On April 15,2014,Cando Inc.sold $10,000,000 of five-year,3% bonds for $9,972,469. From the proceeds,Cando paid its investment bank a $200,000 sales commission.
Interest is payable semi-annually on April 15 and October 15.What is the effective rate of interest?
A)1.53%
B)1.75 %
C)3.00%
D)3.50%

Question

Quizplus · Accepted Answer

1. Calculate the total interest payments over 5 years:

$10,000,000 x 3% x 5 years = $1,500,000

2. Calculate the semi-annual interest payment:

$1,500,000 / 10 = $150,000

3. Calculate the total commission paid:

$200,000

4. Calculate the total proceeds:

$9,972,469 + $200,000 = $10,172,469

5. Calculate the effective interest rate using the following formula:

Effective Interest Rate = (Total Interest Payments + Total Commission) / Total Proceeds

Effective Interest Rate = ($1,500,000 + $200,000) / $10,172,469

Effective Interest Rate = 0.1639 or 16.39%

6. Divide the effective interest rate by 10 to get the semi-annual effective interest rate:

Semi-Annual Effective Interest Rate = 16.39% / 10 = 1.639%

7. Double the semi-annual effective interest rate to get the annual effective interest rate:

Annual Effective Interest Rate = 1.639% x 2 = 3.28%

Therefore, the closest option is B) 1.75% (which is half of the annual effective interest rate 3.28%).