Let's break down the problem and compute the total amount Easton will spend on the car for each option.

Step 1: Set up key information

• Price of the car: $25,083
• Easton’s saved down payment: $2,500
• Loan duration: 36 months (3 years)

Option A:

• APR (Annual Percentage Rate): 2.1%
• Loan term: 36 months
• Easton’s total down payment: $2,500
• Loan amount = Price of the car - Down payment
  = $25,083 - $2,500 = $22,583

Option B:

• APR (Annual Percentage Rate): 6.1%
• Loan term: 36 months
• Easton’s down payment: $2,500 + $2,000 cash back = $4,500
• Loan amount = Price of the car - Down payment
  = $25,083 - $4,500 = $20,583

Step 2: Monthly Payment Formula

We can use the formula for monthly payments on an amortizing loan:

$M = \frac{P \cdot r(1 + r)^n}{(1 + r)^n - 1}$

Where:

• $M$ = monthly payment
• $P$ = loan amount (principal)
• $r$ = monthly interest rate (APR divided by 12)
• $n$ = total number of payments (loan term in months)

Option A:

• $P = 22,583$
• APR = 2.1%, so monthly rate $r = \frac{2.1\%}{12} = \frac{0.021}{12} = 0.00175$
• $n = 36$

Option B:

• $P = 20,583$
• APR = 6.1%, so monthly rate $r = \frac{6.1\%}{12} = \frac{0.061}{12} = 0.005083$
• $n = 36$

Let’s calculate the monthly payments for both options.Let's manually calculate the monthly payments and total cost.

Option A:

• Loan Amount: $P = 22,583$
• APR: 2.1% → Monthly rate $r = \frac{0.021}{12} = 0.00175$
• Loan Term: $n = 36$ months

Using the monthly payment formula:

$M_A = \frac{22,583 \times 0.00175 \times (1 + 0.00175)^{36}}{(1 + 0.00175)^{36} - 1}$

Option B:

• Loan Amount: $P = 20,583$
• APR: 6.1% → Monthly rate $r = \frac{0.061}{12} = 0.005083$
• Loan Term: $n = 36$ months

Similarly:

$M_B = \frac{20,583 \times 0.005083 \times (1 + 0.005083)^{36}}{(1 + 0.005083)^{36} - 1}$

Let me resolve these calculations for you.Here are the results:

Option A:

• Monthly payment: $647.82
• Total amount spent over 36 months: $23,321.58

Option B:

• Monthly payment: $627.11
• Total amount spent over 36 months: $22,575.88

Conclusion:

• Option A (2.1% APR) results in a higher total cost ($23,321.58) but slightly higher monthly payments ($647.82).
• Option B (6.1% APR with $2,000 cash back) results in a lower total cost ($22,575.88) and slightly lower monthly payments ($627.11).

Would you like more details or clarification on any part?

Relative Questions:

1. How is APR applied to car loans?
2. How does a lower down payment affect total loan costs?
3. What are the advantages of cash-back offers in financing?
4. How does loan term length impact monthly payments?
5. Can early repayment lower total interest paid?

Tip:

Always compare the total cost of a loan, not just the monthly payments, to fully assess its affordability.