Lesson 2

1. Lesson 2

1.6. Explore 2

Mathematics 30-3 Module 2

Module 2: Number

What you should have discovered in Try This 2 and Share 2 is that lease payments can be significantly lower than payments on a loan. The reason for this is that lease payments are calculated using the amount the vehicle has depreciated, as opposed to the purchase amount.

The difference in the purchase amount and the depreciation is called the residual value. Residual value refers to the amount the vehicle is worth at the end of a lease.

In Try This 2, the depreciation amount was $23 000, which is significantly lower than the amount borrowed for the purchase amount of $37 000. Since significantly less money was borrowed, the payments required to pay it off are much lower.

But there is a catch—because you’re only financing the depreciation amount, you don’t own the vehicle at the end of the lease.

To summarize, there are two main differences between purchasing and leasing:

When purchasing, you finance the full amount. With leasing, you finance the depreciation amount.
When purchasing, you own the vehicle at the end of the loan period. With leasing, you do not own the vehicle at the end of the lease.

Now that you have a better understanding of the difference between leasing and purchasing, read “Explore the Math” on pages 298 and 299 of your textbook.

Consider the following more detailed purchasing example:

This is a picture of woman next to a kayak.

Thomas Northcut/Lifesize/Thinkstock

Sadia plans to start a small business next summer guiding kayakers on the Kananaskis River. She plans to buy a used truck to pull a kayak trailer. The seller is asking $5400, and Sadia has $1500 she can use for a down payment. She gets a four-year loan for the balance, with monthly payments of $87.89.

What was the total interest charged on the loan?

This problem requires a two-step solution process:

Step 1: Determine the amount of the loan.
Step 2: Determine the total amount paid by Sadia when paying off the loan.

Step 1: Determine the amount of the loan.

Sadia has $1500 for a down payment. Therefore, she must borrow the remaining amount from a bank.

$5400.00 − $1500.00 = $3900.00

Step 2: Determine the total amount paid for the loan.

Sadia makes 48 payments of $87.89. Therefore, the total amount she paid for the loan is 48 × $87.89 = $4218.72.

If Sadia borrowed $3900.00 and paid back $4218.72, the difference must be the interest she was charged.

Often leasing a vehicle will include fees beyond payments and taxes. These can include taxes, a delivery fee, extra-kilometre fees, and a security deposit, which will be returned if there is no excessive damage to the vehicle.