Question

You are considering the purchase of new living room furniture that costs $1,260. The store will allow you to make weekly payments of $27.43 for one year to pay off the loan. What is the EAR of this arrangment?

a.24.90%
b.29.61%
c.28.20%
d.23.65%
e.26.55%

Answer 1

The question asked for the EAR of a loan with weekly payments but did not provide the necessary information to calculate it. Usually, the formula for EAR depends on the nominal interest rate and compounding frequency, neither of which were specified in the question. Thus, it's not possible to confidently provide the correct answer from the choices given.

Step-by-step explanation:

To calculate the Effective Annual Rate (EAR) of a loan agreement where you make weekly payments to pay off the loan in a year, we would need to determine the interest rate that compounds weekly equal to the amount of the loan provided. However, the information given appears to be insufficient or incorrect for computing the EAR directly as key details like the interest rate are missing, and the references provided pertain to different financial scenarios that are not directly applicable to this question.

In usual circumstances, to find the EAR when given a nominal interest rate and the compounding frequency, you would use the following formula:

EAR = (1 + (i/n))^n - 1

Where 'i' is the nominal interest rate (not given in this case) and 'n' is the number of compounding periods per year. Since the question does not provide the nominal interest rate and only gives the payment amounts and the total cost, there is no straightforward way to calculate the EAR accurately without additional information.

For practice, if you had the annual nominal interest rate (let's pretend it's 6%) and it was compounded weekly, you would calculate the EAR as follows:

EAR = (1 + (0.06/52))^52 - 1

However, this does not solve your original question, but it shows the method that would be used if the nominal rate were provided. Hence, without the necessary information to calculate the EAR, it is not possible to accurately answer the question or choose the correct option from the list provided.

Answer 2

The Effective Annual Rate (EAR) of this arrangement is approximately 29.61%. Thus the correct option is b.29.61%

Step-by-step explanation:

To find the EAR, first calculate the total amount paid over the year: $27.43 * 52 weeks = $1,426.36.

The total interest paid is $1,426.36 - $1,260 = $166.36. Then, compute the APR using the formula: APR = (Total Interest / Principal) * (365 days / 7 days). Thus, APR = ($166.36 / $1,260) * (365 / 7) = 0.13895 or 13.90%.

Finally, use the formula to convert APR to EAR: EAR = (1 + APR / n)^n - 1, where n is the number of compounding periods in a year. In this case, it's weekly compounding, so n = 52. Plugging in the values, EAR = (1 + 0.1390 / 52)^52 - 1 = 0.2961 or approximately 29.61%.

Therefore, the effective annual rate for this furniture purchase on weekly payments is approximately 29.61%, making it the most suitable option from the given choices.

Thus the correct option is b.29.61%