Question

Your bank will lend you $10,400 for 30 days at a cost of $151 interest. a. What is your annual rate of interest? (Use 365 days in a yeac. Do not round intermedlate calculations. Round the final answer to 2 decimal places.) Annunl tate of interest. b. What is your effective annual rate? (Use 365 days in a year. Do not round intermediate calculations, Round the final answer to 2 decimal places.) Etfective annual rate

Answer 1

The annual rate of interest on the loan is 17.66%, while the effective annual rate, considering the effect of compounding, is 18.67%.

Step-by-step explanation:

To calculate the annual rate of interest, we can use the formula:

Annual Interest Rate = (Interest / Principal) × (365 / Number of days) × 100%

Substituting the given values:

Annual Interest Rate = ($151 / $10,400) × (365 / 30) × 100%

Annual Interest Rate = 0.01451923 × 12.1667 × 100%

Annual Interest Rate = 17.66%

The effective annual rate (EAR) takes into account the effect of compounding over the year. To find the EAR, we use the formula:

EAR = (1 + (Nominal Rate / Number of Periods))Number of Periods - 1

Since the interest is for 30 days, and for the sake of this example, we assume the bank compounds the interest similarly, the EAR would be:

EAR = (1 + 0.1766 / 12)¹² - 1

EAR = (1 + 0.014717)¹² - 1

EAR = 1.1867 - 1

EAR = 18.67%