VCE General Maths Recursion and Financial Modelling 2021 Exam 1 Mini Test
VCAA General Maths Exam 1
This is the full VCE General Maths Exam with worked solutions. You can also try Mini-Tests, which are official VCAA exams split into short tests you can do anytime.
Number of marks: 8
Reading time: 3 minutes
Writing time: 18 minutes
Instructions
• Answer all questions in pencil on your Multiple-Choice Answer Sheet.
• Choose the response that is correct for the question.
• A correct answer scores 1; an incorrect answer scores 0.
• Marks will not be deducted for incorrect answers.
• No marks will be given if more than one answer is completed for any question.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Recursion and financial modelling - 2021
Recursion and financial modelling
Question 1The following recurrence relation can generate a sequence of numbers.
\(L_0 = 37, L_{n+1} = L_n + C\)
The value of \(L_2\) is 25.
The value of \(C\) is
- A. –6
- B. –4
- C. 4
- D. 6
- E. 37
Use the following information to answer Questions 18 and 19.
Deepa invests $500 000 in an annuity that provides an annual payment of $44 970.55. Interest is calculated annually. The first five lines of the amortisation table are shown below.
| Payment number | Payment ($) | Interest ($) | Principal reduction ($) | Balance ($) |
|---|---|---|---|---|
| 0 | 0.00 | 0.00 | 0.00 | 500 000.00 |
| 1 | 44 970.55 | 20 000.00 | 24 970.55 | 475 029.45 |
| 2 | 44 970.55 | 19 001.18 | 25 969.37 | 449 060.08 |
| 3 | 44 970.55 | 17 962.40 | 422 051.93 | |
| 4 | 44 970.55 | 16 882.08 | 28 088.47 | 393 963.46 |
The principal reduction associated with payment number 3 is
- A. $17 962.40
- B. $25 969.37
- C. $27 008.15
- D. $28 088.47
- E. $44 970.55
The number of years, in total, for which Deepa will receive the regular payment of $44 970.55 is closest to
- A. 12
- B. 15
- C. 16
- D. 18
- E. 20
Sammy purchased a boat for $72 000. The value of the boat is depreciated each year by 10% using the reducing balance method. In the third year, the boat will depreciate in value by 10% of
- A. $47 239.20
- B. $52 488.00
- C. $58 320.00
- D. $64 800.00
- E. $72 000.00
Enrico invests $3000 in an account that pays interest compounding monthly. After four years, the balance of the account is $3728.92. The effective annual interest rate for this investment, rounded to two decimal places, is
- A. 5.45%
- B. 5.52%
- C. 5.56%
- D. 5.59%
- E. 5.60%
Joanna deposited $12 000 in an investment account earning interest at the rate of 2.8% per annum, compounding monthly. She would like this account to reach a balance of $25 000 after five years. To achieve this balance, she will make an extra payment into the account each month, immediately after the interest is calculated. The minimum value of this payment is closest to
- A. $113.85
- B. $174.11
- C. $580.16
- D. $603.22
- E. $615.47
Bimal has a reducing balance loan. The balance, in dollars, of the loan from month to month, \(B_n\), is modelled by the recurrence relation below.
\(B_0 = 450 000, B_{n+1} = R B_n - 2633\)
Given that the loan will be fully repaid in 20 years, the value of \(R\) is closest to
- A. 1.003
- B. 1.0036
- C. 1.03
- D. 1.036
- E. 1.36
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
- A. 1.85%
- B. 2.21%
- C. 2.79%
- D. 3.14%
- E. 4.07%
End of Multiple-Choice Question Book
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