Question

key question # 18 (continued)

1. calculate the kilometre surcharge on each below. (8 marks)

a. allowable usage: 45000 km; actual usage 66976 km. $0.22/km surcharge
b. allowable usage: 60000 km; actual usage 65173 km. $0.09/km surcharge
c. allowable usage: 80000 km; actual usage 86593 km. $0.07/km surcharge
d. allowable usage: 100000 km; actual usage 93237 km. $0.14/km surcharge

1. calculate the cost of leasing each of the vehicles described below assuming the security deposit was not returned. (6 marks)

a. $2500 down payment
$400 refundable security deposit
60 monthly payments of $324.99
pst (8%) and gst (5%) on each monthly payment
allowable usage: 90000 km; actual usage 106584 km. $0.13/km surcharge

b. $500 down payment
$200 refundable security deposit
24 monthly payments of $156.00
pst (8%) and gst (5%) on each monthly payment
allowable usage: 40000 km; actual usage 51759 km. $0.20/km surcharge

1. richard decided to purchase his vehicle after the lease ran out. the purchase price of the vehicle is $11700.00. his previous lease payments were $457.25 monthly for 3 years not including gst and pst. he originally gave a down payment of $5500. what is the total purchase price of the vehicle if you include the cost of leasing and that he is paying cash for the purchase of the vehicle? (4 marks)

Explanation:

Calculate kilometre surcharges for Question 2

For each sub-question, the surcharge is calculated by multiplying the excess kilometres by the rate per kilometre.
Excess kilometres are calculated as:

$$\text{Excess km} = \max(0, \text{Actual usage} - \text{Allowable usage})$$

• a.

$$\text{Excess km} = 66976 - 45000 = 21976\text{ km}$$

$$\text{Surcharge} = 21976 \times \$0.22 = \$4834.72$$

• b.

$$\text{Excess km} = 65173 - 60000 = 5173\text{ km}$$

$$\text{Surcharge} = 5173 \times \$0.09 = \$465.57$$

• c.

$$\text{Excess km} = 86593 - 80000 = 6593\text{ km}$$

$$\text{Surcharge} = 6593 \times \$0.07 = \$461.51$$

• d.

$$\text{Excess km} = 93237 - 100000 \le 0 \implies 0\text{ km}$$

$$\text{Surcharge} = \$0.00$$

Calculate total leasing costs for Question 3

Using Leasing Cost Calculation and Sales Tax Application, we find the total cost. Since the security deposit is not returned, it is added to the total cost.
Total tax rate:

$$\text{PST} + \text{GST} = 8\% + 5\% = 13\%$$

Monthly payment with tax:

$$\text{Monthly Payment}_{\text{tax}} = \text{Base Payment} \times 1.13$$

• a.

$$\text{Monthly Payment}_{\text{tax}} = \$324.99 \times 1.13 = \$367.2387$$

$$\text{Total Monthly Payments} = 60 \times \$367.2387 = \$22034.32$$

$$\text{Excess km} = 106584 - 90000 = 16584\text{ km}$$

$$\text{Surcharge} = 16584 \times \$0.13 = \$2155.92$$

$$\text{Total Cost} = \$2500\text{ (down)} + \$400\text{ (deposit)} + \$22034.32 + \$2155.92 = \$27090.24$$

• b.

$$\text{Monthly Payment}_{\text{tax}} = \$156.00 \times 1.13 = \$176.28$$

$$\text{Total Monthly Payments} = 24 \times \$176.28 = \$4230.72$$

$$\text{Excess km} = 51759 - 40000 = 11759\text{ km}$$

$$\text{Surcharge} = 11759 \times \$0.20 = \$2351.80$$

$$\text{Total Cost} = \$500\text{ (down)} + \$200\text{ (deposit)} + \$4230.72 + \$2351.80 = \$7282.52$$

Calculate total purchase price for Question 4

We calculate the total cost including the lease payments and the final purchase price.
Assuming taxes (PST 8% + GST 5% = 13%) apply to both the lease payments and the final purchase price:

• Lease Payments with Tax:

$$\text{Monthly Payment}_{\text{tax}} = \$457.25 \times 1.13 = \$516.6925$$

$$\text{Total Lease Payments} = 36 \times \$516.6925 = \$18600.93$$

• Down Payment:

$$\$5500.00$$

• Purchase Price with Tax:

$$\text{Purchase Price}_{\text{tax}} = \$11700.00 \times 1.13 = \$13221.00$$

• Total Cost:

$$\text{Total} = \$5500.00 + \$18600.93 + \$13221.00 = \$37321.93$$

Answer:

Question 2

a. \(\$4834.72\)
b. \(\$465.57\)
c. \(\$461.51\)
d. \(\$0.00\)

Question 3

a. \(\$27090.24\)
b. \(\$7282.52\)

Question 4

\(\$37321.93\)