The car payment plan that has an APR of 1.9% is, on the short term, pocket
friendly.
The correct responses are;
- First part: The amount of loan Molly needs is $22,495
- Second part: Molly's monthly payment will be approximately $286.2
- Third part: The total interest Molly will pay using the plan is approximately $1,545.8
- Fourth part: The amount the car costs Molly using the plan is approximately $26,540.8
Reasons:
The question parameters are;
Molly is comparing Auto Loans on Jeep website
Selling price of the Jeep, P = $25,495
The down payment Molly has = $2,500
The Cash Allowance = $500
Number of months of payment, n = 84 months
The Annual Percentage Rate, APR, r = 1.9%
First Part:
Loan needed = $25,495 - $2,500 - $500 = $22,495
The amount of loan Molly needs = $22,495
Second Part:
The monthly payment is given by the formula;
- [tex]\displaystyle M = \mathbf{\dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}}[/tex]
Therefore;
[tex]\displaystyle M = \dfrac{22,495 \times \left(\dfrac{0.019}{12} \right) \times \left(1+\dfrac{0.019}{12} \right)^{84} }{\left(1+\dfrac{0.019}{12} \right)^{84} - 1} \approx \mathbf{286.2}[/tex]
Molly's monthly payment will be M ≈ $286.2
Third part:
The total interest, I = Sum of payment - Loan amount
∴ The total interest, I ≈ $286.2/month × 84 month - $22,495 ≈ $1,545.8
The total interest Molly will pay using the loan, I ≈ $1,545.8
Fourth part:
The cost of the car, C, using the 1.9% APR financing plan is the sum of the down payment plus sum of the loan repayment
Therefore;
C ≈ $2,500 + $286.2/month × 84 months = $26,540.8
The cost of the car using the 1.9% APR financing plan, C ≈ $26,540.8
The question parameters obtained from a similar question are;
Selling price of the car = $25,495
Financing = 1.9% APR for 84 months with a cash allowance of $500
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