QUESTION IMAGE
Question
key question # 18 (continued)
- 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
- 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
- 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)
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</pre_analysis>
<reasoning>
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.
\[\text{Excess km} = 66976 - 45000 = 21976\text{ km}\]
\[\text{Surcharge} = 21976 \times \ LXI0 4834.72\]
- b.
\[\text{Excess km} = 65173 - 60000 = 5173\text{ km}\]
\[\text{Surcharge} = 5173 \times \ LXI0 465.57\]
- c.
\[\text{Excess km} = 86593 - 80000 = 6593\text{ km}\]
\[\text{Surcharge} = 6593 \times \ LXI0 461.51\]
- 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.
\[\text{Monthly Payment}_{\text{tax}} = \ LXI0 367.2387\]
\[\text{Total Monthly Payments} = 60 \times \ LXI0 22034.32\]
\[\text{Excess km} = 106584 - 90000 = 16584\text{ km}\]
\[\text{Surcharge} = 16584 \times \ LXI0 2155.92\]
\[\text{Total Cost} = \ LXI0 400\text{ (deposit)} + \ LXI1 2155.92 = \$27090.24\]
- b.
\[\text{Monthly Payment}_{\text{tax}} = \ LXI0 176.28\]
\[\text{Total Monthly Payments} = 24 \times \ LXI0 4230.72\]
\[\text{Excess km} = 51759 - 40000 = 11759\text{ km}\]
\[\text{Surcharge} = 11759 \times \ LXI0 2351.80\]
\[\text{Total Cost} = \ LXI0 200\text{ (deposit)} + \ LXI1 2351.80 = \$7282.52\]
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:
\[\text{Monthly Payment}_{\text{tax}} = \ LXI0 516.6925\]
\[\text{Total Lease Payments} = 36 \times \ LXI0 18600.93\]
- Down Payment:
\[\$5500.00\]
- Purchase Price with Tax:
\[\text{Purchase Price}_{\text{tax}} = \ LXI0 13221.00\]
- Total Cost:
\[\text{Total} = \ LXI0 18600.93 + \ LXI1 37321.93\]
</reasoning>
<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
\(\$37321.93\)
</answer>
<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Algebra",
"Leasing Cost Calculation"
]
}
</post_analysis>
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<pre_analysis>
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"explain_then_answer",
"tutor"
],
"needs_drawing": false,
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],
"new_concepts": [
"Kilometre Surcharge Calculation",
"Lease-to-Own Total Cost"
],
"current_concepts": [
"Leasing Cost Calculation",
"Sales Tax Application",
"Kilometre Surcharge Calculation",
"Lease-to-Own Total Cost"
]
}
</pre_analysis>
<reasoning>
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.
\[\text{Excess km} = 66976 - 45000 = 21976\text{ km}\]
\[\text{Surcharge} = 21976 \times \ LXI0 4834.72\]
- b.
\[\text{Excess km} = 65173 - 60000 = 5173\text{ km}\]
\[\text{Surcharge} = 5173 \times \ LXI0 465.57\]
- c.
\[\text{Excess km} = 86593 - 80000 = 6593\text{ km}\]
\[\text{Surcharge} = 6593 \times \ LXI0 461.51\]
- 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.
\[\text{Monthly Payment}_{\text{tax}} = \ LXI0 367.2387\]
\[\text{Total Monthly Payments} = 60 \times \ LXI0 22034.32\]
\[\text{Excess km} = 106584 - 90000 = 16584\text{ km}\]
\[\text{Surcharge} = 16584 \times \ LXI0 2155.92\]
\[\text{Total Cost} = \ LXI0 400\text{ (deposit)} + \ LXI1 2155.92 = \$27090.24\]
- b.
\[\text{Monthly Payment}_{\text{tax}} = \ LXI0 176.28\]
\[\text{Total Monthly Payments} = 24 \times \ LXI0 4230.72\]
\[\text{Excess km} = 51759 - 40000 = 11759\text{ km}\]
\[\text{Surcharge} = 11759 \times \ LXI0 2351.80\]
\[\text{Total Cost} = \ LXI0 200\text{ (deposit)} + \ LXI1 2351.80 = \$7282.52\]
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:
\[\text{Monthly Payment}_{\text{tax}} = \ LXI0 516.6925\]
\[\text{Total Lease Payments} = 36 \times \ LXI0 18600.93\]
- Down Payment:
\[\$5500.00\]
- Purchase Price with Tax:
\[\text{Purchase Price}_{\text{tax}} = \ LXI0 13221.00\]
- Total Cost:
\[\text{Total} = \ LXI0 18600.93 + \ LXI1 37321.93\]
</reasoning>
<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
\(\$37321.93\)
</answer>
<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Algebra",
"Leasing Cost Calculation"
]
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</post_analysis>