Question

You are late paying your cable bi again. It was due 5 days ago and you have been charged $25. Your bill was $125. What is the period rate? Convert to a percent and round to 2 decimal places QUESTION 2 You ars late paying your cable bif again. It wat due 11 days ago and you have been charged $24. Your bill was $120. What is the Eliective Annual Rate? Convert to a percent and round to 2 decimal places QUESTION 3 Your roommate let you borron $113 to buy the PS5 3 months ago. You just paid him back today and gave him $28 extra for interest. What is the offective annual rate? Convart to a percent, round to 2 decimal places.

Answer 1

The period rate is calculated based on the penalties or interest charged for a specific period, which can be converted to a percent of the original bill. The Effective Annual Rate (EAR) considers the compounding of these charges over the course of a year and can be calculated using the formula which accounts for the frequency of compounding.

Step-by-step explanation:

Understanding Period Rate and Effective Annual Rate (EAR)

When it comes to late payments for bills such as cable, financial firms often charge a penalty or interest. To understand this better, let's see how to calculate the period rate and the Effective Annual Rate (EAR).

Question 1: Calculating the Period Rate

The period rate is the interest charged for a specific period, in this case, per day. If you were charged $25 for being late 5 days on a $125 bill, the daily period rate in dollars is $25 / 5 days = $5 per day. To convert this to a percentage of the original bill, it would be ($5 / $125) * 100 = 4% per day.

Question 2: Calculating the Effective Annual Rate (EAR)

If you are charged $24 for an 11-day late payment on a bill of $120, the daily period rate would be ($24 / 11 days) = approximately $2.18 per day. To find the EAR, we would need to compound this daily rate over the course of a year. However, without the compounding frequency, it is assumed to be daily. The formula for EAR in this simplistic scenario (ignoring continuous compounding) is (1 + daily rate)^365 - 1. Substituting the daily rate as a decimal, EAR would be ((1 + 0.01815)^365 - 1) * 100, resulting in an EAR of a very high percentage due to daily compounding, suggesting the penalties for this credit product would be exorbitant over the course of a year.

Question 3: Calculating EAR for Personal Loan

Borrowing $113 and paying back an extra $28 over 3 months indicates an interest amount of $28. To annualize this for EAR, we consider the compounding effect over four quarters in a year. The EAR formula would be (1 + ($28/$113))^(4) - 1, converted to a percentage and rounded to two decimal places giving us the EAR.

Calculations of EAR typically assume the compounding frequency is important as it can significantly affect how much is actually paid in interest. In financial literacy, understanding the terms such as period rates and compounding frequencies is essential for managing personal finances effectively.

Answer 2

The period rate is 500% and the Effective Annual Rate is 1021.26%. The Effective Annual Rate for borrowing $113 with an additional $28 paid as interest over 3 months is 132.33%.

Step-by-step explanation:

To calculate the period rate, we divide the late fee by the number of days the payment is late. In this case, the late fee is $25 and the payment is 5 days late, so the period rate is $25/5 = $5 per day. To convert to a percent, we multiply by 100 to get 500%. Therefore, the period rate is 500%.

To calculate the Effective Annual Rate (EAR), we first need to calculate the daily rate. In this case, the late fee is $24 and the payment is 11 days late, so the daily rate is $24/11 = $2.18 per day. Next, we calculate the EAR using the formula (1 + daily rate)^365 - 1. Plugging in the values, we get (1 + 2.18/100)^365 - 1 = 1021.26%. Therefore, the Effective Annual Rate is 1021.26%.

To calculate the Effective Annual Rate (EAR), we need to use the formula EAR = (1 + periodic rate)^n - 1, where n is the number of periods. In this case, the loan was borrowed $113 for 3 months and an additional $28 was paid as interest. Therefore, the total amount paid back is $113 + $28 = $141. To calculate the periodic rate, we divide the interest by the principal ($28/$113) and multiply by the number of periods in a year (12 for monthly). Plugging in the values, we get (1 + $28/$113)^12 - 1 = 132.33%. Therefore, the Effective Annual Rate is 132.33%.