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
$150.52
$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
$150.52
$142.64
$162.33
Answers
GPT-4o mini
To calculate the total monthly interest and insurance for your new car purchase, we need to break this down into two parts: the monthly loan payment (including interest) and the monthly insurance premium.
1. **Calculate Monthly Loan Payment:**
- Amount of loan (car price): $17,000
- APR for excellent credit: 5.90%
- Assuming a loan term of 60 months (4 years) for calculation purposes.
First, convert the APR to a monthly interest rate:
\[
\text{Monthly interest rate} = \frac{5.90\%}{12} = \frac{0.059}{12} \approx 0.00491667
\]
Using the formula for monthly payments on an installment loan:
\[
M = P \frac{r(1+r)^n}{(1+r)^n - 1}
\]
Where:
- \(M\) = monthly payment
- \(P\) = loan amount ($17,000)
- \(r\) = monthly interest rate
- \(n\) = number of payments (60)
Substituting the values in:
\[
M = 17000 \cdot \frac{0.00491667(1+0.00491667)^{60}}{(1+0.00491667)^{60} - 1}
\]
Calculating this step-by-step:
- Calculate \((1 + r)^{60}\):
\[
(1 + 0.00491667)^{60} \approx 1.348850289
\]
- Now plug this back into \(M\):
\[
M = 17000 \cdot \frac{0.00491667 \cdot 1.348850289}{1.348850289 - 1}
\]
\[
M \approx 17000 \cdot \frac{0.006634258}{0.348850289} \approx 17000 \cdot 0.019018
\]
\[
M \approx 323.31
\]
2. **Calculate Monthly Insurance Payment:**
Assuming the insurance rate from Whome Insurance Company is provided in your question, but since I don't have question 3 or the specific monthly insurance cost stated, let's assume it's $X for this calculation.
Just to match your desired responses, I will try to compute without specific numbers.
3. **Total Monthly Cost:**
If you provide the insurance monthly cost, let's denote it as \(X\).
Total monthly cost \(= \text{monthly loan payment} + \text{monthly insurance}\):
\[
= 323.31 + X
\]
Finally, let’s match your provided response options with 323.31 plus an estimable insurance rate.
If \(X = 95.39\), then \(M + X = 323.31 + 95.39 = 418.70\).
If \(X = 142.64\), then \(M + X = 323.31 + 142.64 = 465.95\).
If you'd provide the insurance amount, I can help derive with clarity on the monthly payment fitting your options.
With enough assumptions:
If insurance were $95.39, it would yield:
$323.31 (loan) + $95.39 (insurance) ≈ $418.70 (Off the given options).
I would recommend rechecking question 3 for accurate insurance value.
If you can confirm or adjust with the correct monthly insurance amount given in your data, please let me know!
1. **Calculate Monthly Loan Payment:**
- Amount of loan (car price): $17,000
- APR for excellent credit: 5.90%
- Assuming a loan term of 60 months (4 years) for calculation purposes.
First, convert the APR to a monthly interest rate:
\[
\text{Monthly interest rate} = \frac{5.90\%}{12} = \frac{0.059}{12} \approx 0.00491667
\]
Using the formula for monthly payments on an installment loan:
\[
M = P \frac{r(1+r)^n}{(1+r)^n - 1}
\]
Where:
- \(M\) = monthly payment
- \(P\) = loan amount ($17,000)
- \(r\) = monthly interest rate
- \(n\) = number of payments (60)
Substituting the values in:
\[
M = 17000 \cdot \frac{0.00491667(1+0.00491667)^{60}}{(1+0.00491667)^{60} - 1}
\]
Calculating this step-by-step:
- Calculate \((1 + r)^{60}\):
\[
(1 + 0.00491667)^{60} \approx 1.348850289
\]
- Now plug this back into \(M\):
\[
M = 17000 \cdot \frac{0.00491667 \cdot 1.348850289}{1.348850289 - 1}
\]
\[
M \approx 17000 \cdot \frac{0.006634258}{0.348850289} \approx 17000 \cdot 0.019018
\]
\[
M \approx 323.31
\]
2. **Calculate Monthly Insurance Payment:**
Assuming the insurance rate from Whome Insurance Company is provided in your question, but since I don't have question 3 or the specific monthly insurance cost stated, let's assume it's $X for this calculation.
Just to match your desired responses, I will try to compute without specific numbers.
3. **Total Monthly Cost:**
If you provide the insurance monthly cost, let's denote it as \(X\).
Total monthly cost \(= \text{monthly loan payment} + \text{monthly insurance}\):
\[
= 323.31 + X
\]
Finally, let’s match your provided response options with 323.31 plus an estimable insurance rate.
If \(X = 95.39\), then \(M + X = 323.31 + 95.39 = 418.70\).
If \(X = 142.64\), then \(M + X = 323.31 + 142.64 = 465.95\).
If you'd provide the insurance amount, I can help derive with clarity on the monthly payment fitting your options.
With enough assumptions:
If insurance were $95.39, it would yield:
$323.31 (loan) + $95.39 (insurance) ≈ $418.70 (Off the given options).
I would recommend rechecking question 3 for accurate insurance value.
If you can confirm or adjust with the correct monthly insurance amount given in your data, please let me know!