You are considering the purchase of new living room furniture that costs $1,360. The store will allow you to make weekly payments of $29.25 for one year to pay off the loan. What is the EAR of this arrangment?

Multiple Choice

22.41%

21.29%

23.74%

26.31%

25.06%

The problem asks for the **Effective Annual Rate (EAR)** on a financing arrangement for new living room furniture. To calculate the EAR, we need to:

1. **Determine the loan amount**: The total cost is $1,360.
2. **Identify the payment terms**: Weekly payments of $29.25 for 52 weeks (one year).
3. **Find the nominal interest rate** implied by these terms, and then use it to calculate the EAR.

### Step-by-Step Solution:

**Step 1: Calculate the total payments over the year**
\[
\text{Total payments} = 52 \times 29.25 = 1,521
\]

The amount of extra payment due to interest is:
\[
\text{Interest paid} = 1,521 - 1,360 = 161
\]

**Step 2: Solve for the weekly interest rate (using an approximation of the loan formula)**
We use the formula for the payment of a loan:
\[
P = \frac{r \cdot PV}{1 - (1 + r)^{-n}}
\]
Where:
- $ P = 29.25 $ is the weekly payment.
- $ PV = 1,360 $ is the loan amount.
- $ r $ is the weekly interest rate.
- $ n = 52 $ is the number of payments.

Rearranging this formula to solve for $ r $, we can approximate the weekly rate and then convert it to the EAR.

**Step 3: Calculate the EAR**
Once the weekly interest rate $ r $ is determined, the EAR can be calculated using the formula:
\[
\text{EAR} = (1 + r)^{52} - 1
\]

Using financial calculations, the correct answer for this particular set of terms is approximately:

\[
\boxed{25.06\%}
\]

Would you like a detailed breakdown of the calculations? Here are some related questions:

1. How is the formula for calculating the loan payment derived?
2. What is the difference between EAR and APR?
3. Can you explain the concept of compounding interest more deeply?
4. How do nominal interest rates relate to effective interest rates?
5. What role does payment frequency play in loan cost?

**Tip**: The EAR provides a clearer picture of the actual cost of borrowing because it includes the effect of compounding interest.

You are considering the purchase of new living room furniture that costs $1,360. The store will allow you to make weekly payments of $29.25 for one year to pay off the loan. What is the EAR of this arrangement? Multiple Choice: 22.41%, 21.29%, 23.74%, 26.31%, 25.06%

Learn how to calculate the Effective Annual Rate (EAR) for a $1,360 furniture loan with weekly payments of $29.25 for one year. This problem covers loan payment formulas, interest rates, and compounding, making it ideal for finance students or advanced high school learners. Discover step-by-step calculations and the final EAR of 25.06%.

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