To calculate the financing options for the 2021 Dodge Charger, we will look at two banks: BB&T and Sunflower. We will also calculate the one-time payment cost, including the car's price and state sales tax.
Step 1: Base Information
- Price of the vehicle: $30,250
- Odometer Reading: 2,200 miles
- Color: Blue
- VIN #: 5R27DL188S
Step 2: Sales Tax Calculation (Tennessee)
Tennessee has a state sales tax rate of approximately 7%. Local sales taxes can also apply, but we'll assume 7% for this calculation unless specified otherwise.
Sales Tax Calculation:
\[ \text{Sales Tax} = \text{Price of Vehicle} \times \text{Sales Tax Rate} \] \[ \text{Sales Tax} = 30,250 \times 0.07 = 2,117.50 \]
Step 3: Total Cost of the Car (One-time payment)
Total Cost Calculation:
\[ \text{Total Cost of Car} = \text{Price of Vehicle} + \text{Sales Tax} \] \[ \text{Total Cost of Car} = 30,250 + 2,117.50 = 32,367.50 \]
Step 4: Financing Options
Next, we'll assume some typical financing parameters for both banks. For this example, we'll use the following assumptions for both banks:
- Loan Amount: $30,250 (we'll assume no down payment)
- Loan Term: 60 months (5 years)
- Interest Rate: Let's assume Bank #1 (BB&T) offers 5% and Bank #2 (Sunflower) offers 6%.
Bank #1 (BB&T)
Formula for Monthly Payment (PMT): \[ PMT = \frac{P \times r(1 + r)^n}{(1 + r)^n - 1} \] Where:
- \(P\) = principal (loan amount = $30,250)
- \(r\) = monthly interest rate (annual rate/12)
- \(n\) = number of payments (loan term in months)
Monthly Payment Calculation for BB&T:
\[ r = \frac{5%}{12} = 0.0041667 \] \[ n = 60 \] \[ PMT = \frac{30,250 \times 0.0041667(1 + 0.0041667)^{60}}{(1 + 0.0041667)^{60} - 1} \] \[ PMT = \frac{30,250 \times 0.0041667 \times 1.28368}{0.28368} \approx \frac{162.68}{0.28368} \approx 573.45 \]
Total Cost for BB&T:
\[ \text{Total Cost} = PMT \times n \] \[ \text{Total Cost} = 573.45 \times 60 = 34,407 \]
Bank #2 (Sunflower)
Monthly Payment Calculation for Sunflower:
Using 6% interest: \[ r = \frac{6%}{12} = 0.005 \] \[ PMT = \frac{30,250 \times 0.005(1 + 0.005)^{60}}{(1 + 0.005)^{60} - 1} \] \[ PMT = \frac{30,250 \times 0.005 \times 1.34885}{0.34885} \approx \frac{203.25}{0.34885} \approx 582.94 \]
Total Cost for Sunflower:
\[ \text{Total Cost} = PMT \times n \] \[ \text{Total Cost} = 582.94 \times 60 = 34,976.40 \]
Step 5: Compare Banks
-
Bank #1 (BB&T)
- Monthly Payment: $573.45
- Total Cost: $34,407
-
Bank #2 (Sunflower)
- Monthly Payment: $582.94
- Total Cost: $34,976.40
Best option: Bank #1 (BB&T) since it has a lower total cost.
Step 6: Cost of One-time Payment
Total Cost of Car including sales tax: \[ \text{Total Cost of Car} = 32,367.50 \]
Step 7: Savings from Paying Up Front
To find out how much is saved by paying upfront versus financing with the better bank (BB&T): \[ \text{Savings} = \text{Total Cost of Car} - \text{Total Cost from BB&T} \] \[ \text{Savings} = 32,367.50 - 34,407 = -2,039.50 \]
In this calculation, you would not save money by financing with Bank #1. Instead, it shows that financing is more expensive.
Summary
- Total Cost of Car (One-time Payment): $32,367.50
- Best Bank Option: BB&T
- Savings by paying up front: You incur an additional cost, specifically -$2,039.50 when financing.
This means you would be spending more if you finance than if you simply pay for the vehicle outright.
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