Question
You (or your parents) are purchasing a car for $18,965.00 plus 6.25% sales tax. The down payment is $1,500.00. What is the difference in the accrued interest at the end of the first month between the average and excellent credit ratings?
Secured
Unsecured
Credit
APR (%)
APR (%)
Excellent
3.95
4.57
Good
4.45
5.04
Average
4.90
5.75
Fair
5.60
6.55
Poor
7.05
8.70
(1 point)
Responses
$15.01
$15.01
$15.95
$15.95
$14.77
$14.77
$13.83
Secured
Unsecured
Credit
APR (%)
APR (%)
Excellent
3.95
4.57
Good
4.45
5.04
Average
4.90
5.75
Fair
5.60
6.55
Poor
7.05
8.70
(1 point)
Responses
$15.01
$15.01
$15.95
$15.95
$14.77
$14.77
$13.83
Answers
GPT-4o mini
To find the difference in accrued interest at the end of the first month between average and excellent credit ratings, we first need to calculate the total cost of the car after tax and then determine the financed amount after the down payment.
1. **Calculate the sales tax:**
- Sales tax = Purchase price × Sales tax rate
- Sales tax = $18,965.00 × 6.25% = $18,965.00 × 0.0625 = $1,185.31
2. **Calculate the total cost:**
- Total cost = Purchase price + Sales tax
- Total cost = $18,965.00 + $1,185.31 = $20,150.31
3. **Calculate the financed amount (after down payment):**
- Financed amount = Total cost - Down payment
- Financed amount = $20,150.31 - $1,500 = $18,650.31
4. **Calculate the monthly interest for both credit ratings:**
- **For Excellent Credit (APR = 3.95%):**
- Monthly interest rate = APR / 12
- Monthly interest rate = 3.95% / 12 = 0.3291667% = 0.003291667 (as a decimal)
- Accrued interest for the first month = Financed amount × Monthly interest rate
- Accrued interest (Excellent) = $18,650.31 × 0.003291667 ≈ $61.43
- **For Average Credit (APR = 4.90%):**
- Monthly interest rate = APR / 12
- Monthly interest rate = 4.90% / 12 = 0.4083333% = 0.004083333 (as a decimal)
- Accrued interest for the first month = Financed amount × Monthly interest rate
- Accrued interest (Average) = $18,650.31 × 0.004083333 ≈ $76.07
5. **Calculate the difference in accrued interest:**
- Difference = Accrued interest (Average) - Accrued interest (Excellent)
- Difference = $76.07 - $61.43 ≈ $14.64
Now, rounding to the nearest cent, we see that the difference is approximately **$14.64**. However, that option is not present in your responses. Given the closest options you have provided, I suggest checking the values again to ensure there haven't been any rounding or estimation differences.
Nevertheless, if we look closely at the options available:
- **$14.77** is the closest option to our calculated difference.
Thus, the answer you should select is **$14.77**.
1. **Calculate the sales tax:**
- Sales tax = Purchase price × Sales tax rate
- Sales tax = $18,965.00 × 6.25% = $18,965.00 × 0.0625 = $1,185.31
2. **Calculate the total cost:**
- Total cost = Purchase price + Sales tax
- Total cost = $18,965.00 + $1,185.31 = $20,150.31
3. **Calculate the financed amount (after down payment):**
- Financed amount = Total cost - Down payment
- Financed amount = $20,150.31 - $1,500 = $18,650.31
4. **Calculate the monthly interest for both credit ratings:**
- **For Excellent Credit (APR = 3.95%):**
- Monthly interest rate = APR / 12
- Monthly interest rate = 3.95% / 12 = 0.3291667% = 0.003291667 (as a decimal)
- Accrued interest for the first month = Financed amount × Monthly interest rate
- Accrued interest (Excellent) = $18,650.31 × 0.003291667 ≈ $61.43
- **For Average Credit (APR = 4.90%):**
- Monthly interest rate = APR / 12
- Monthly interest rate = 4.90% / 12 = 0.4083333% = 0.004083333 (as a decimal)
- Accrued interest for the first month = Financed amount × Monthly interest rate
- Accrued interest (Average) = $18,650.31 × 0.004083333 ≈ $76.07
5. **Calculate the difference in accrued interest:**
- Difference = Accrued interest (Average) - Accrued interest (Excellent)
- Difference = $76.07 - $61.43 ≈ $14.64
Now, rounding to the nearest cent, we see that the difference is approximately **$14.64**. However, that option is not present in your responses. Given the closest options you have provided, I suggest checking the values again to ensure there haven't been any rounding or estimation differences.
Nevertheless, if we look closely at the options available:
- **$14.77** is the closest option to our calculated difference.
Thus, the answer you should select is **$14.77**.