C1.4 · Compare costs of buying new, leasing, and buying used

Ontario Grade 11 Mathematics

Transportation and Travel

A practical way to compare vehicle choices over the same period

What you will learn

• Identify the costs to include when comparing buying new, leasing, and buying used.
• Use repeated calculations to estimate each choice's cost over the same length of time.
• Compare the results and explain what assumptions could change the decision.

Start with a fair comparison

• Set one time period for every option.
• Check what each quoted amount includes.
• Use estimates that match the same period and driving needs.

List the costs for each choice

• A purchase can have a resale amount at the end; a lease usually does not give you one.
• Include relevant fees and estimated upkeep for the chosen period.
• Make clear which possible costs are left out.

Add the estimates and make a decision

• Add costs that happen during the same time period.
• Subtract estimated resale value for a vehicle you buy and later sell.
• A lower estimated cost is useful information, but check the assumptions too.

Use a calculator or spreadsheet carefully

• Multiply repeated payments by the number of payments.
• Check that amounts use the same units and time period.
• Keep estimates and confirmed costs clearly separate.

What to count over the chosen period

Worked example

Compare three choices over three years

1. Set the comparison period
   Use three years for all three choices. This makes the totals comparable. The lease has thirty-six monthly payments because there are twelve months in each year.
2. Find the new vehicle estimate
   Add the purchase cost and upkeep, then subtract the money expected from selling the vehicle. Subtracting the resale amount accounts for money received at the end.
   $$\mathrm{CAD}\ 31{,}640 + \mathrm{CAD}\ 1{,}800 - \mathrm{CAD}\ 14{,}000 = \mathrm{CAD}\ 19{,}440$$
3. Find the lease estimate
   Multiply the monthly payment by thirty-six, then add the starting amount, return fee, and upkeep. There is no resale amount to subtract because the vehicle is returned.
   $$36 \times \mathrm{CAD}\ 475 + \mathrm{CAD}\ 2{,}000 + \mathrm{CAD}\ 400 + \mathrm{CAD}\ 900 = \mathrm{CAD}\ 20{,}400$$
4. Find the used vehicle estimate
   Add the purchase cost and upkeep, then subtract the estimated resale amount. The larger upkeep estimate reflects the assumption in this sample; it is not a guarantee of future repairs.
   $$\mathrm{CAD}\ 16{,}950 + \mathrm{CAD}\ 3{,}600 - \mathrm{CAD}\ 9{,}000 = \mathrm{CAD}\ 11{,}550$$
5. Compare the totals
   The used option has the lowest estimated cost in this set of estimates. The worker should still check the vehicle's condition and whether the estimated upkeep and resale amounts are reasonable.

Worked example

Check how a lease limit changes the comparison

1. Keep the period consistent
   Use two years for all options. The lease has twenty-four monthly payments. Include the kilometre charge because the problem says the driver expects it to apply.
2. Calculate the new option
   Add purchase cost and upkeep, then subtract estimated resale. The result is the estimated cost after two years, based on the stated amounts.
   $$\mathrm{CAD}\ 30{,}510 + \mathrm{CAD}\ 1{,}200 - \mathrm{CAD}\ 20{,}000 = \mathrm{CAD}\ 11{,}710$$
3. Calculate the lease option
   First find the total of the repeated payments. Add the starting amount, return fee, upkeep, and kilometre charge to include all listed lease costs.
   $$24 \times \mathrm{CAD}\ 520 + \mathrm{CAD}\ 1{,}500 + \mathrm{CAD}\ 350 + \mathrm{CAD}\ 700 + \mathrm{CAD}\ 900 = \mathrm{CAD}\ 15{,}930$$
4. Calculate the used option
   Add the purchase and upkeep estimates, then subtract the amount expected from selling the vehicle at the end.
   $$\mathrm{CAD}\ 18{,}080 + \mathrm{CAD}\ 2{,}500 - \mathrm{CAD}\ 12{,}000 = \mathrm{CAD}\ 8{,}580$$
5. Interpret the result
   The used option is lowest in this estimate. The lease total depends on the kilometre charge applying. If the driver stays within the limit, that cost may not apply, so the lease estimate would be lower by CAD 900.

Common mistakes and how to avoid them

Lesson summary

• Choose one time period for all three options.
• Add payments, purchase costs, upkeep, and expected fees that apply.
• For a purchase, subtract expected resale value if you plan to sell.
• Compare the estimates and check assumptions that could change them.

Check your understanding

Key terms

Upkeep

Routine servicing and repairs needed to keep a vehicle in use.

Resale value

The amount you estimate receiving when you sell a vehicle.

Lease

An agreement to pay to use a vehicle for a set period, usually with conditions for its return.

Estimate

A carefully chosen approximate amount, rather than a guaranteed final cost.

Continue through MEL3E

View the complete Ontario Grade 11 Mathematics learning path

• C1.1 · Interpret driver-licensing procedures, costs, and restrictions
• C1.2 · Describe procedures for buying or leasing a vehicle
• C1.3 · Compare vehicle insurance factors and costs
• C1.5 · Explain consequences of irresponsible vehicle operation
• C1.6 · Compare business costs and benefits of using a vehicle
• C1.7 · Solve fixed and variable vehicle-cost problems

About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation C1.4. It is a study resource, not an official curriculum publication.

Official curriculum reference

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