Question

John is looking for a new car. Je has a down payment of $1,500.00 and wants to pay $250.00 per month for 5 years. The best deal he found for an amortized loan is his local bank, at a rate of 2.35%. What is the highest price car he should consider buying?

Answer 1

John should consider buying a car with a maximum price of $11,874.14.

Step-by-step explanation:

To find the highest price car John should consider buying, we need to calculate the total loan amount he can afford based on his down payment and monthly payments. First, calculate the total payment over 5 years by multiplying the monthly payment ($250.00) by the number of months (5 years * 12 months/year = 60 months) to get $15,000. Then, subtract the down payment ($1,500.00) from the total payment to get $13,500. To find the highest price car, divide $13,500 by (1 + 2.35%)^5 to calculate the present value.

Using the present value formula:

1. Loan amount = Total Payment / (1 + Interest Rate)^5
2. Loan amount = $13,500 / (1 + 2.35%)^5

Calculating the loan amount:

• Loan amount = $13,500 / (1 + 0.0235)^5
• Loan amount = $13,500 / (1.0235)^5
• Loan amount ≈ $11,874.14

Therefore, John should consider buying a car with a maximum price of $11,874.14 to stay within his budget.

Answer 2

The highest price car John should consider buying is $2,685.99

The Breakdown

To calculate the highest price car John should consider buying, we need to determine the total amount he can borrow based on his down payment and monthly payment.

Calculating the total amount John can borrow using the monthly payment and loan term:

Monthly payment: $250.00

Loan term: 5 years

Total amount borrowed = Monthly payment x Loan term

Total amount borrowed = $250.00 x 5

Total amount borrowed = $1,250.00

Calculating the total loan amount, including the down payment:

Total loan amount = Total amount borrowed + Down payment

Total loan amount = $1,250.00 + $1,500.00

Total loan amount = $2,750.00

Calculating the maximum price of the car John should consider buying, taking into account the interest rate:

Maximum price = Total loan amount / (1 + Interest rate)

Maximum price = $2,750.00 / (1 + 0.0235)

Maximum price = $2,750.00 / 1.0235

Maximum price ≈ $2,685.99

Therefore, the highest price car John should consider buying is $2,685.99.