VCE General Maths Recursion and Financial Modelling 2024 Exam 2 Mini Test 2
VCAA General Maths Exam 2
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: 11
Reading time: 3 minutes
Writing time: 16 minutes
Instructions
• Answer all questions in the spaces provided.
• Write your responses in English.
• In all questions where a numerical answer is required, you should only round your answer when instructed to do so.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Recursion and financial modelling - 2024 to 2022 - Exam 2 (Part 2)
Emi takes out a reducing balance loan of $500 000.
The interest rate is 5.3% per annum, compounding monthly.
Emi makes regular monthly repayments of $3071.63 for the duration of the loan, with only the final repayment amount being slightly different from all the other repayments.
Determine the total cost of Emi’s loan, rounding your answer to the nearest cent, and state the number of payments required to fully repay the loan.
total cost =
number of payments =
Arthur takes out a new loan of $60 000 to pay for an overseas holiday.
Interest on this loan compounds weekly.
The balance of the loan, in dollars, after \(n\) weeks, \(V_n\), can be determined using a recurrence relation of the form
\(V_0 = 60 000, \quad V_{n+1} = 1.0015V_n - d\)
a. Show that the interest rate for this loan is 7.8% per annum. 1 mark
b. Determine the value of \(d\) in the recurrence relation if
i. Arthur makes interest-only repayments 1 mark
ii. Arthur fully repays the loan in five years. Round your answer to the nearest cent. 1 mark
c. Arthur decides that the value of \(d\) will be 300 for the first year of repayments.
If Arthur fully repays the loan with exactly three more years of repayments, what new value of \(d\) will apply for these three years?
Round your answer to the nearest cent. 1 mark
d. For what value of \(d\) does the recurrence relation generate a geometric sequence? 1 mark
To purchase additional workplace equipment, Pina took out a reducing balance loan of $580 000 with interest calculated monthly.
The balance of the loan, in dollars, after \(n\) months, \(L_n\), can be modelled by the recurrence relation
\(L_0 = 580\,000, \quad L_{n+1} = 1.002L_n - 3045.26\)
a. Showing recursive calculations, determine the balance of the loan after two months.
Round your answer to the nearest cent. 1 mark
b. Determine the annual compound interest rate for this loan. 1 mark
c. The final repayment that is required to fully pay off the loan is smaller than all other repayments by an amount less than one dollar.
Determine this small amount in dollars, rounded to the nearest cent. 1 mark
d. The original recurrence relation
\(L_0 = 580\,000, \quad L_{n+1} = 1.002L_n - 3045.26\)
models the loan being fully repaid in a certain number of years.
Using a different multiplication factor (other than 1.002) the loan would be fully repaid one year sooner.
Determine this multiplication factor.
Round your answer to four decimal places. 1 mark
End of Question and Answer Book
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