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CORE, FUR1 2020 VCAA 30 MC

Twenty years ago, Hector invested a sum of money in an account earning interest at the rate of 3.2% per annum, compounding monthly.

After 10 years, he made a one-off extra payment of $10 000 to the account.

For the next 10 years, the account earned interest at the rate of 2.8% per annum, compounding monthly.

The balance of his account today is $686 904.09

The sum of money Hector originally invested is closest to

  1. $355 000
  2. $370 000
  3. $377 000
  4. $384 000
  5. $385 000
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♦ Mean mark 41%.

 

 


 

 
 
 
 
 
 

 

 

 
 
 
 
 
 

 

CORE, FUR1 2018 VCAA 19 MC

Daniel borrows $5000, which he intends to repay fully in a lump sum after one year.

The annual interest rate and compounding period for five different compound interest loans are given below:
 
• Loan I – 12.6% per annum, compounding weekly
• Loan II – 12.8% per annum, compounding weekly
• Loan III – 12.9% per annum, compounding weekly
• Loan IV – 12.7% per annum, compounding quarterly
• Loan V – 13.2% per annum, compounding quarterly

When fully repaid, the loan that will cost Daniel the least amount of money is

  1. Loan I.
  2. Loan II.
  3. Loan III.
  4. Loan IV.
  5. Loan V.
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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*, FUR2 2006 VCAA 3

The company prepares for this expenditure by establishing three different investments.

  1. $7000 is invested at a simple interest rate of 6.25% per annum for eight years.
  2. Determine the total value of this investment at the end of eight years.   (2 marks)
  3. $10 000 is invested at an interest rate of 6% per annum compounding quarterly for eight years.
  4. Determine the total value of this investment at the end of eight years.
  5. Write your answer correct to the nearest dollar.   (1 mark)
  6. $500 is deposited into an account with an interest rate of 6.5% per annum compounding monthly.
  7. Deposits of $200 are made to this account on the last day of each month after interest has been paid.
  8. Determine the total value of this investment at the end of eight years.
  9. Write your answer correct to the nearest dollar.   (1 mark) 

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a.   
   
   

  


    

b.  

 

  


  

c.   

   

CORE*, FUR2 2006 VCAA 2

It is estimated that inflation will average 2% per annum over the next eight years.

If a new machine costs $60 000 now, calculate the cost of a similar new machine in eight years time, adjusted for inflation. Assume no other cost change.

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

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CORE*, FUR2 2008 VCAA 2

Michelle decided to invest some of her money at a higher interest rate. She deposited $3000 in an account paying 8.2% per annum, compounding half yearly.

  1. Write down an expression involving the compound interest formula that can be used to find the value of Michelle’s $3000 investment at the end of two years. Find this value correct to the nearest cent.   (2 marks)

  2. How much interest will the $3000 investment earn over a four-year period?

     

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

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a.  

 
 
 

 

b.  

MARKER’S COMMENT: A TVM calculator could also be used to solve this question.
 

 

 
 

CORE*, FUR2 2009 VCAA 3

The golf club’s social committee has $3400 invested in an account which pays interest at the rate of 4.4% per annum compounding quarterly.

  1. Show that the interest rate per quarter is 1.1%.   (1 mark)

  2. Determine the value of the $3400 investment after three years.

     

    Write your answer in dollars correct to the nearest cent.   (1 mark)

  3. Calculate the interest the $3400 investment will earn over six years.

     

    Write your answer in dollars correct to the nearest cent.   (2 marks)

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a.  


 

b.   

 
 
 

 

c.  

 

 

CORE*, FUR2 2010 VCAA 3

Simple Saver is a simple interest investment in which interest is paid annually.

Growth Plus is a compound interest investment in which interest is paid annually.

Initially, $8000 is invested with both Simple Saver and Growth Plus.

The graph below shows the total value (principal and all interest earned) of each of these investments over a 15 year period.

The increase in the value of each investment over time is due to interest
 

BUSINESS, FUR2 2010 VCAA 3
 

  1. Which investment pays the highest annual interest rate, Growth Plus or Simple Saver?

     

    Give a reason to justify your answer.   (1 mark)

  2. After 15 years, the total value (principal and all interest earned) of the Simple Saver investment is $21 800.

     

    Find the amount of interest paid annually.   (1 mark)

  3. After 15 years, the total value (principal and all interest earned) of the Growth Plus investment is $24 000.

     

    1. Write down an equation that can be used to find the annual compound interest rate, .   (1 mark)

    2. Determine the annual compound interest rate.

       

      Write your answer as a percentage correct to one decimal place.   (1 mark)

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a.  

♦♦♦ Part (a) was “very” poorly answered although exact data unavailable.
MARKER’S COMMENT: Most students ignored the word “rate” and instead referred to the eventual return of each investment.


  

b.  


  

c.i.  


  

c.ii.   
 
 
   

CORE*, FUR2 2011 VCAA 3

Tania purchased a house for $300 000.

She will have to pay stamp duty based on this purchase price.

Stamp duty rates are listed in the table below. 

     BUSINESS, FUR2 2011 VCAA 3
 

  1. Calculate the amount of stamp duty that Tania will have to pay.   (1 mark)

  2. Assuming that her house will increase in value at a rate of 3.17% per annum, what will the value of Tania's house be after 5 years?

     

    Write your answer to the nearest thousand dollars.   (1 mark)

Tania bought her house at the start of 2011.

  1. If the rate of increase in value remains at 3.17% per annum, at the start of which year will the value of Tania's house first exceed $450 000?   (2 marks)

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a.   
   
♦♦ Part (a) was “poorly answered” although exact data is unavailable.
MARKER’S COMMENT: A majority of students did not understand how to use the table.

 

b.  

 
 

 

c.   

 

MARKER’S COMMENT: Many students who correctly found lost a mark by failing to identify the exact year. 

CORE*, FUR2 2014 VCAA 2

A sponsor of the cricket club has invested $20 000 in a perpetuity.

The annual interest from this perpetuity is $750.

The interest from the perpetuity is given to the best player in the club every year, for a period of 10 years.

  1. What is the annual rate of interest for this perpetuity investment?   (1 mark)

  2. After 10 years, how much money is still invested in the perpetuity?   (1 mark)

  1. The average rate of inflation over the next 10 years is expected to be 3% per annum.
    1. Michael was the best player in 2014 and he considered purchasing cricket equipment that was valued at $750.
    2. What is the expected price of this cricket equipment in 2015?   (1 mark)

    3. What is the 2014 value of cricket equipment that could be bought for $750 in 2024?  Write your answer, correct to the nearest dollar.   (1 mark)

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a.   
 
   

 

    

b.  


  

c.i.  


  

c.ii.   

 
 

CORE*, FUR1 2008 VCAA 9 MC

An amount of $8000 is invested for a period of 4 years.

The interest rate for this investment is 7.2% per annum compounding quarterly.

The interest earned by the investment in the fourth year (in dollars) is given by

A.  

B.   

C.   

D.  

E.  

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♦♦ Mean mark 33%.
MARKERS’ COMMENT: The most common errors were not converting and applying the interest rate to a quarterly one.


 

 

 

 

 

CORE*, FUR1 2008 VCAA 6 MC

Sam and Charlie each invest $5000 for three years.

Sam’s investment earns simple interest at the rate of 7.5% per annum.

Charlie’s investment earns interest at the rate of 7.5% per annum compounding annually.

At the conclusion of three years, correct to the nearest cent, Sam will have

A.   $86.48 less than Charlie.

B.   $86.48 more than Charlie.

C.   $132.23 less than Charlie.

D.   $132.23 more than Charlie.

E.   the same as Charlie.

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CORE*, FUR1 2006 VCAA 8 MC

The points on the graph below show the balance of an investment at the start of each quarter for a period of six years.

The same rate of interest applied for these six years.
 

In relation to this investment, which one of the following statements is true?

A.   interest is compounding annually and is credited annually

B.   interest is compounding annually and is credited quarterly

C.   interest is compounding quarterly and is credited quarterly

D.   simple interest is paid on the opening balance and is credited annually

E.   simple interest is paid on the opening balance and is credited quarterly

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♦ Mean mark 37%.
MARKERS’ COMMENT: Graphical analysis of financial situations is a requirement of the study design and deserves attention.

CORE*, FUR1 2012 VCAA 8 MC

$15 000 is invested for 12 months.

For the first six months the interest rate is 6.1% per annum compounding monthly

After six months the interest rate increases to 6.25% per annum compounding monthly.

The total interest earned by this investment over 12 months is closest to 

A.   $926

B.   $935

C.   $941

D.   $953

E.   $965

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♦ Mean mark 42%.

 

CORE*, FUR1 2013 VCAA 3 MC

$10 000 is invested for five years. Interest is earned at a rate of 8% per annum, compounding quarterly.

Which one of the following calculations will give the total interest earned, in dollars, by this investment?

A.     

B.     

C.   

D.   

E.  

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♦ Mean mark 40%.