Questions: Kim is purchasing a 40,000 vehicle. There are two options to pay for the vehicle: financing a 0% loan for 48 months or a 4 year lease with a down payment of 4,000 and payments of 800 per month. If she wants to choose the option with the lower total cost over the life of the vehicle, which should she choose? Select the correct answer below: Loan Lease

Solution Steps

To determine which option has the lower total cost over the life of the vehicle, we need to calculate the total cost for both the loan and the lease options.

1. For the loan option, the total cost is simply the price of the vehicle since there is no interest.
2. For the lease option, the total cost includes the down payment plus the monthly payments over the lease period.

The total cost for the loan option is simply the price of the vehicle: \[ \text{Total Cost}_{\text{Loan}} = 40000 \]

The total cost for the lease option includes the down payment and the total of the monthly payments over the lease duration: \[ \text{Total Cost}_{\text{Lease}} = \text{Down Payment} + (\text{Monthly Payment} \times \text{Lease Duration}) \] Substituting the values: \[ \text{Total Cost}_{\text{Lease}} = 4000 + (800 \times 48) = 4000 + 38400 = 42400 \]

Now we compare the total costs: \[ \text{Total Cost}_{\text{Loan}} = 40000 \] \[ \text{Total Cost}_{\text{Lease}} = 42400 \] Since \( 40000 < 42400 \), the loan option is cheaper.

Final Answer