Automobile lease vs. purchase A car dealer offers a purchase...

Automobile lease vs. purchase $A$ car dealer offers a purchase option and a lease option on all new cars. Suppose you are interested in a car that can be bought outright for $\$ 25,000$ or leased for a start-up fee of $\$ 1200$ plus monthly payments of $\$ 350$. a. Find the linear function $y=f(m)$ that gives the total amount you have paid on the lease option after $m$ months. b. With the lease option, after a 48 -month (4-year) term, the car has a residual value of $\$ 10,000,$ which is the amount that you could pay to purchase the car. Assuming no other costs, should you lease or buy?

Automobile lease vs. purchase $A$ car dealer offers a purchase option and a lease option on all new cars. Suppose you are interested in a car that can be bought outright for $\$ 25,000$ or leased for a start-up fee of $\$ 1200$ plus monthly payments of $\$ 350$.
a. Find the linear function $y=f(m)$ that gives the total amount you have paid on the lease option after $m$ months.
b. With the lease option, after a 48 -month (4-year) term, the car has a residual value of $\$ 10,000,$ which is the amount that you could pay to purchase the car. Assuming no other costs, should you lease or buy?

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Key Concepts

Linear Functions

Linear functions model relationships where one quantity changes at a constant rate with respect to another. In financial contexts, they are used to represent costs that include a fixed initial fee (the intercept) and consistent, repeating charges (the slope) over time.

Residual Value

Residual value is the estimated remaining value of an asset at the end of a lease or depreciation period. It is critical in evaluating total costs, as it represents the amount one has to pay (or recoup) when transitioning from leasing to ownership.

Cost Analysis

Cost analysis is the process of evaluating all the monetary factors associated with different options to determine which is more economical. It involves summing fixed and variable costs over a period to compare alternatives, such as leasing versus purchasing in automotive finance.

Lease vs Purchase Decision

The lease versus purchase decision involves comparing the overall expenses, including upfront fees, recurring payments, and terminal costs like residual values, to decide whether leasing or buying an asset provides better financial value over time.

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