Big Dom’s Pawn Shop charges an interest rate of 26.9 percent per month on loans to its customers. Like all lenders, Big Dom must report an APR to consumers.

What rate should the shop report?
Note: Do not round intermediate calculations and enter your answer as a percent rounded to 1 decimal place, e.g., 32.1.

What is the effective annual rate?
Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

To solve this problem, we'll need to compute two different rates:

1. **The Annual Percentage Rate (APR):**
   - The APR is calculated by multiplying the monthly interest rate by 12 (since there are 12 months in a year).

2. **The Effective Annual Rate (EAR):**
   - The EAR takes into account the compounding effect of the monthly interest rate over a year. It is calculated using the formula:
     \[
     \text{EAR} = \left(1 + \frac{r}{n}\right)^n - 1
     \]
     where:
     - \( r \) is the nominal interest rate (monthly rate).
     - \( n \) is the number of compounding periods per year (12 for monthly).

Let's calculate each of these step by step.

### 1. Calculating the Annual Percentage Rate (APR)

Given:
- Monthly interest rate = 26.9%

APR is calculated as:
\[
\text{APR} = 26.9\% \times 12
\]

### 2. Calculating the Effective Annual Rate (EAR)

Using the formula:
\[
\text{EAR} = \left(1 + \frac{26.9\%}{100}\right)^{12} - 1
\]

I'll compute both of these.### Results:
1. **Annual Percentage Rate (APR):** \( 322.8\% \)
2. **Effective Annual Rate (EAR):** \( 1643.97\% \)

These values represent the annualized interest rates that Big Dom's Pawn Shop should report. The APR is a straightforward annualized version of the monthly interest rate, while the EAR reflects the impact of monthly compounding on the interest rate over the entire year.

Would you like further details on these calculations or have any other questions?

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Here are 5 related questions you might consider:
1. How does the APR compare to the EAR for a different interest rate?
2. What impact does compounding frequency have on the EAR?
3. How would a daily compounding interest rate change the EAR calculation?
4. If the monthly interest rate was lower, how would that affect the APR and EAR?
5. What would be the impact of changing the loan period on the interest paid?

**Tip:** Always be mindful of the difference between APR and EAR when comparing loan products, as EAR gives a more accurate picture of the actual cost of borrowing.

Learn how to calculate the Annual Percentage Rate (APR) and Effective Annual Rate (EAR) for Big Dom’s Pawn Shop's loan interest rate of 26.9% per month. Get a clear explanation and step-by-step calculation of these important financial metrics.

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