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CORE, FUR2 2020 VCAA 10

Samuel now invests $500 000 in an annuity from which he receives a regular monthly payment.

The balance of the annuity, in dollars, after    months,  , can be modelled by a recurrence relation of the form

  1. Calculate the balance of this annuity after two months if  .   (1 mark)

  2. Calculate the annual compound interest rate percentage for this annuity if  .   (1 mark)

  3. For what value of    would this investment act as a simple perpetuity?   (1 mark)

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a.  
 

 

♦ Mean mark 48%.
b.  
 

 

♦ Mean mark 36%.
c.  
 
 
   

CORE, FUR2 2020 VCAA 8

 

Samuel has a reducing balance loan.

The first five lines of the amortisation table for Samuel’s loan are shown below.
 


 

Interest is calculated monthly and Samuel makes monthly payments of $1600.

Interest is charged on this loan at the rate of 3.6% per annum.

  1. Using the values in the amortisation table
    1. calculate the principal reduction associated with payment number 3.   (1 mark)
    2. Calculate the balance of the loan after payment number 4 is made.
    3. Round your answer to the nearest cent.   (1 mark)
  2. Let be the balance of Samuel’s loan after months.
  3. Write down a recurrence relation, in terms of   and  , that could be used to model the month-to-month balance of the loan.   (1 mark)

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  1.  i.
  2. ii.

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a.i.  
   
   

 

♦ Mean mark part a.ii. 39%.

a.ii.  
   

 

 

♦♦ Mean mark part b. 30%.

b.  
 

CORE, FUR2-NHT 2019 VCAA 7

Tisha plays drums in the same band as Marlon.

She would like to buy a new drum kit and has saved $2500.

  1. Tisha could invest this money in an account that pays interest compounding monthly.

     

    The balance of this investment after months, could be determined using the recurrence relation below
     
           
     
    Calculate the total interest that would be earned by Tisha's investment in the first five months.

     

    Round your answer to the nearest cent.   (2 marks)

Tisha could invest the $2500 in a different account that pays interest at the rate of 4.08% per annum, compounding monthly. She would make a payment of $150 into this account every month.

  1. Let be the value of Tisha's investment after months.

     

    Write down a recurrence relation, in terms of , and , that would model the change in the value of this investment.   (1 mark)

  2. Tisha would like to have a balance of $4500, to the nearest dollar, after 12 months.

     

    What annual interest rate would Tisha require?

     

    Round your answer to two decimal places.   (1 mark)

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a.   

 

 

b.   

 

c.   

 
 
 
 
 
 

 

CORE, FUR2 2018 VCAA 4

 

Julie deposits some money into a savings account that will pay compound interest every month.

The balance of Julie’s account, in dollars, after months,  , can be modelled by the recurrence relation shown below.

 

  1. How many dollars does Julie initially invest?   (1 mark)
  2. Recursion can be used to calculate the balance of the account after one month.
    1. Write down a calculation to show that the balance in the account after one month, , is  $12 074.40.   (1 mark)
    2. After how many months will the balance of Julie’s account first exceed $12 300?   (1 mark)
  3. A rule of the form    can be used to determine the balance of Julie's account after months.
    1. Complete this rule for Julie’s investment after months by writing the appropriate numbers in the boxes provided below.   (1 mark)

    2. Balance = 
       
      		  × 
       
      		  
    3. What would be the value of    if Julie wanted to determine the value of her investment after three years?   (1 mark)

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a.   
 

b.i.  
   
   

 

b.ii.  
 
 

 

 
c.i.  

 
c.ii. 

CORE, FUR2 2017 VCAA 6

Alex sends a bill to his customers after repairs are completed.

If a customer does not pay the bill by the due date, interest is charged.

Alex charges interest after the due date at the rate of 1.5% per month on the amount of an unpaid bill.

The interest on this amount will compound monthly.

  1. Alex sent Marcus a bill of $200 for repairs to his car.

     

    Marcus paid the full amount one month after the due date.

     

    How much did Marcus pay?   (1 mark)

Alex sent Lily a bill of $428 for repairs to her car.

Lily did not pay the bill by the due date.

Let be the amount of this bill months after the due date.

  1. Write down a recurrence relation, in terms of , and , that models the amount of the bill.   (2 marks)

  2. Lily paid the full amount of her bill four months after the due date.

     

    How much interest was Lily charged?

     

    Round your answer to the nearest cent.   (1 mark)

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a.   
   
   

♦ Mean mark part (b) 47%.
MARKER’S COMMENT: A recurrence relation has the initial value written first. Know why    is incorrect.

 

b.   

 

c.   
   

♦♦ Mean mark part (c) 29%.

 

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 be the value of Shirley’s loan, in dollars, after months.

A recurrence relation that models the value of is

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CORE, FUR2 SM-Bank VCE 3

Luke purchased a new pizza oven for his restaurant for $23 500.

He can depreciate the pizza oven using the reducing balance method at a rate of 12.5% per year.

  1. If represents the value of the pizza oven after years, write a recurrence relation that models its value.   (1 mark)

  2. During what year will the pizza oven's value drop below $15 000?   (1 mark)

Luke has been advised that he can use flat rate depreciation at 10% of the purchase price.

  1. After 4 years, show which depreciation method gives the pizza oven the highest value?   (1 mark)

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a.   
 
   
 
   

  


  

b.   
 
 
 

  

  
c.  


 

CORE*, FUR2 2016 VCAA 6

Ken’s first caravan had a purchase price of $38 000.

After eight years, the value of the caravan was $16 000.

  1. Show that the average depreciation in the value of the caravan per year was $2750.   (1 mark)

  2. Let be the value of the caravan years after it was purchased.

     

    Assume that the value of the caravan has been depreciated using the flat rate method of depreciation.

     

    Write down a recurrence relation, in terms of and , that models the value of the caravan.   (1 mark)

  3. The caravan has travelled an average of 5000 km in each of the eight years since it was purchased.

     

    Assume that the value of the caravan has been depreciated using the unit cost method of depreciation.

     

    By how much is the value of the caravan reduced per kilometre travelled?   (1 mark)

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a.    


♦♦ Mean mark (a) 39%.
MARKER’S COMMENT: A “show that” question should include an equation
  

b.   
 

♦♦ Mean mark (b) 33%.
MARKER’S COMMENT: A lack of attention to detail and careless errors were common!
  

c.   
   

 


♦♦ Mean mark (c) 29%.