Question

Your roommate let you borrow $263 to buy the PS5 2 months ago. You just paid him back today and gave him $26 extra for interest. What is the effective annual rate? Convert to a percent, round to 2 decimal places.

Answer 1

The effective annual rate (EAR) of the interest paid for borrowing money to buy a PS5 is calculated using the formula EAR = (Interest / Principal) / Time * 100. With an interest of $26 on the principal of $263 for 2 months, the EAR is 11.86% when rounded to two decimal places.

Step-by-step explanation:

To calculate the effective annual rate (EAR) of the interest charged on the borrowed amount for a PS5, we can use the formula for the simple interest since the interest does not compound in this scenario. The formula for the EAR is EAR = (Interest / Principal) / Time * 100, where 'Interest' is the total interest paid, 'Principal' is the borrowed amount, and 'Time' is the period the money was borrowed for in years.

In this case, the Interest is $26, the Principal is $263, and since the loan was for 2 months (which is ⅓ of a year), Time is ⅓ year. Plugging the numbers into the formula, we have ⅓ year as 2/12 to convert it into the fraction of the year, which simplifies to ⅓.

EAR = ($26 / $263) / (⅓) * 100 = 0.09885496183 / (⅓) * 100 = 0.1186259542 * 100 = 11.86259542%

When rounded to two decimal places, the effective annual rate is 11.86%.