On the next page you will take out a loan from a bank and compute the monthly payment & total amount paid for the vehicle over the life of the loan. You will also compute the price of the car if you choose not to take out a loan.

Question

2020 Hyundai Kona
$20,200
Vin #: 3K44DM19XS
Odometer Reading: 2,200 miles Color: Blue
2021 Dodge Charger
$30,250
Vin #: 5R27DL188S
Odometer Reading: 12,500 miles Color: White
2021 Ford Focus
$24,535
Vin #: 2701GH1DM2 Odometer Reading: 14,509

PMT =
Bank Information:
Bank #1: BB&T: 12% for 4 years
Bank #2: Sunflower: 9% for 6 years

1.) Vehicle chosen:
Financing Option: Calculate financing for both banks. Work must be shown to receive credit.
Bank #1 (BB&T)
vs. Bank #2 (Sunflower)
Monthly Payment
Total Cost of the Car
Monthly Payment
Total Cost of the Car
Which bank is the best option? Writing a Check Option
Determine how much it would cost to make a one time payment for the vehicle at checkout. Work must be shown to receive credit (include the cost of the car and the TN sales tax but do not include any other fees or discounts).
Total Cost of Car:
How much money would you save paying up front versus financing with the better bank?

Vehicle chosen:

Financing Option: Calculate financing for both banks. Work must be shown legibly to receive credit.
Bank #1 (BB&T)
vs. Bank #2 (Sunflower)
Monthly Payment
Total Cost of the Car
Which bank is the best option?
Writing a Check Option Work must be shown legibly to receive credit.
Monthly Payment
Total Cost of the Car
Determine how much it would cost to make a one time payment for the vehicle at checkout. Show your calculations below (include the cost of the car and the TN sales tax but do not include any other fees or discounts).
Total Cost of Car:
How much money would you save paying up front versus financing with the better bank?

Vehicle chosen:

Financing Option: Calculate financing for both banks. Work must be shown legibly to receive credit.
Bank #1 (BB&T) vs.
Bank #2 (Sunflower)
Monthly Payment
Total Cost of the Car
Monthly Payment
Total Cost of the Car
Which bank is the best option?
Writing a Check Option Work must be shown legibly to receive credit.
Determine how much it would cost to make a one time payment for the vehicle at checkout. Show your calculations below (include the cost of the car and the TN sales tax but do not include any other fees or discounts).
Total Cost of Car:
How much money would you save paying up front versus financing with the better bank?

Answer 1

To analyze the financing options for the vehicles given, let’s break down the calculations step by step.

Vehicle Chosen

Let’s choose the 2021 Ford Focus priced at $24,535.

State Sales Tax Calculation

For Tennessee, the state sales tax on vehicle purchases is 7%.

• Sales Tax = Purchase Price × Sales Tax Rate \[ \text{Sales Tax} = 24,535 \times 0.07 = 1,717.45 \]
• Total Cost of Car = Purchase Price + Sales Tax \[ \text{Total Cost} = 24,535 + 1,717.45 = 26,252.45 \]

Financing Options

Bank #1: BB&T

• Loan Amount: $24,535 (the cost of the car)
• Interest Rate: 12% annual
• Loan Term: 4 years (48 months)

Calculating Monthly Payment using the formula: \[ PMT = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] Where:

• \(P\) = loan principal (amount borrowed)
• \(r\) = monthly interest rate (annual rate / 12)
• \(n\) = number of payments (loan term in months)

Convert the annual interest rate to a monthly interest rate: \[ r = \frac{12%}{12} = 0.01 \] And \(n = 48\).

Plugging the numbers into the formula: \[ PMT = 24,535 \frac{0.01(1 + 0.01)^{48}}{(1 + 0.01)^{48} - 1} \] Calculating \((1 + 0.01)^{48} \approx 1.488863\): \[ PMT = 24,535 \frac{0.01 \cdot 1.488863}{1.488863 - 1} \approx 24,535 \frac{0.01488863}{0.488863} \approx 24,535 \cdot 0.030473 \approx 748.52 \]

Total Cost of the Car with Bank #1: \[ \text{Total Payments} = 748.52 \times 48 = 35,964.96 \]

Bank #2: Sunflower

• Loan Amount: $24,535
• Interest Rate: 9% annual
• Loan Term: 6 years (72 months)

Convert the annual interest rate to a monthly interest rate: \[ r = \frac{9%}{12} = 0.0075 \] And \(n = 72\).

Plugging the numbers into the formula: \[ PMT = 24,535 \frac{0.0075(1 + 0.0075)^{72}}{(1 + 0.0075)^{72} - 1} \] Calculating \((1 + 0.0075)^{72} \approx 1.747422\): \[ PMT = 24,535 \frac{0.0075 \cdot 1.747422}{1.747422 - 1} \approx 24,535 \frac{0.01310566}{0.747422} \approx 24,535 \cdot 0.0175443 \approx 430.91 \]

Total Cost of the Car with Bank #2: \[ \text{Total Payments} = 430.91 \times 72 = 31,025.52 \]

Summary of Financing

• Bank #1 (BB&T):

  • Monthly Payment: $748.52
  • Total Cost of Car: $35,964.96

• Bank #2 (Sunflower):

  • Monthly Payment: $430.91
  • Total Cost of Car: $31,025.52

Which Bank is the Best Option?

Bank #2 (Sunflower) is the better option as it has lower monthly payments and a lower total cost.

Total Cost of Car (Writing a Check Option)

• Total Cost of Car: $26,252.45

Savings Calculation

Savings from paying upfront versus financing with the better bank (Sunflower): \[ \text{Savings} = \text{Total Cost with Sunflower} - \text{Total Cost of car if paid upfront} \] \[ \text{Savings} = 31,025.52 - 26,252.45 = 4,773.07 \]

Final Summary

• Vehicle Chosen: 2021 Ford Focus
• Bank Chosen: Sunflower
• Monthly Payment: $430.91
• Total Cost with Bank: $31,025.52
• Total Cost if Paid Upfront: $26,252.45
• Total Savings by Paying Upfront: $4,773.07