Question

Use the table for interest rate questions. Round to the nearest penny.
Secured Unsecured
Credit APR APR
Excellent 4.75% 5.50%
Good 5.00% 5.90%
Average 5.85% 6.75%
Fair 6.40% 7.25%
Poor 7.50% 8.40%

You are purchasing a car for $12,465.00 plus 5.65% sales tax. You make a $1,300.00 down payment and have a fair credit score. How much interest is due at the end of the first month?
$
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Answer 1

To calculate the interest due at the end of the first month for the car purchase, we first need to find the total amount after taxes, the loan amount after the down payment, and then apply the interest rate for a fair credit score.

### Step 1: Calculate the total cost including sales tax

1. **Sales tax rate:** 5.65%
2. **Car price:** $12,465.00

\[
\text{Sales tax} = \text{Car price} \times \text{Sales tax rate} = 12,465.00 \times 0.0565 = 705.97
\]

3. **Total cost including tax:**

\[
\text{Total cost} = \text{Car price} + \text{Sales tax} = 12,465.00 + 705.97 = 13,170.97
\]

### Step 2: Subtract the down payment to find the loan amount

1. **Down payment:** $1,300.00

\[
\text{Loan amount} = \text{Total cost} - \text{Down payment} = 13,170.97 - 1,300.00 = 11,870.97
\]

### Step 3: Find the monthly interest rate

1. **APR for fair credit:** 6.40%
2. **Monthly interest rate:**

\[
\text{Monthly interest rate} = \frac{\text{APR}}{12} = \frac{6.40\%}{12} = 0.5333\% = \frac{6.40}{100} \div 12 = 0.005333
\]

### Step 4: Calculate the interest for the first month

1. **Interest for the first month:**

\[
\text{Interest} = \text{Loan amount} \times \text{Monthly interest rate} = 11,870.97 \times 0.005333 = 63.38
\]

### Conclusion

The interest due at the end of the first month is:

\[
\boxed{63.38}
\]