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Recursion and Finance, GEN1 2024 VCAA 21 MC

Lee took out a loan of $121 000, with interest compounding monthly. He makes monthly repayments of $2228.40  for five years until the loan is repaid in full.

The total interest paid by Lee is closest to

  1. $4434
  2. $5465
  3. $10539
  4. $12 704
Show Answers Only

\(D\)

Show Worked Solution
\(\text{Repayments}\) \( =2228.40\times 12\times 5\)
  \(=$133\,704\)
\(\text{Interest}\) \(=$133\,704-$121\,000\)
  \(=$12\,704\)

\(\Rightarrow D\)

CORE, FUR1 2019 VCAA 23 MC

Joseph borrowed $50 000 to buy a new car.

Interest on this loan is charged at the rate of 7.5% per annum, compounding monthly.

Joseph will fully repay this loan with 60 monthly repayments over five years.

Immediately after the 59th repayment is made, Joseph still owes $995.49

The value of his final repayment, to the nearest cent, will be

  1.    $995.49
  2.    $998.36
  3.  $1001.71
  4.  $1001.90
  5.  $1070.15
Show Answers Only

`C`

Show Worked Solution

`text(Monthly interest rate) = 7.5/12`

`:.\ text(Final payment)` `= 995.49 (1 + 7.5/(12 xx 100))`
  `= $1001.71`

 
`=>  C`

CORE, FUR1 2017 VCAA 19-20 MC

Shirley would like to purchase a new home. She will establish a loan for $225 000 with interest charged at the rate of 3.6% per annum, compounding monthly.

Each month, Shirley will pay only the interest charged for that month.

Part 1

After three years, the amount that Shirley will owe is

  1.    $73 362
  2.  $170 752
  3.  $225 000
  4.  $239 605
  5.  $245 865

 
Part 2

Let `V_n` be the value of Shirley’s loan, in dollars, after `n` months.

A recurrence relation that models the value of `V_n` is

  1. `V_0 = 225\ 000,qquadV_(n + 1) = 1.003 V_n`
  2. `V_0 = 225\ 000,qquadV_(n + 1) = 1.036 V_n`
  3. `V_0 = 225\ 000,qquadV_(n + 1) = 1.003 V_n - 8100`
  4. `V_0 = 225\ 000,qquadV_(n + 1) = 1.003 V_n - 675`
  5. `V_0 = 225\ 000,qquadV_(n + 1) = 1.036 V_n - 675`
Show Answers Only

`text(Part 1:)\ C`

`text(Part 2:)\ D`

Show Worked Solution

`text(Part 1)`

`text(If the loan payments are interest only,)`

`text(the principal outstanding after 3 years)`

`text(remains $225 000.)`

`=> C`
 

`text(Part 2)`

`text(Monthly interest rate)`

`= 3.6/12 = 0.3text(%) = 0.003`
 

`text(Monthly payment)`

`= 225\ 000 xx 0.3text(%)`

`= $675`
 

`:.\ text(Recurrence Relation is)`

`V_(n + 1) = 1.003V_n – 675`

`=> D`

CORE*, FUR2 2007 VCAA 1

Khan wants to buy some office furniture that is valued at $7000.

  1. i.  A store requires 25% deposit. Calculate the deposit.  (1 mark)

The balance is to be paid in 24 equal monthly instalments. No interest is charged.

  1. ii. Determine the amount of each instalment. Write your answer in dollars and cents.  (1 mark)

Another store offers the same $7000 office furniture for $500 deposit and 36 monthly instalments of $220.

 

  1. i.  Determine the total amount paid for the furniture at this store.  (1 mark)
  2. ii. Calculate the annual flat rate of interest charged by this store.

     

        Write your answer as a percentage correct to one decimal place.  (2 marks)

A third store has the office furniture marked at $7000 but will give 15% discount if payment is made in cash at the time of sale.

  1. Calculate the cash price paid for the furniture after the discount is applied.  (1 mark) 
Show Answers Only
  1. i.  `$1750`
  2. ii.`$218.75`
  3. i.  `$8420`
  4. ii.  `7.3text{%}`
  5. `$5950`
Show Worked Solution
a.i.    `text(Deposit)` `= 25text(%) xx 7000`
    `= $1750`

 
a.ii.   `text(Installment amount)`

`= ((7000 – 1750))/24`

`= $218.75`
 

b.i.    `text(Total paid)` `= 500 + 36 xx 220`
    `= $8420`

 

b.ii.   `text(Total interest paid)`

`= 8420 – 7000`

`= $1420`

 

`I` `= (PrT)/100`
`1420` `= (6500 xx r xx 3)/100`
`:. r` `= (1420 xx 100)/(6500 xx 3)`
  `= 7.282…`
  `= 7.3text{%  (1 d.p.)}`

 

c.    `text(Cash price)` `= 7000 – 15text(%) xx 7000`
    `= 7000 – 1050`
    `= $5950`

CORE*, FUR2 2012 VCAA 1

A club purchased new equipment priced at $8360. A 15% deposit was paid.

  1. Calculate the deposit.  (1 mark)
  2. i.  Determine the amount of money that the club still owes on the equipment after the deposit is paid.  (1 mark)

The amount owing will be fully repaid in 12 instalments of $650.

  1. ii. Determine the total interest paid.  (1 mark)
Show Answers Only
  1. `$1254`
  2. i.  `$7106`
  3. ii. `$684`
Show Worked Solution
a.    `text(Deposit)` `= 15text(%) xx 8360`
    `= $1254`

 

b.i.    `text(Amount still owed)` `= 8360 − 1254`
    `= $7106`

 

b.ii.    `text(Total repayments)` `= 12 xx 650`
    `= $7800`

 
`:.\ text(Total interest paid)`

`= 7800 – 7106`

`= $694`

CORE*, FUR2 2014 VCAA 4

The cricket club borrowed $400 000 to build a clubhouse.

Interest is calculated at the rate of 4.5% per annum, compounding monthly.

The cricket club will make monthly repayments of $2500.

After a number of monthly repayments, the balance of the loan will be reduced to $143 585.33.

What percentage of the next monthly repayment will reduce the balance of the loan?

Write your answer, correct to the nearest percentage.  (2 marks)

Show Answers Only

`text(78%)`

Show Worked Solution

`text(Loan balance) = $143\ 585.33`

♦♦♦ Mean mark 10%.

`text(Interest in the next repayment)`

`= 4.5/(12 xx 100) xx 143\ 585.33`

`= 538.44…`

 

`:.\ text(Principal amount of next repayment)`

`= 2500 – 538.44`

`= 1.961.55…`

 

`:.\ text(% of repayment reducing loan)`

`= (1961.55…)/2500 xx 100text(%)`

`= 78.46…`

`= 78text{%  (nearest %)}`

CORE*, FUR1 2015 VCAA 5 MC

The purchase price of a car is $20 000.

A deposit of $5000 is paid.

The balance will be repaid with 60 monthly repayments of $400.

The total amount of interest charged is

A.      $1000

B.      $4000

C.      $9000

D.   $19 000

E.   $24 000

Show Answers Only

`C`

Show Worked Solution

`text(Amount borrowed)\ =20\ 000 – 5000 = $15\ 000`

`text(Total paid in 60 repayments)`

`=400 xx 60 = $24\ 000`

`:.\ text(Interest charged)` `= 24\ 000 – 15\ 000`
  `= $9000`

`=> C`

CORE*, FUR1 2005 VCAA 9 MC

Sally planned to repay a loan fully with six equal monthly repayments of  `$800`.

Interest was calculated monthly on the reducing balance.

Sally missed the third payment, but made a double payment of  `$1600`  in the fourth month.

Which of the following statements is true?

A.   The same amount of interest is paid each month.

B.  The amount owing after three months is the same as the amount owed after two months.

C.  The amount owing after three months is less than the amount owed after two months.

D.   To fully repay the loan, Sally will pay less than $4800.

E.   To fully repay the loan, Sally will pay more than $4800. 

Show Answers Only

`E`

Show Worked Solution
`text(Total amount of repayments)` `= $800 xx 6`
  `= $4800`

 
`text(If she missed the)\ 3^text(rd)\ text(payment, she will have)`

`text(to pay interest on the missing)\ 3^text(rd)\ text(payment),`

`text(so she will pay more than $4800 in total to)`

`text(compensate for the added interest.)`

`=>  E`

CORE*, FUR1 2011 VCAA 4 MC

Nathan bought a $2500 bedroom suite on a contract that involves no deposit and an interest-free loan for a period of 48 months.

He has to pay an initial set-up fee of $25.

In addition, he pays an administration fee of $3.95 per month.

The total amount that Nathan will have to pay in fees for the entire 48 months, as a percentage of the original price of $2500,  is closest to

A.   1.6%

B.   4.0%

C.   7.6%

D.   8.5%

E.   8.6%

Show Answers Only

`E`

Show Worked Solution
`text(Total fees)` `= 25 + (3.95 xx 48)`
  `= 214.6`

 

`text(Fees as a % of Original Price)`

`= 214.6 / 2500 xx text(100%)`

`=8.584 text(%)`

`= 8.6text{%  (to 1 d.p.)}`

`=> E`