How many SCSA Mathematics Applications questions cover Loans, investments and annuities?

AusGrader has 112 SCSA Mathematics Applications questions on Loans, investments and annuities, all with instant AI grading and detailed marking feedback.

SCSA Mathematics Applications Loans, investments and annuities

5 sample questions with marking guides and sample answers · Avg. score: 25%

Q14

2024

QCAA

Paper 1

1 mark

Q14

1 mark

Which option will not change the effective annual rate of interest for a loan?

changing the nominal annual rate of interest

changing the period when interest is charged

changing the repayment amount for each period

changing the number of compounding periods per year

Q11

2023

QCAA

Paper 1

1 mark

Q11

1 mark

An annuity with an initial zero balance has ＄500 deposited at the end of every month. The annuity earns 4.8% p.a. interest, compounding monthly. At the end of the fourth month, the balance is closest to

＄2002

＄2008

＄2012

＄2014

Q14

2021

SCSA

Paper 2

11 marks

Q14

Patrick has retired and invested his lump sum superannuation payout of ＄717 850 at a rate of 5.7% per annum compounded monthly. He begins the investment strategy from 1 January.

Q14a

Patrick will receive ＄4500 at the end of each month for general living expenses and will also receive a further ＄4000 at the end of each year for an annual holiday.

Q14a (i)

1 mark

Identify this type of investment account.

Descriptor	Marks
states correct answer	1

Q14a (ii)

4 marks

Determine the balance in the account at the end of the first year.

N = 12, I = 5.7, PV = $-717\ 850$ , PMT = 4500, P/Y = 12, C/Y = 12
FV = 704 420.20

Balance at end of year 1 = $704\ 420.20 - 4000 = ＄700\ 420.20$

Marking Criteria

Descriptor	Marks
uses at least 4 correct values for N, I, PV, PMT, P/Y, C/Y	1
uses all correct values for N, I, PV, PMT, P/Y, C/Y	1
determines correct value for FV	1
determines correct end of year balance	1

Q14a (iii)

3 marks

Determine the balance in the account at the end of the second year.

N = 12, I = 5.7, PV = $-700\ 420.20$ , PMT = 4500, P/Y = 12, C/Y = 12
FV = 685 970.53

Balance at end of year 2 = $685\ 970.53 - 4000 = ＄681\ 970.53$

Marking Criteria

Descriptor	Marks
uses correct value for PV	1
determines correct FV	1
determines correct end of year 2 balance	1

Q14b

3 marks

When Patrick retired, he also considered the option of setting up a perpetuity with his superannuation payout still at 5.7% per annum compounded monthly. Calculate the quarterly payments Patrick would have received with this perpetuity in place.

N = 2 (can be any value), I = 5.7, PV = $-717\ 850$ , FV = 717 850, P/Y = 4, C/Y = 12

Quarterly payments = ＄10 278.03

Marking Criteria

Descriptor	Marks
uses at least 4 correct values for N, I, PV, FV, P/Y, C/Y	1
uses all correct values for N, I, PV, FV, P/Y, C/Y	1
states correct quarterly payments	1

Q16

2022

SCSA

Paper 2

7 marks

Q16

After paying a deposit for his new apartment, Declan obtains a bank loan for the remaining amount of ＄112 000 at 3.26% per annum compounded monthly. He can currently afford to repay ＄970 per month at the end of every month.

Q16a

3 marks

Calculate how much he would owe after the 40th repayment.

Using the financial app with
N = 40, I = 3.26, PV = -112 000, PMT = 970, P/Y = C/Y = 12
FV = 83 910.19

He would owe ＄83 910.19 after the 40th repayment

Marking Criteria

Descriptor	Marks
states at least 4 correct entries	1
states all correct entries	1
states correct answer	1

Q16b

4 marks

Declan decided to deposit a one-off extra amount of ＄1600, after the 16th repayment. Calculate the new amount he would owe after the 40th repayment.

Step 1. Using the financial app
N = 16, I = 3.26, PV = –112 000, PMT = 970, P/Y = C/Y = 12
FV = ＄101 128.46
New PV = ＄101 128.46 − 1600 = ＄99 528.46

Step 2. Using financial app
N = 24(40 − 16), I = 3.26, PV = −99 528.46, PMT = 970, P/Y = C/Y = 12
FV = ＄82 202.54

New amount owing after the 40th repayment is ＄82 202.54

Marking Criteria

Descriptor	Marks
states all correct entries in step 1	1
correctly subtracts 1600 from FV in step 1 to give new PV	1
states all correct entries in step 2	1
correctly determines new FV	1

2023

SCSA

Paper 2

16 marks

Sonia secures a bank loan to buy a professional gaming computer. The loan has reducible interest. Information about the loan is shown below.

Loan issued: Start of October 2023.
Starting balance: ＄9200.
Interest: Compounded monthly.
Repayments: ＄290 per month.

After the first monthly payment at the end of October 2023, Sonia’s balance is ＄8992.80.

Q9a

2 marks

Use the information above to show that the annual interest rate is 10.8%.

Interest for the first month = $(8992.80 + 290) - 9200 = 82.80$

Annual interest rate = $\frac{82.80}{9200} \times 100 \times 12 = 10.8\%$

Marking Criteria

Descriptor	Marks
correctly calculates the interest for the first month	1
correctly calculates annual interest rate	1

Q9b

2 marks

Determine a recursive rule to model the balance of the loan at the end of each month.

Descriptor	Marks
states correct rule	1
states correct initial value	1

Q9c (i)

1 mark

Determine the balance of the loan at the end of November 2023.

Descriptor	Marks
determines correct balance	1

Q9c (ii)

2 marks

Determine the total amount of interest incurred in the first three months.

$82.80 + (0.009 \times 8992.80) + (0.009 \times 8783.74) = ＄242.79$

Marking Criteria

Descriptor	Marks
determines correct interest for each month	1
sums each interest	1

Q9c (iii)

1 mark

Determine the balance of the loan at the end of May 2024.

Descriptor	Marks
determines correct balance	1

Q9d

1 mark

Determine how many months it takes to repay the loan.

Descriptor	Marks
determines correct value	1

Q9e

2 marks

Determine the final repayment and the total amount repaid.

$T_{37} = 150.64$
Therefore, the final repayment is $＄150.64 \times 1.009 = ＄152$

Total amount repaid = $37 \times 290 + 152 = ＄10\,882$

Marking Criteria

Descriptor	Marks
determines correct final repayment	1
determines correct total amount repaid	1

Q9f

1 mark

Calculate the total interest paid on the loan.

Descriptor	Marks
determines correct value	1

Q9g

4 marks

Sonia is paid every fortnight in her employment. Instead of monthly repayments of ＄290, she is now considering making fortnightly repayments of ＄145, with the interest calculated fortnightly. Use mathematical evidence to show what difference this would make and advise Sonia what her savings might be.

Interest each fortnight $\frac{10.8}{26} = 0.41538\%$ (5 d.p.)

$A_{n+1} = \left(1 + \frac{0.108}{26}\right)A_n - 145, A_0 = 9200$

74 repayments and total repaid = $74 \times 145 - 28.92 = ＄10\,701.08$

Sonia should use fortnightly repayments to save $10\,882 - 10\,701.08 = ＄180.92$

She would also pay off the loan quicker.

Marking Criteria

Descriptor	Marks
determines correct number of repayments	1
calculates the total repaid	1
determines correct final savings	1
gives correct advice	1

SCSA Mathematics Applications Loans, investments and annuities

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