Unit F: Finance

Financing Loans for Vehicle Purchases and Leases

Example 4

Britta purchased a car for $24 985.00. Four years later, the car is worth $11 200.00.

How much value did Britta's car lose due to depreciation?
Calculate the depreciation per year.

Solutions

The depreciation over four years can be found by subtracting the present value of the car from the initial cost of the car.

$\begin{array}{rcl} depreciation & = & initial cost of vehicle - present value of vehicle \\ = & $ 24 985.00 - $ 11 200.00 \\ = & $ 13 785.00 \end{array}$

Britta's car lost $13 785.00 due to depreciation.
To calculate the depreciation per year, divide the depreciation amount by the number of years.

The depreciation per year is

$\frac{$ 13 785}{4 years} = $ 3 446.25$

Britta's car depreciated $3 446.25 per year.

Example 5

Markus leases a $19 567.42 van for 42 months. Markus' monthly payments are $419.00.

Calculate the total cost of the lease.
The van has a residual value of $7 500.00. If Markus purchases the van at the end of the lease, what is the total amount that Markus would pay for the van?
Instead of leasing, Markus has the option to buy the van at an interest rate of 7%. What will his monthly payment be?
What is the total amount that Markus will pay for the van if he purchases it?
How much more will Markus pay for the van if he leases it first?

Solutions

$\begin{array}{rcl} total cost of lease & = & monthly payment \times number of monthly payments \\ = & $ 419.00 / month \times 42 months \\ = & $ 17 598.00 \end{array}$

The total that Markus paid in lease payments is $17 598.00.
To find the purchase price, add the cost of the lease payments and the residual value.

$17 598.00 + $7 500.00 = $25 098.00

The total amount that Markus would pay for the van is $25 098.00.

Use the Monthly Payment Calculator to find the monthly payment. Record the information in a chart.

principal	19 567.42
annual interest rate	7
number of monthly payments	42

Substitute the values from the chart into the Monthly Payment Calculator and then click

to find the monthly payment.

If Markus buys the van, the monthly payment will be $526.64.

$\begin{array}{rcl} total cost of loan & = & monthly payment \times number of monthly payments \\ = & $ 526.64 / month \times 42 months \\ = & $ 22 118.88 \end{array}$

Markus will pay $22 118.88 for the van.
Find the difference between the total cost of the lease and the total cost of the loan for the van (use the values found in part b and part d above).

$\begin{array}{rcl} total cost of the lease - total cost of the loan & = & $ 25 098.00 - $ 22 118.88 \\ = & $ 2 979.12 \end{array}$

Markus will pay an additional $2 979.12 if he buys the van after the lease.

When leasing a vehicle, it is important to not exceed the kilometre allowance to avoid penalties.

Example 6

When Marilyn returned a car after a 36 month lease, the odometer reading was 24 536 km. The kilometre allowance for the lease was 20 000 km. If the cost of excess kilometres is $0.32/km, what penalty will Marilyn pay for exceeding the kilometre allowance?

Solution

The extra kilometres driven is equal to the difference between the number of kilometres driven and the kilometre allowance of 20 000 km.

\begin{array}{rcl} extra kilometres & = & 24 536 - 20 000 \\ = & 4 536 \end{array}

Marilyn exceeded the kilometre allowance by 4 536 km. Multiply this value by the cost per extra kilometre.

\begin{array}{rcl} penalty & = & cost / km \times extra km driven \\ = & $ 0.32 \times 4 536 \\ = & $ 1 451.52 \end{array}

Marilyn will pay a penalty of $1 451.52 when she returns the car at the end of the lease.