- Multiply the monthly payment by the total number of months (\(36\)) to get \(\$13,284.00\).
- Calculate the excess mileage (\(3,676\) miles) and multiply by the rate (\(\$0.15\)) to find the charge of \(\$551.40\).
- Add the initial payment of \(\$3,300.00\), the total monthly payments, and the excess mileage charge together.
- The total lease cost is \(\boxed{17135.40}\).
Explanation
- Problem Analysis
To determine the total cost of Mike's vehicle lease, we need to account for all payments involved. This includes the initial upfront payment, the cumulative monthly payments over the three-year lease term, and any additional charges incurred for exceeding the allotted mileage limit. We are given:
- Initial payment: \(\$3,300.00\)
- Monthly payment: \(\$369.00\)
- Lease duration: \(3\) years (\(36\) months)
- Mileage allowance: \(36,000\) miles
- Total miles driven: \(39,676\) miles
- Excess mileage charge: \(\$0.15\) per mile over the limit.
- Calculating Total Monthly Payments
First, calculate the total cost of the monthly payments over the lease term. Since the lease lasts for three years and there are \(12\) months in each year, the total number of months is \(3 \times 12 = 36\) months. Multiplying this by the monthly payment:
\[36 \text{ months} \times \$369.00/\text{month} = \$13,284.00\]
This represents the total base cost of the payments over the three years.
- Calculating Excess Mileage Charges
Next, we determine the excess mileage charges. Mike drove \(39,676\) miles, which exceeds the allowance of \(36,000\) miles. The total number of excess miles is:
\[39,676 \text{ miles} - 36,000 \text{ miles} = 3,676 \text{ miles}\]
Now, multiply the excess mileage by the charge of \(\$0.15\) per mile:
\[3,676 \text{ miles} \times \$0.15/\text{mile} = \$551.40\]
This is the additional fee added to the lease contract.
- Final Calculation
Finally, sum the initial payment, the total of all monthly payments, and the excess mileage charges to find the total lease cost:
\[\$3,300.00 (\text{initial}) + \$13,284.00 (\text{monthly}) + \$551.40 (\text{excess}) = \$17,135.40\]
Thus, the total cost of the lease is \(\$17,135.40\). The final answer is \(\boxed{17135.40}\).
Examples
Lease agreements are common in vehicle ownership and real estate. Understanding how to calculate the total cost of a lease, including recurring fees and potential surcharges for usage limits (like mileage or occupancy), is an essential life skill. By performing these calculations, individuals can better manage their budget, compare different financing options, and avoid unexpected financial burdens at the end of a contract.