SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Recursion and Finance, GEN2 2023 VCAA 6

Arthur invests $600 000 in an annuity that provides him with a monthly payment of $3973.00.

Interest is calculated monthly.

Three lines of the amortisation table for this annuity are shown below.

  1. The interest rate for the annuity is 0.42% per month.
  2. Determine the interest rate per annum.   (1 mark)

  3. Using the values in the table, complete the next line of the amortisation table.
  4. Write your answers in the spaces provided in the table below.
  5. Round all values to the nearest cent.   (1 mark)

  1. Let be the balance of Arthur's annuity, in dollars, after months.
  2. Write a recurrence relation in terms of and that can model the value of the annuity from month to month.   (1 mark)

  3. The amortisation tables above show that the balance of the annuity reduces each month.
  4. If the balance of an annuity remained constant from month to month, what name would be given to this type of annuity?   (1 mark)

Show Answers Only

a.    

b.   

c.   

d.   

Show Worked Solution

a.    
 

b.   

♦♦ Mean mark (b) 40%.

 
c.   

♦ Mean mark (c) 41%.

 
d.   

CORE, FUR2 2021 VCAA 9

Sienna invests $152 431 into an annuity from which she will receive a regular monthly payment of $900 for 25 years. The interest rate for this annuity is 5.1% per annum, compounding monthly.

  1. Let be the balance of the annuity after monthly payments. A recurrence relation written in terms of and can model the value of this annuity from month to month.
  2. Showing recursive calculations, determine the value of the annuity after two months.
  3. Round your answer to the nearest cent.   (2 marks)

  4. After two years, the interest rate for this annuity will fail to 4.6%.
  5. To ensure that she will still receive the same number of $900 monthly payments, Sienna will add an extra one-pff amount into the annuity at this time.
  6. Determine the value of this extra amount that Sienna will add.
  7. Round your answer to the nearest cent.   (1 mark)

Show Answers Only
Show Worked Solution

a.   

 
 
 

 

b.     

 

 

 

 

 

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)

Show Answers Only
Show Worked Solution
a.  
 

 

♦ Mean mark 48%.
b.  
 

 

♦ Mean mark 36%.
c.  
 
 
   

CORE, FUR1 2018 VCAA 17-18 MC

The value of an annuity investment, in dollars, after years, , can be modelled by the recurrence relation shown below.

 
Part 1

What is the value of the regular payment added to the principal of this annuity investment?

  1.   $34.00
  2. $156.40
  3. $466.00
  4. $500.00
  5. $656.40

 
Part 2

Between the second and third years, the increase in the value of this investment is closest to

  1.   $656
  2.   $658
  3.   $661
  4. $1315
  5. $1975
Show Answers Only

Show Worked Solution


 

 

 

CORE, FUR1 SM-Bank VCAA 1-2 MC

Part 1

Candy deposits $80 000 into a savings account that earns 5% interest per annum, compounded annually.

At the end of the first year, Candy withdraws $5600.

What is the balance of Candy's savings account at the start of the second year?

 

Part 2

If is the balance of Candy's account at the start of year , a recurrence equation that can be used to model the balance of the account over time is

Show Answers Only

Show Worked Solution

 

 
 

 

CORE, FUR2 SM-Bank VCE 2

Spiro is saving for a car. He has an account with $3500 in it at the start of the year.

At the end of each month, Spiro adds another $180 to the account.

The account pays 3.6% interest per annum, compounded monthly.

    1. What is the interest rate per month?   (1 mark)
    2. Write a recurrence relation that models Spiro's investment, with representing the balance of his account after months.   (1 mark)
  2. What will be the balance of Spiro's account after 3 months?
  3. Write your answer correct to the nearest cent.   (1 mark)

Show Answers Only

Show Worked Solution

a.i.   
   

 

a.ii.   
   
   
     
     

  


  

b.