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Financial Maths, STD2 F4 2024 HSC 27

A couple borrows $30 000 to be repaid in equal monthly repayments of $280 over 10 years.

After following this repayment plan for 5 years, they decide to decrease their monthly repayment to $250. As a result, it will take them an additional two years to pay off their loan.

How much more will they repay in total by making this change?   (3 marks)

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\(\text{Extra repaid}\ =$4200\)

Show Worked Solution

\(\text{Original plan:}\)

\(\text{Total repayments}\ =10 \times 12=120\)

\(\text{Amount repaid}\ =120 \times 280=$33\ 600\)
 

\(\text{New plan:}\)

\(\text{Repayments at \$280}\ =5 \times 12=60\)

\(\text{Repayments at \$250}\ =7 \times 12=84\)

\(\text{Amount repaid}\ = 60 \times 280 + 84 \times 250 =$37\ 800\)

\(\text{Extra repaid}\ =37\ 800-33\ 600=$4200\)

Financial Maths, STD2 F4 2022 HSC 36

Frankie borrows $200 000 from a bank. The loan is to be repaid over 23 years at a rate of 7.2% per annum, compounded monthly. The repayments have been set at $1485 per month.

The interest charged and the balance owing for the first three months of the loan are shown in the spreadsheet below.
 

  1. What are the values of `A` and `B`?   (2 marks)

  2. After 50 months of repaying the loan, Frankie decides to make a lump sum payment of $ 40 000 and to continue making the monthly repayments of $1485. The loan will then be fully repaid after a further 146 monthly repayments.
  3. How much less will Frankie pay overall by making the lump sum payment?   (3 marks)

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a.    `A=$1198.29,\ \ B=$199\ 139.86`

b.    `$78\ 800`

Show Worked Solution

a.    `text{Monthly interest rate}\ =7.2/12=0.6text{%}`

`A=199\ 715 xx 0.6/100=$1198.29`

`B` `=P+I-R`
  `=199\ 428.29 + 1196.57-1485=$199\ 139.86`

 

b.    `text{Total payments if lump sum not paid}`

`= (23xx12) xx 1485=$409\ 860`
   

`text{Total payments if lump sum paid}`

`=40\ 000 + (50 + 146) xx 1485=$331\ 060`
   

`text{Savings by paying the lump sum}`

`=409\ 860-331\ 060=$78\ 800`


♦♦♦ Mean mark (b) 17%.
 

Financial Maths, STD2 F4 2018 HSC 29e

Andrew borrowed $20 000 to be repaid in equal monthly repayments of $243 over 10 years. Having made this monthly repayment for 4 years, he increased his monthly repayment to $281. As a result, Andrew paid off the loan one year earlier.

How much less did he repay altogether by making this change?   (2 marks)

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`$636`

Show Worked Solution

`text(Total original repayments)= 10 xx 12 xx 243= $29\ 160`

`text(Actual repayments)= 4 xx 12 xx 243\ +\ 5 xx 12 xx 281= $28\ 524`

`:.\ text(Savings)= 29\ 160-28\ 524= $636`

Financial Maths, STD2 F4 2015 HSC 29b

Jamal borrowed  $350 000  to be repaid over 30 years, with monthly repayments of  $1880. However, after 10 years he made a lump sum payment of  $80 000. The monthly repayment remained unchanged. The graph shows the balances owing over the period of the loan.
 

2015 29b

Over the period of the loan, how much less did Jamal pay by making the lump sum payment?   (2 marks)

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`$100\ 480`

Show Worked Solution

`text(Without the lump sum payment)`

♦ Mean mark 34%.

`text(Total repayments)= 30 xx 12 xx 1880= $676\ 800`

`text(With the lump sum payment)`

`text(Total repayments)` `= (22 xx 12 xx $1880) + $80\ 000`
  `= $496\ 320 + $80\ 000= $576\ 320`

  
`:.\ text(Amount Jamal saved)`

`= 676\ 800-576\320= $100\ 480`