon Payment / Discount Rate) x [1 - 1 / (1 + Discount Rate)^(Number of Periods)]

In this case, the coupon payment is $75, the discount rate is 3.5% (half of the 7% effective annual rate), and the number of periods is 14 (since there are 7 years with 2 semiannual periods per year).

Present Value = ($75 / 0.035) x [1 - 1 / (1.035)^14]
Present Value = $1,043.58

Since there are exactly six months before the first interest payment, we need to subtract half of the first coupon payment from the present value:

Present Value - ($75 / 2) = $1,043.58 - $37.50 = $1,006.08

Therefore, the closest amount to the value of the bond is $1,044, which is closest to option C.

Which of the Following Amounts Is Closest to the Value