Question
You purchase a new car for $17,000 and are able to acquire a loan because of your excellent credit score. How much is the total interest and insurance per month if you use the Whome Insurance Company from question 3 for your insurance coverage and don't qualify for the safe driver discount?
Credit
APR (%)
Excellent
5.90
Good
6.35
Average
6.85
Fair
7.40
Poor
8.15
(1 point)
Responses
$95.39
$95.39
$150.52
$150.52
$142.64
$142.64
$162.33
Credit
APR (%)
Excellent
5.90
Good
6.35
Average
6.85
Fair
7.40
Poor
8.15
(1 point)
Responses
$95.39
$95.39
$150.52
$150.52
$142.64
$142.64
$162.33
Answers
GPT-4o mini
To determine the monthly interest and insurance cost for the car loan, we first need to calculate the monthly loan payment using the given APR, and then add the insurance cost.
1. **Loan amount**: $17,000
2. **APR for excellent credit**: 5.90%
3. **Loan term**: We'll assume a standard loan term, which is often 5 years (60 months) if not specified.
### Step 1: Calculate Monthly Payment Using APR
The formula for monthly loan payment (M) on an amortizing loan is given by:
\[
M = P \times \frac{r(1+r)^n}{(1+r)^n-1}
\]
Where:
- \(P\) = loan amount ($17,000)
- \(r\) = monthly interest rate (APR/12)
- \(n\) = number of payments (loan term in months)
1. **Calculate monthly interest rate**:
\[
r = \frac{5.90\%}{100}/12 \approx 0.00491667
\]
2. **Number of payments**:
\[
n = 60 \text{ months}
\]
3. **Substituting the values into the formula**:
\[
M = 17000 \times \frac{0.00491667(1+0.00491667)^{60}}{(1+0.00491667)^{60}-1}
\]
First, calculate \((1 + r)^{n}\):
\[
(1 + 0.00491667)^{60} \approx 1.348418
\]
Now plug everything back into the formula:
\[
M = 17000 \times \frac{0.00491667 \times 1.348418}{1.348418 - 1} \approx 17000 \times \frac{0.006630} {0.348418} \approx 17000 \times 0.01904 \approx 323.68
\]
So, the monthly payment for the loan is approximately $323.68.
### Step 2: Add Insurance Cost
We need to know the monthly insurance cost from Whome Insurance Company. However, if we don't have that value specified, we can assume an average insurance cost. For this example, let's assume that the monthly insurance cost is $100 (you might need to adjust based on the actual cost).
### Step 3: Calculate Total Monthly Cost
Now sum the loan payment and the insurance cost:
\[
\text{Total monthly cost} = \text{Loan payment} + \text{Insurance} = 323.68 + 100 \approx 423.68
\]
Since none of the options exactly match the calculations, let's assume that with the insurance you would correctly refer to/about $142.64 just for loan interest (not the overall) and see if any of the sums resemble that.
So referring to just how much would be manageable per month might be able-related to how monthly payments of other terms could meet $150.52 as the projection if prefaced correctly.
If we were more precise from context, especially without exact figures, it may vary widely in assumptions. Please advise on what the insurance cost is to provide a more accurate total.
1. **Loan amount**: $17,000
2. **APR for excellent credit**: 5.90%
3. **Loan term**: We'll assume a standard loan term, which is often 5 years (60 months) if not specified.
### Step 1: Calculate Monthly Payment Using APR
The formula for monthly loan payment (M) on an amortizing loan is given by:
\[
M = P \times \frac{r(1+r)^n}{(1+r)^n-1}
\]
Where:
- \(P\) = loan amount ($17,000)
- \(r\) = monthly interest rate (APR/12)
- \(n\) = number of payments (loan term in months)
1. **Calculate monthly interest rate**:
\[
r = \frac{5.90\%}{100}/12 \approx 0.00491667
\]
2. **Number of payments**:
\[
n = 60 \text{ months}
\]
3. **Substituting the values into the formula**:
\[
M = 17000 \times \frac{0.00491667(1+0.00491667)^{60}}{(1+0.00491667)^{60}-1}
\]
First, calculate \((1 + r)^{n}\):
\[
(1 + 0.00491667)^{60} \approx 1.348418
\]
Now plug everything back into the formula:
\[
M = 17000 \times \frac{0.00491667 \times 1.348418}{1.348418 - 1} \approx 17000 \times \frac{0.006630} {0.348418} \approx 17000 \times 0.01904 \approx 323.68
\]
So, the monthly payment for the loan is approximately $323.68.
### Step 2: Add Insurance Cost
We need to know the monthly insurance cost from Whome Insurance Company. However, if we don't have that value specified, we can assume an average insurance cost. For this example, let's assume that the monthly insurance cost is $100 (you might need to adjust based on the actual cost).
### Step 3: Calculate Total Monthly Cost
Now sum the loan payment and the insurance cost:
\[
\text{Total monthly cost} = \text{Loan payment} + \text{Insurance} = 323.68 + 100 \approx 423.68
\]
Since none of the options exactly match the calculations, let's assume that with the insurance you would correctly refer to/about $142.64 just for loan interest (not the overall) and see if any of the sums resemble that.
So referring to just how much would be manageable per month might be able-related to how monthly payments of other terms could meet $150.52 as the projection if prefaced correctly.
If we were more precise from context, especially without exact figures, it may vary widely in assumptions. Please advise on what the insurance cost is to provide a more accurate total.