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 determine the monthly total interest and insurance costs, we first need to calculate the monthly payment for the loan based on the given APR and then add the monthly insurance cost.
### Step 1: Calculate Monthly Loan Payment
We will use the formula for the monthly payment on an amortizing loan:
\[
M = P \frac{r(1+r)^n}{(1+r)^n - 1}
\]
Where:
- \(M\) = monthly payment
- \(P\) = principal amount (loan amount)
- \(r\) = monthly interest rate (annual rate / 12)
- \(n\) = number of payments (loan term in months)
Assuming you take out a loan for the full purchase price of the car ($17,000) and for a term of 5 years (60 months), the calculations are as follows:
1. Principal \(P = 17,000\)
2. Annual Interest Rate (APR) = 5.90%
3. Monthly Interest Rate (\(r\)) = \(5.90\% / 12\) = \(0.00491667\)
4. Number of Payments (\(n\)) = 5 years * 12 months/year = 60 months
Calculating the Monthly Payment \(M\):
\[
M = 17000 \cdot \frac{0.00491667(1+0.00491667)^{60}}{(1+0.00491667)^{60}-1}
\]
Calculating the numerator and denominator:
- \((1 + 0.00491667)^{60} \approx 1.348850\)
- Thus, the equation simplifies:
\[
M = 17000 \cdot \frac{0.00491667 \cdot 1.348850}{1.348850 - 1}
\]
Calculating:
\[
M = 17000 \cdot \frac{0.00662837}{0.348850}
\]
\[
M \approx 17000 \cdot 0.019017
\]
\[
M \approx 323.29
\]
### Step 2: Determine Monthly Insurance Cost
You mentioned Whome Insurance Company, but without a specific insurance premium, I can't calculate it. If you have a specific amount for the insurance cost per month, please provide it.
### Step 3: Calculate Total Monthly Payment
Assuming you have an insurance cost that you provide, we will add it to the monthly payment:
Total Monthly Cost = Monthly Loan Payment + Monthly Insurance Cost
Given the options, if we assume some reasonable value for the insurance premium (e.g. $95), we can derive potential options, but you'll need to confirm or provide the monthly insurance amount for accurate results.
If we had the monthly insurance (for example, let’s say it was $100) then:
Total = \(323.29 + 100 = 423.29\) (which may exceed the given options).
### Conclusion
To finalize the solutions for the options \(95.39, 150.52, 142.64, 162.33\), you would need to provide the rate from "Whome Insurance Company." Without that, we cannot accurately select the correct option from the given answers.
### Step 1: Calculate Monthly Loan Payment
We will use the formula for the monthly payment on an amortizing loan:
\[
M = P \frac{r(1+r)^n}{(1+r)^n - 1}
\]
Where:
- \(M\) = monthly payment
- \(P\) = principal amount (loan amount)
- \(r\) = monthly interest rate (annual rate / 12)
- \(n\) = number of payments (loan term in months)
Assuming you take out a loan for the full purchase price of the car ($17,000) and for a term of 5 years (60 months), the calculations are as follows:
1. Principal \(P = 17,000\)
2. Annual Interest Rate (APR) = 5.90%
3. Monthly Interest Rate (\(r\)) = \(5.90\% / 12\) = \(0.00491667\)
4. Number of Payments (\(n\)) = 5 years * 12 months/year = 60 months
Calculating the Monthly Payment \(M\):
\[
M = 17000 \cdot \frac{0.00491667(1+0.00491667)^{60}}{(1+0.00491667)^{60}-1}
\]
Calculating the numerator and denominator:
- \((1 + 0.00491667)^{60} \approx 1.348850\)
- Thus, the equation simplifies:
\[
M = 17000 \cdot \frac{0.00491667 \cdot 1.348850}{1.348850 - 1}
\]
Calculating:
\[
M = 17000 \cdot \frac{0.00662837}{0.348850}
\]
\[
M \approx 17000 \cdot 0.019017
\]
\[
M \approx 323.29
\]
### Step 2: Determine Monthly Insurance Cost
You mentioned Whome Insurance Company, but without a specific insurance premium, I can't calculate it. If you have a specific amount for the insurance cost per month, please provide it.
### Step 3: Calculate Total Monthly Payment
Assuming you have an insurance cost that you provide, we will add it to the monthly payment:
Total Monthly Cost = Monthly Loan Payment + Monthly Insurance Cost
Given the options, if we assume some reasonable value for the insurance premium (e.g. $95), we can derive potential options, but you'll need to confirm or provide the monthly insurance amount for accurate results.
If we had the monthly insurance (for example, let’s say it was $100) then:
Total = \(323.29 + 100 = 423.29\) (which may exceed the given options).
### Conclusion
To finalize the solutions for the options \(95.39, 150.52, 142.64, 162.33\), you would need to provide the rate from "Whome Insurance Company." Without that, we cannot accurately select the correct option from the given answers.