Question

Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 6.50%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year. What is the effective annual rate on the loan?

Answer 1

Answer:

• 6.66%

Explanation:

The effective annual rate, EAR, of a loan is calculated with the formula:

       $EAR=\bigg[1+\dfrac{nominal\text{ }rate}{n}\bigg]^{n}}-1$

Where:

• nominal rate = annual percentage rate = 6.50%
• n = number of periods = 4

Substituting and computing:

      $EAR=\bigg[1+\dfrac{6.50\%}{4}\bigg]^{4}}-1=0.0666$

Convert to percentage, multiplying by 100: 6.66%