Question

The semiannual, 8-year bonds of Alto Music are selling at par and have an effective annual yield of 8.6285 percent. What is the amount of each interest payment if the face value of the bonds is $1,000?

A. $41.50
B. $42.25
C. $43.15
D. $85.00
E. $86.29

Answer 1

The nominal semiannual interest rate is 4.31425% of the face value, which is $1,000. Hence, each semiannual interest payment is $43.14, and the closest answer is C. $43.15.

Step-by-step explanation:

The student's question asks to determine the amount of each interest payment for Alto Music's 8-year bonds with a face value of $1,000 and an effective annual yield of 8.6285 percent. Since the bonds are selling at par and it is given that the interest is semiannual, the nominal interest rate can be computed by dividing the annual yield by 2. Therefore, each semiannual interest payment can be calculated using the formula:

Interest Payment = (Face Value) × (Nominal Interest Rate per period)

The nominal interest rate per period (semiannual) is half of the annual yield, so we have:

Nominal Interest Rate per period = 8.6285% / 2 = 4.31425%

Therefore, the amount of each semiannual interest payment is:

Interest Payment = $1,000 × 4.31425% = $43.14

Since $43.14 is closest to option C, the correct answer is $43.15.