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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?

Respuesta :

Edufirst

Answer:

  • 6.66%

Explanation:

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

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

Where:

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

Substituting and computing:

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

Convert to percentage, multiplying by 100: 6.66%

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