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B3.2 · Compare buying new, leasing, and buying used vehicles

Learn to compare buying new, leasing, and buying used vehicles through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Personal Finance

A practical way to compare costs, use, and ownership

A vehicle can be obtained in different ways. You can buy a new vehicle, lease a vehicle for an agreed period, or buy a used vehicle. Each choice has different costs and conditions. A fair comparison uses the same time period and considers what the driver has at the end. This lesson uses simple estimates and practical details to compare the three options. The examples are estimates, not promises about actual vehicle costs.

What you will learn

1. Understand the three choices

Buying a new vehicle means purchasing one that has not previously been owned by another driver. The buyer owns it and can keep it, sell it, or trade it in. A new vehicle often costs more at first than a similar used vehicle. Its value may also fall as it is used.
Leasing means paying to use a vehicle for an agreed period. The leasing company usually remains the owner. The agreement may set a maximum distance, called a mileage limit, and may charge for extra distance or damage beyond normal wear. At the end, the driver usually returns the vehicle or follows an agreed purchase option.
Buying a used vehicle means purchasing a vehicle that had a previous owner. Its purchase price is often lower than that of a similar new vehicle, but its condition and repair needs can vary. A buyer should consider the vehicle’s age, distance driven, and maintenance history.

2. Compare costs for the same period

A comparison is more useful when every option covers the same length of time. For example, compare each choice over three years rather than comparing a three-year lease with the full purchase price of a vehicle kept for ten years.
For a purchased vehicle, one simple estimate is the purchase price minus the amount expected from selling it later, plus estimated maintenance and repair costs. The expected sale amount is called resale value. This estimate describes the cost of using the vehicle during the comparison period, not the amount paid on the purchase day.
For a lease, add the payments and any upfront amount or required fees for the same period. The driver usually does not have a vehicle to sell at the end. For a used vehicle, include expected maintenance and repairs because they affect the estimated cost.
These estimates leave out costs such as insurance and fuel unless the problem gives them. Include those costs when reliable amounts are available. Taxes, financing costs, and lease-end charges can also change the real total. State what is included so the comparison is clear.
Estimated purchase-use cost\text{Estimated purchase-use cost}=purchase price\text{purchase price}-resale value\text{resale value}+maintenance and repairs

3. Consider use and ownership, not only cost

The lowest estimated cost is not automatically the best fit. A driver who travels long distances should check whether a lease’s mileage limit fits their usual driving. A driver who wants to keep a vehicle for many years may prefer owning one. Someone seeking a lower purchase price may consider a used vehicle, while also checking its condition and possible repair needs.
A comparison should note what the driver has at the end of the chosen period. A buyer may still own a vehicle that can be kept or sold. A person returning a leased vehicle usually gives it back and may face charges if the agreement’s conditions were not met.
Ask: What is the estimated cost over the same period? How far will the driver travel? What maintenance or repairs are likely? Does the driver want to own a vehicle at the end? The answers make the comparison more personal and useful.

A comparison checklist

ChoiceWhat to include in a cost estimateWhat to check
Buy newPurchase price, expected resale value, maintenanceHow long the vehicle will be kept
LeasePayments, upfront amount, stated feesMileage limit, return conditions, end-of-lease plans
Buy usedPurchase price, expected resale value, maintenance and repairsCondition, distance driven, service record

Worked example

Example 1: Compare estimated three-year costs

A driver is comparing three options over three years. A new vehicle costs CAD 32,000 and is expected to sell for CAD 18,000 after three years. Estimated maintenance is CAD 1,200. A lease costs CAD 420 per month for 36 months, plus CAD 1,800 upfront. A used vehicle costs CAD 16,000, is expected to sell for CAD 8,000 after three years, and has estimated maintenance and repairs of CAD 3,000. Which option has the lowest estimated cost, before insurance, fuel, taxes, and financing?
  1. Set the comparison period
    All three options cover three years, so their estimated costs can be compared fairly over the same period. The listed exclusions mean these are partial cost estimates.
  2. Estimate the new-vehicle cost
    Subtract the expected sale amount from the purchase price to estimate the value lost during use. Then add estimated maintenance.
    32,000−18,000+1,200=15,20032{,}000-18{,}000+1{,}200=15{,}200
  3. Estimate the lease cost
    There are 36 monthly payments. Multiply the monthly payment by 36, then add the upfront amount. In this example, the driver returns the vehicle, so there is no resale value to subtract.
    420×36+1,800=16,920420\times36+1{,}800=16{,}920
  4. Estimate the used-vehicle cost
    Subtract the expected sale amount from the purchase price, then add estimated maintenance and repairs.
    16,000−8,000+3,000=11,00016{,}000-8{,}000+3{,}000=11{,}000
  5. Compare the results
    The used vehicle has the lowest estimated three-year cost in these figures. This does not prove it is the best choice; the vehicle’s condition and the repair estimate still matter.
    11,000<15,200<16,92011{,}000<15{,}200<16{,}920
Answer: The used vehicle has the lowest estimated three-year cost at CAD 11,000. The new-vehicle estimate is CAD 15,200, and the lease estimate is CAD 16,920.
Check: The lease payments total CAD 15,120 because CAD 420 multiplied by 36 is CAD 15,120. Adding CAD 1,800 gives CAD 16,920. All three estimates cover three years.

Worked example

Example 2: Match a vehicle choice to driving needs

A driver expects to travel about 24,000 km each year and wants to keep a vehicle for at least six years. A lease offer allows 18,000 km per year and lasts three years. The driver has found a used vehicle with a service record, but its repair costs are uncertain. What should the driver consider before choosing?
  1. Estimate the driver's distance
    Multiply the expected yearly distance by the three-year lease term. This gives the driver's estimated total distance during the agreement.
    24,000×3=72,000 km24{,}000\times3=72{,}000\text{ km}
  2. Find the lease allowance
    Multiply the allowed yearly distance by the three-year term. Comparing this allowance with the driver’s estimate shows whether the driving plan fits the stated limit.
    18,000×3=54,000 km18{,}000\times3=54{,}000\text{ km}
  3. Compare distance and time plans
    The driver’s estimate is 18,000 km above the lease allowance. Also, the lease lasts three years while the driver wants a vehicle for at least six years. The driver should ask about extra-distance charges and consider what they would do after the lease ends.
    72,000−54,000=18,000 km72{,}000-54{,}000=18{,}000\text{ km}
  4. Investigate the used vehicle
    A service record is useful, but it cannot guarantee future repair costs. The driver should get a realistic condition and repair estimate, then compare costs over the same six-year period as the other choices.
Answer: The lease may not fit the driver’s distance or six-year plan without extra costs or another vehicle arrangement after three years. The used vehicle may better suit long-term ownership, but its condition and likely repair costs should be investigated before choosing.
Check: The lease allows 54,000 km over three years, while the driver expects 72,000 km. The difference is 18,000 km, so the driver should check the agreement’s extra-distance terms.

Common mistakes and how to avoid them

Comparing a lease’s total payments with a purchased vehicle’s full price without considering its later sale value.
Correction: Use the same time period and subtract the purchase option’s expected resale value when estimating its use cost.
Assuming a lease has no costs beyond the monthly payment.
Correction: Check the upfront amount, fees, mileage limit, and return conditions in the agreement.
Choosing a used vehicle based only on its lower purchase price.
Correction: Consider its condition and likely maintenance and repair costs as well.

Lesson summary

Check your understanding

Question 1

A driver leases a vehicle for 24 months at CAD 390 per month, with CAD 1,000 upfront. What is the estimated lease cost before other charges?
  1. CAD 8,360
  2. CAD 9,360
  3. CAD 10,360
  4. CAD 11,360
Show answer and explanation
CAD 10,360
Multiply CAD 390 by 24 to get CAD 9,360. Add the CAD 1,000 upfront amount to get an estimated total of CAD 10,360, which is option 3.

Question 2

Which detail is especially important to check when considering a lease?
  1. The agreement’s mileage limit and return conditions
  2. The used vehicle’s service record
  3. The new vehicle’s expected resale amount
  4. The used vehicle’s purchase price
Show answer and explanation
The agreement’s mileage limit and return conditions
Mileage limits and return conditions are part of the lease agreement and may affect the cost of returning the vehicle.

Question 3

A used vehicle costs CAD 14,000, is expected to sell for CAD 7,000 after the comparison period, and has CAD 2,500 in estimated repairs. What is its estimated use cost?
  1. CAD 4,500
  2. CAD 9,500
  3. CAD 23,500
  4. CAD 16,500
Show answer and explanation
CAD 9,500
Subtract the expected resale amount and add repairs: CAD 14,000 minus CAD 7,000 plus CAD 2,500 is CAD 9,500.

Key terms

Lease
An agreement to pay to use a vehicle for a set period, subject to stated conditions.
Resale value
The amount a vehicle may bring when it is sold later.
Mileage limit
The maximum distance allowed under a lease agreement before extra charges may apply.
Maintenance
Regular care that helps keep a vehicle working, such as scheduled servicing.

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About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MBF3C), expectation B3.2. It is a study resource, not an official curriculum publication.

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