VCE General Maths Recursion and Financial Modelling 2024 Exam 2 Mini Test 1
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: 10
Reading time: 2.5 minutes
Writing time: 15 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 - Exam 2 (Part 1)
Emi operates a mobile dog-grooming business.
The value of her grooming equipment will depreciate.
Based on average usage, a rule for the value, in dollars, of the equipment, \(V_n\), after \(n\) weeks is
\(V_n = 15000 - 60n\)
Assume that there are exactly 52 weeks in a year.
a. By what amount, in dollars, does the value of the grooming equipment depreciate each week? 1 mark
b. Emi plans to replace the grooming equipment after four years.
What will be its value, in dollars, at this time? 1 mark
c. \(V_n\) is the value of the grooming equipment, in dollars, after \(n\) weeks.
Write a recurrence relation in terms of \(V_0\), \(V_{n+1}\) and \(V_n\) that can model this value from one week to the next. 1 mark
d. The value of the grooming equipment decreases from one year to the next by the same percentage of the original $15 000 value.
What is this annual flat rate percentage? 1 mark
Emi invested profits of $10 000 into a savings account that earns interest compounding fortnightly, for one year.
The effective interest rate, rounded to two decimal places, is 5.07%.
Assume that there are exactly 26 fortnights in a year.
a. What is the nominal percentage rate of interest for the account?
Round your answer to two decimal places. 1 mark
b. Explain why the nominal interest rate appears lower than the effective interest rate. 1 mark
Emi decides to invest a $300 000 inheritance into an annuity.
Let \(E_n\) be the balance of Emi’s annuity after \(n\) months.
A recurrence relation that can model the value of this balance from month to month is
\(E_0 = 300 000, \quad E_{n+1} = 1.003E_n - 2159.41\)
a. Showing recursive calculations, determine the balance of the annuity after two months.
Round your answer to the nearest cent. 1 mark
b. For how many years will Emi receive the regular payment? 1 mark
c. Calculate the annual compound interest rate for this annuity. 1 mark
d. If Emi wanted the annuity to act as a perpetuity, what monthly payment, in dollars, would she receive? 1 mark
End of Question and Answer Book
VCE is a registered trademark of the VCAA. The VCAA does not endorse or make any warranties regarding this study resource. Past VCE exams and related content can be accessed directly at www.vcaa.vic.edu.au
