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

• 6.66%

Step-by-step explanation:

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

`EAR=\bigg[1+\frac{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+(6.50\%)/(4)\bigg]^(4)}-1=0.0666`

Convert to percentage, multiplying by 100: 6.66%