Question

key question # 18

1. calculate the cost of leasing each of the vehicles described below, assuming that the security deposit will be returned at the end of the lease? (9 marks)

a. $1500 down payment
$300 refundable security deposit
36 monthly payments of $365.00
pst (8%) and gst (5%) on each monthly payment

b. $7000 down payment
$600 refundable security deposit
60 monthly payments of $519.00
pst (8%) and gst (5%) on each monthly payment

c. $3500 down payment
$225 refundable security deposit
48 monthly payments of $179.97
pst (8%) and gst (5%) on each monthly payment

Explanation:

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<reasoning>

Understand the leasing cost components

To find the total cost of leasing each vehicle, we must sum all non-refundable payments. Since the security deposit is fully refunded at the end of the lease, it does not contribute to the final net cost.

The total cost consists of:

1. The down payment.
2. The monthly payments including taxes (PST of \(8\%\) and GST of \(5\%\)).

The total tax rate applied to each monthly payment is:
\[
\text{Total Tax Rate} = 8\% + 5\% = 13\% = 0.13
\]

Calculate the cost for vehicle a

For vehicle a, the parameters are:

• Down payment: \(\$1500\)
• Monthly payment before tax: \(\$365.00\)
• Number of months: \(36\)

First, calculate the monthly payment including tax:
\[
\text{Monthly Payment with Tax} = \$365.00 \times (1 + 0.13) = \$365.00 \times 1.13 = \$412.45
\]

Next, calculate the total of all monthly payments:
\[
\text{Total Monthly Payments} = \$412.45 \times 36 = \$14,848.20
\]

Add the down payment to find the total lease cost:
\[
\text{Total Cost}_a = \$1500 + \$14,848.20 = \$16,348.20
\]

Calculate the cost for vehicle b

For vehicle b, the parameters are:

• Down payment: \(\$7000\)
• Monthly payment before tax: \(\$519.00\)
• Number of months: \(60\)

First, calculate the monthly payment including tax:
\[
\text{Monthly Payment with Tax} = \$519.00 \times 1.13 = \$586.47
\]

Next, calculate the total of all monthly payments:
\[
\text{Total Monthly Payments} = \$586.47 \times 60 = \$35,188.20
\]

Add the down payment to find the total lease cost:
\[
\text{Total Cost}_b = \$7000 + \$35,188.20 = \$42,188.20
\]

Calculate the cost for vehicle c

For vehicle c, the parameters are:

• Down payment: \(\$3500\)
• Monthly payment before tax: \(\$179.97\)
• Number of months: \(48\)

First, calculate the monthly payment including tax:
\[
\text{Monthly Payment with Tax} = \$179.97 \times 1.13 = \$203.3661
\]

Next, calculate the total of all monthly payments:
\[
\text{Total Monthly Payments} = \$203.3661 \times 48 = \$9,761.5728
\]

Rounding to the nearest cent, the total monthly payments are \(\$9,761.57\).

Add the down payment to find the total lease cost:
\[
\text{Total Cost}_c = \$3500 + \$9,761.57 = \$13,261.57
\]
</reasoning>

<answer>

Question 1a

The total cost of leasing vehicle a is \(\$16,348.20\).

Question 1b

The total cost of leasing vehicle b is \(\$42,188.20\).

Question 1c

The total cost of leasing vehicle c is \(\$13,261.57\).
</answer>

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Answer:

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<reasoning>

Understand the leasing cost components

To find the total cost of leasing each vehicle, we must sum all non-refundable payments. Since the security deposit is fully refunded at the end of the lease, it does not contribute to the final net cost.

The total cost consists of:

1. The down payment.
2. The monthly payments including taxes (PST of \(8\%\) and GST of \(5\%\)).

The total tax rate applied to each monthly payment is:
\[
\text{Total Tax Rate} = 8\% + 5\% = 13\% = 0.13
\]

Calculate the cost for vehicle a

For vehicle a, the parameters are:

• Down payment: \(\$1500\)
• Monthly payment before tax: \(\$365.00\)
• Number of months: \(36\)

First, calculate the monthly payment including tax:
\[
\text{Monthly Payment with Tax} = \$365.00 \times (1 + 0.13) = \$365.00 \times 1.13 = \$412.45
\]

Next, calculate the total of all monthly payments:
\[
\text{Total Monthly Payments} = \$412.45 \times 36 = \$14,848.20
\]

Add the down payment to find the total lease cost:
\[
\text{Total Cost}_a = \$1500 + \$14,848.20 = \$16,348.20
\]

Calculate the cost for vehicle b

For vehicle b, the parameters are:

• Down payment: \(\$7000\)
• Monthly payment before tax: \(\$519.00\)
• Number of months: \(60\)

First, calculate the monthly payment including tax:
\[
\text{Monthly Payment with Tax} = \$519.00 \times 1.13 = \$586.47
\]

Next, calculate the total of all monthly payments:
\[
\text{Total Monthly Payments} = \$586.47 \times 60 = \$35,188.20
\]

Add the down payment to find the total lease cost:
\[
\text{Total Cost}_b = \$7000 + \$35,188.20 = \$42,188.20
\]

Calculate the cost for vehicle c

For vehicle c, the parameters are:

• Down payment: \(\$3500\)
• Monthly payment before tax: \(\$179.97\)
• Number of months: \(48\)

First, calculate the monthly payment including tax:
\[
\text{Monthly Payment with Tax} = \$179.97 \times 1.13 = \$203.3661
\]

Next, calculate the total of all monthly payments:
\[
\text{Total Monthly Payments} = \$203.3661 \times 48 = \$9,761.5728
\]

Rounding to the nearest cent, the total monthly payments are \(\$9,761.57\).

Add the down payment to find the total lease cost:
\[
\text{Total Cost}_c = \$3500 + \$9,761.57 = \$13,261.57
\]
</reasoning>

<answer>

Question 1a

The total cost of leasing vehicle a is \(\$16,348.20\).

Question 1b

The total cost of leasing vehicle b is \(\$42,188.20\).

Question 1c

The total cost of leasing vehicle c is \(\$13,261.57\).
</answer>

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