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Financial Maths, STD2 F1 EQ-Bank 42

Sienna buys a new car and pays a total of $2,200 in stamp duty.

Stamp duty is calculated on the vehicle as follows:

    • 3% of market value up to \(\$45\,000\)
    • 5% of market value over \(\$45\,000\)

Determine the market value of Sienna's car.   (2 marks)

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\(\$62\,000\)

Show Worked Solution

\(\text{Stamp duty on first}\ \$45\,000=0.03\times 45\,000=\$1350\)

\(\text{Remaining stamp duty}=2200-1350=\$850\)

\(\text{Amount over}\ \$45\,000=\dfrac{850}{0.05}=\$17\,000\)

\(\therefore\ \text{Market value}=45\,000+17\,000=\$62\,000\)

Financial Maths, STD2 F1 EQ-Bank 36

Lachlan buys a 4WD with a market value of \(\$58\,200\).

Stamp duty is calculated on the vehicle as follows:

    • 3% of market value up to \(\$45\,000\)
    • 5% of market value over \(\$45\,000\)

Calculate the amount of stamp duty payable by Lachlan.   (2 marks)

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\(\$2010\)

Show Worked Solution

\(\text{Stamp duty on first}\ \$45\,000=0.03\times 45\,000=\$1350\)

\(\text{Amount over}\ \$45\,000=58\,200-45\,000=\$13\,200\)

\(\text{Stamp duty on excess}=0.05\times 13\,200=\$660\)

\(\therefore\ \text{Total stamp duty}=1350+660=\$2010\)

Financial Maths, STD2 F1 EQ-Bank 30

Aanya is buying a used car with a sale price of \(\$15\,800\). In addition to the sale price, the following costs are charged:

    • transfer of registration $50
    • stamp duty which is calculated at $3 for every $100, or part thereof, of the sale price.

Aanya is considering two loan options to finance the total amount payable for the car.

Loan A 

 - A bank loan with simple interest at 6.5% per annum.

 - Repaid in equal monthly repayments over 4 years.

Loan B

 - A dealership loan with simple interest at 5.8% per annum

 - Repaid in equal monthly repayments over 5 years.
 

  1. Calculate the total amount Aanya needs to borrow.   (1 mark)
  2. Calculate the monthly repayment for each loan option, correct to the nearest cent and identify which loan has the lowest monthly repayment.   (3 marks)
  3. Identify ONE disadvantage of choosing this loan compared to the other.   (1 mark)
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a.    \(\$16\,324\)

b.  \(\text{Loan B has the lowest monthly repayment (\$350.97 < \$428.51)}\)

c.  \(\text{Loan B costs}\ \ 21\,057.96-20\,568.24=\$489.72\ \ \text{more in total repayments.}\)

Show Worked Solution

a.    \(\text{Calculate total amount to borrow:}\)

\(\text{Stamp duty}=\dfrac{15\,800}{100}\times 3=158\times 3=\$474\)

\(\text{Total borrowed}=15\,800+50+474=\$16\,324\)
 

b.    \(\text{Loan A:}\)

\(I=Prn=16\,324\times 0.065\times 4=\$4244.24\)

\(\text{Total to repay}=16\,324+4244.24=\$20\,568.24\)

\(\text{Monthly repayment}=\dfrac{20\,568.24}{48}=428.505\approx \$428.51\)
 

\(\text{Loan B:}\)

\(I=Prn=16\,324\times 0.058\times 5=\$4733.96\)

\(\text{Total to repay}=16\,324+4733.96=\$21\,057.96\)

\(\text{Monthly repayment}=\dfrac{21\,057.96}{60}=350.966\approx \$350.97\)
 

\(\text{Loan B has the lowest monthly repayment (\$350.97 < \$428.51)}\)
 

c.    \(\text{Consider the total repayments of each loan (see part b):}\)

\(\text{Loan B costs}\ \ 21\,057.96-20\,568.24=\$489.72\ \ \text{more in total repayments.}\)

Financial Maths, STD2 F1 EQ-Bank 29

A second-hand motorbike has a sale price of \(\$12\,400\). In addition to the sale price, the following costs are charged:

  • transfer of registration $85
  • stamp duty which is calculated at $4.50 for every $100, or part thereof, of the sale price.

Jordan borrows the total amount to be paid for the motorbike, including transfer of registration and stamp duty. Simple interest at the rate of 8.5% per annum is charged on the loan. The loan is to be repaid in equal monthly repayments over 2 years.

Calculate Jordan's monthly repayment, correct to the nearest cent. (5 marks)

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\(\$635.85\)

Show Worked Solution

\(\text{Stamp duty}=\dfrac{12\,400}{100}\times 4.5=\$558\)

\(\text{Total borrowed}=12\,400+85+558=\$13\,043\)

\(\text{Interest} =Prn=13\,043\times 0.085\times 2=\$2217.31\)

\(\text{Total to repay}=13\,043+2217.31=\$15\,260.31\)

 
\(\therefore\ \text{Monthly repayment}=\dfrac{15\,260.31}{24}=635.846\approx \$635.85\)

Financial Maths, STD1 F3 2025 HSC 24

A used car has a sale price of $24 200. In addition to the sale price, the following costs are charged:

  • transfer of registration $50
  • stamp duty which is calculated at $3 for every $100, or part thereof, of the sale price.

Kat borrows the total amount to be paid for the car, including transfer of registration and stamp duty. Simple interest at the rate of 6.8% per annum is charged on the loan. The loan is to be repaid in equal monthly repayments over 3 years.

Calculate Kat’s monthly repayment.   (5 marks)

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\($835.31\)

Show Worked Solution

\(\text{Stamp Duty} =\dfrac{24\ 200}{100}\times 3=$726\)

\(\text{Total Cost}\ \) \(\text{= Price + Transfer + Stamp Duty}\)
  \(\text{= }24\ 200+50+726\)
  \(\text{= }$24\ 976\)

 
\(\text{Interest}=Prn=24\,976\times 0.068\times 3=$5095.104\)

\(\text{Loan amount}\ \) \(\text{= Total Cost + Interest}\)
  \(\text{= }24\ 976+5095.104\)
  \(\text{= }$30\ 071.104\)

 
\(\text{3 years}= 3 \times 12=36\ \text{months}\)

\(\text{Monthly repayment}\) \(=\dfrac{30\ 071.104}{36}\)
  \(=$835.308444\)
  \(\approx $835.31\)

♦♦ Mean mark 46%.

Financial Maths, STD2 F1 EQ-Bank 38

Alex is buying a used car which has a sale price of  $13 380. In addition to the sale price there are the following costs:

2014 27a1

  1. Stamp Duty for this car is calculated at $3 for every $100, or part thereof, of the sale price.  
    Calculate the Stamp Duty payable.   (1 mark)

  2. Alex wishes to take out comprehensive insurance for the car for 12 months.

     

    The cost of comprehensive insurance is calculated using the following:
     
          2014 27a2
    Find the total amount that Alex will need to pay for comprehensive insurance.   (3 marks)

  3. Alex has decided he will take out the comprehensive car insurance rather than the less expensive non-compulsory third-party car insurance.

  4.  

    What extra cover is provided by the comprehensive car insurance?   (1 mark)

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a.    `$402`

b.    `$985.74`

c.    `text(Comprehensive insurance also covers Alex for damage to his own car.)`

Show Worked Solution

a.    `($13\ 380)/100 = 133.8`

♦♦♦ Mean mark (a) 12%
IMPORTANT: “or part thereof ..” requires students to round up to 134 to get the right multiple of $3 for their calculation.

`text(Stamp duty)= 134 xx $3= $402`
 

b.    `text(Base rate)= $845`

`text(FSL) =\ text(1%) xx 845 = $8.45`

`text(Stamp)` `=\ text(5.5%) xx(845 + 8.45)`
  `= 46.9397…`
  `= $46.94\ text{(nearest cent)}`

 
`text(GST)= 10 text(%) xx(845 + 8.45)= 85.345= $85.35`

`:.\ text(Total cost)` `= 845 + 8.45 + 46.94 + 85.35`
  `= $985.74`

 

♦ Mean mark (c) 34%.

 
c.    `text(Comprehensive insurance covers Alex for damage done)`

`text{to his own car as well.}`

Financial Maths, STD2 F1 EQ-Bank 34

Ralph buys a utility vehicle with a market value of $63 500.

Stamp duty is calculated on the vehicle as follows:

  • 3% of market value up to $45 000
  • 5% of market value over $45 000

Calculate the amount of stamp duty payable by Ralph.   (2 marks)

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`$2275`

Show Worked Solution
`text(Stamp Duty)` `= 3text(%) xx 45\ 000 + 5text(%) xx (63\ 500-45\ 000)`
  `= 3text(%) xx 45\ 000 + 5text(%) xx 18\ 500`
  `= $2275`