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Recursion and Finance, GEN2 2024 VCAA 8

Emi takes out a reducing balance loan of $500 000.

The interest rate is 5.3% per annum, compounding monthly.

Emi makes regular monthly repayments of $3071.63 for the duration of the loan, with only the final repayment amount being slightly different from all the other repayments.

Determine the total cost of Emi's loan, rounding your answer to the nearest cent, and state the number of payments required to fully repay the loan.   (2 marks)
 


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♦♦ Mean mark 29%.

Recursion and Finance, GEN2 2023 VCAA 7

Arthur takes out a new loan of $60 000 to pay for an overseas holiday.

Interest on this loan compounds weekly.

The balance of the loan, in dollars, after weeks, , can be determined using a recurrence relation of the form

  1. Show that the interest rate for this loan is 7.8% per annum.   (1 mark)

  2. Determine the value of in the recurrence relation if
    1. Arthur makes interest-only repayments   (1 mark)
    2. Arthur fully repays the loan in five years. Round your answer to the nearest cent.   (1 mark)
  3. Arthur decides that the value of will be 300 for the first year of repayments.  
  4. If Arthur fully repays the loan with exactly three more years of repayments, what new value of will apply for these three years? Round your answer to the nearest cent.   (1 mark)
  5. For what value of does the recurrence relation generate a geometric sequence?   (1 mark)

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a.   

b.i. 

b.ii.

c.   

d.   

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a.   



♦♦ Mean mark (a) 32%.



 
b.i. 
 

b.ii.

 
 
 
 
 
 

 

 



♦ Mean mark (b)(i) 47%.
♦ Mean mark (b)(ii) 40%.



c.   

 
 
 
 
 
 

 

 

 
 
 
 
 
 

 

 



♦♦ Mean mark (c) 32%.



d.    



♦♦♦ Mean mark (d) 11%.



CORE, FUR2 2021 VCAA 8

For renovations to the coffee shop, Sienna took out a reducing balance loan of $570 000 with interest calculated fortnightly.

The balance of the loan, in dollars, after fortnights, can be modelled by the recurrence relation
 

                 
 

  1. Calculate the balance of this loan after the first fortnightly repayment is made.   (1 mark)

  2. Show that the compound interest rate for this loan is 2.6% per annum.   (1 mark)

  3. For the loan to be fully repaid, to the nearest cent, Sienna's final repayment will be a larger amount.
  4. Determine this final repayment amount.
  5. Round your answer to the nearest cent.   (1 mark)

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a.  
   


b. 


 

 

 

c. 

 

 

 

 

 

CORE, FUR1 2021 VCAA 24 MC

Bob borrowed $400 000 to buy an apartment.

The interest rate for this loan was 3.14% per annum, compounding monthly.

A scheduled monthly repayment that allowed Bob to fully repay the loan in 20 years was determined.

Bob decided, however, to make interest-only repayments for the first two years.

After these two years the interest rate changed. Bob was still able to pay off the loan in the 20 years by repaying the scheduled amount each month.

The interest rate, per annum, for the final 18 years of the loan was closest to

  1. 1.85%
  2. 2.21%
  3. 2.79%
  4. 3.14%
  5. 4.07%
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♦♦ Mean mark 33%.

 

 

  

CORE, FUR2 2020 VCAA 11

Samuel took out a new reducing balance loan.

The interest rate for this loan was 4.1% per annum, compounding monthly.

The balance of the loan after four years of monthly repayments was $329 587.25

The balance of the loan after seven years of monthly repayments was $280 875.15

Samuel will continue to make the same monthly repayment.

To ensure the loan is fully repaid, to the nearest cent, the required final repayment will be lower.

In the first seven years, Samuel made 84 monthly repayments.

From this point on, how many more monthly repayments will Samuel make to fully repay the loan?   (2 marks)

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♦♦ Mean mark 21%.

 

 

 

CORE, FUR1-NHT 2019 VCAA 22-23 MC

Armand borrowed $12 000 to pay for a holiday.

He will be charged interest at the rate of 6.12% per annum, compounding monthly.

This loan will be repaid with monthly repayments of $500.
 

Part 1

After four months, the total interest that Armand will have paid is closest to

  1.   $231
  2.   $245
  3.   $255
  4.   $734
  5. $1796

 
Part 2

After eight repayments, Armand decided to increase the value of his monthly repayments.

He will make a number of monthly repayments of $850 and then one final repayment that will have a smaller value.

This final repayment has a value closest to

  1. $168
  2. $169
  3. $180
  4. $586
  5. $681
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CORE, FUR1 2017 VCAA 24 MC

Xavier borrowed $245 000 to pay for a house.

For the first 10 years of the loan, the interest rate was 4.35% per annum, compounding monthly.

Xavier made monthly repayments of $1800.

After 10 years, the interest rate changed.

If Xavier now makes monthly repayments of $2000, he could repay the loan in a further five years.

The new annual interest rate for Xavier’s loan is closest to

  1.  0.35%
  2.  4.1%
  3.  4.5%
  4.  4.8%
  5.  18.7%
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CORE, FUR2 2016 VCAA 7

 

Ken has borrowed $70 000 to buy a new caravan.

He will be charged interest at the rate of 6.9% per annum, compounding monthly.

  1. For the first year (12 months), Ken will make monthly repayments of $800.

    1. Find the amount that Ken will owe on his loan after he has made 12 repayments.   (1 mark)
    2. What is the total interest that Ken will have paid after 12 repayments?   (1 mark)
  2. After three years, Ken will make a lump sum payment of $L in order to reduce the balance of his loan.
  3. This lump sum payment will ensure that Ken’s loan is fully repaid in a further three years.
  4. Ken’s repayment amount remains at $800 per month and the interest rate remains at 6.9% per annum, compounding monthly.
  5. What is the value of Ken’s lump sum payment, $L?
  6. Round your answer to the nearest dollar.   (2 marks)

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a.i.

a.ii.

b. 

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a.i.  

♦ Mean mark 46%.

 

♦♦ Mean mark 26%.

a.ii.   
   
   

  
b.   

♦♦♦ Mean mark 20%.
MARKER’S COMMENT: Correct input tables allowed for a method mark if answers were calculated incorrectly.

   

  

 

  

 

CORE*, FUR2 2008 VCAA 5

Michelle took a reducing balance loan for $15 000 to purchase her car. Interest is calculated monthly at a rate of 9.4% per annum.

In order to repay the loan Michelle will make a number of equal monthly payments of $350.

The final repayment will be less than $350.

  1. How many equal monthly payments of $350 will Michelle need to make?   (1 mark)

  2. How much of the principal does Michelle have left to pay immediately after she makes her final $350 payment? Find this amount correct to the nearest dollar.   (1 mark)

Exactly one year after Michelle established her loan the interest rate increased to 9.7% per annum. Michelle decided to increase her monthly payment so that the loan would be fully paid in three years (exactly four years from the date the loan was established).

  1. What is the new monthly payment Michelle will make? Write your answer correct to the nearest cent.   (2 marks)

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a.  

♦♦ Mean mark of all parts (combined) was 23%.
MARKER’S COMMENT: This part was not well done. An area where students consistently struggle each year.

  


  

b.  

  


  

c.  

 

   

  

CORE*, FUR2 2015 VCAA 5

Jane and Michael borrow $50 000 to expand their business.

Interest on the unpaid balance is charged to the loan account monthly.

The $50 000 is to be fully repaid in equal monthly repayments of $485.60 for 12 years.

  1. Determine the annual compounding rate of interest.

     

    Write your answer correct to two decimal places.   (1 mark)

  2. Calculate the amount that will be paid off the principal at the end of the first year.

     

    Write your answer correct to the nearest dollar.   (1 mark)

  3. Halfway through the term of the loan, at the end of the sixth year, Jane and Michael make an additional one-off payment of $3500.

     

    Assume no other changes are made to their loan conditions.

     

    Determine how much time Jane and Michael will save in repaying their loan.

     

    Give your answer correct to the nearest number of months.   (2 marks)

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a.   

  


  

b.  

MARKER’S COMMENT: Showing solver “input” allowed a possible error mark in part (b) even if part (a) was incorrect.

  

 
 

 

c.   

 


  

 

 
 

CORE*, FUR1 2015 VCAA 8 MC

Cindy took out a reducing balance loan of $8400 to finance an overseas holiday.

Interest was charged at a rate of 9% per annum, compounding quarterly.

Her loan is to be fully repaid in six years, with equal quarterly payments.

After three years, Cindy will have reduced the balance of her loan by approximately

A.     9%

B.   35%

C.   43%

D.   50%

E.   57%

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♦♦ Mean mark 33%.

 

 

 

 
 

CORE*, FUR1 2009 VCAA 9 MC

To purchase a house Sam has borrowed $250 000 at an interest rate of 4.45% per annum, fixed for ten years.

Interest is calculated monthly on the reducing balance of the loan. Monthly repayments are set at $1382.50.

After 10 years, Sam renegotiates the conditions for the balance of his loan. The new interest rate will be 4.25% per annum. He will pay $1750 per month.

The total time it will take him to pay out the loan fully is closest to

A.   17 years.

B.   20 years.

C.   21 years.

D.   22 years.

E.   23 years.

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♦ Mean mark 45%.

 

 

 

 

 

CORE*, FUR1 2011 VCAA 9 MC

Xavier borrows $45 000 from the bank to buy a car.

He is offered a reducing balance loan for three years with an interest rate of 9.75% per annum, compounding monthly.

He can repay this loan by making 36 equal monthly payments.

Instead, Xavier decides to repay the loan in 18 equal monthly payments.

If there are no penalties for repaying the loan early, the amount he will save is closest to

A.   $2697

B.   $3530

C.   $3553

D.   $6581

E.   $7083

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♦ Mean mark 44%.

 

 

 

 

 
 

CORE*, FUR1 2013 VCAA 9 MC

The following information relates to the repayment of a home loan of $300 000.
 
• The loan is to be repaid fully with monthly payments of $2500.
• Interest compounds monthly.
• After the first monthly payment has been made, the amount owing on the loan is $299 000.

Which one of the following statements is true?

  1. After two months, $297 995 is still owing on the loan.
  2. $1000 of interest has been paid in the first month.
  3. The loan will be fully repaid in less than 15 years.
  4. Halfway through the term of the loan, the amount still owing will be $150 000.
  5. Payments of $2750 rather than $2500 per month will reduce the time to repay the loan fully by more than three years. 
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♦♦ Mean mark 29%.

 
 

 

 

CORE*, FUR1 2006 VCAA 9 MC

Jenny borrowed $18 000. She will fully repay the loan in five years with equal monthly payments.

Interest is charged at the rate of 9.2% per annum, calculated monthly, on the reducing balance.

The amount Jenny has paid off the principal immediately following the tenth repayment is

A.   $1876.77

B.   $2457.60

C.   $3276.00

D.   $3600.44

E.   $3754.00

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♦♦ Mean mark 27%.