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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%.

v1 Financial Maths, STD2 F1 SM-Bank 1

Samantha buys a luxury boat with a market value of $78 000.

Stamp duty is calculated on the boat as follows:

  • 4% of market value up to $50 000
  • 6% of market value over $50 000

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

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`$3680`

Show Worked Solution
`text(Stamp Duty)` `= 4text(%) xx 50\ 000+6text(%) xx (78\ 000-50\ 000)`
  `= 4text(%) xx 50\ 000+6text(%) xx 28\ 000`
  `=$3680`

Financial Maths, STD2 F1 EQ-Bank 40

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 30

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`