• Mathematics General
• Year 12

# Loans, Investments and Annuities

approx. 12 hrs

6 topics

39 concepts

Enrol in Loans, Investments and Annuities to optimise your academic outcomes in Mathematics.

Available in
ACT NT QLD SA TAS VIC WA

### Overview

Loans, Investments and Annuities enables students to solve practical problems associated with taking out or refinancing a mortgage and making investments. We will help students understand the concepts and techniques in loans, investments and annuities and how to apply reasoning skills to solve related questions. Students will  develop proficiency when using a CAS calculator. Learning to select the relevant data to process, interpreting the results and communicating a response in the context of the question.

### Topics & Concepts We Cover

This learning program is made up of the following 6 topics, broken down into 39 concepts.

• #### Modelling Linear Growth and Decay 13 concepts

1. Use a graphing calculator to generate sequences from recurrence relations

2. Using a rule to find the value of a simple interest loan or investment after n years

3. Using a rule to find the value of an asset after n units of use

4. Using a rule to find the value of an asset after flat-rate depreciation after n years

5. Use a recurrence model to analyse unit cost depreciation with a graphing calculator

6. Modelling unit cost depreciation with a recurrence relation

7. Use a recurrence model to analyse flat rate depreciation with a graphing calculator

8. Modelling simple interest with a recurrence relation

9. Use a recurrence model to analyse a simple interest investment or loan with a graphing calculator

10. Modelling flat rate depreciation with a recurrence relation

11. Write a rule for determining the nth term for linear growth or decay

12. Use a calculator to generate a sequence of numbers from a rule

13. Generate a sequence from a first-order linear recurrence relation

• #### Modelling Geometric Growth and Decay 7 concepts

1. Using a graphing calculator to solve geometric growth and decay problems

2. Using a rule to solve reducing balance depreciation problems

3. Modelling compound interest with a recurrence relation with different compounding periods

4. Using a rule to solve compound interest problems

5. Modelling reducing balance depreciation with a recurrence relation

6. Writing rules for the nth term of a sequence generated from a geometric recurrence relation

7. Modelling compound interest with a recurrence relation that compounds yearly

• #### Nominal and Effective Interest Rates 3 concepts

1. Convert between nominal and compounding interest rates

2. Compare loans and investments with effective interest rates

3. Calculate effective interest rates with a graphing calculator

• #### Combining Geometric and Linear Growth and Decay 7 concepts

1. Generate a sequence from a recurrence relation that combines geometric and linear growth and decay

2. Model real-life situations using a recurrence relation combining geometric and linear growth and decay

3. Use a recurrence relation to analyse a reducing balance loan with a graphing calculator

4. Read and interpret an amortisation table for reducing balance loans

5. Use a Financial Solver to solve interest-only loan problems

6. Model a reducing balance loan with a recurrence relation

7. Use a Financial Solver to solve reducing balance loan problems

• #### Annuities 5 concepts

1. Use a Financial Solver to analyse an annuity and solve related problems

2. Using a recurrence relation to analyse an annuity with a graphing calculator

3. Modelling an annuity with a recurrence relation

4. Use a Financial Solver to solve perpetuity problems

5. Read and interpret an amortisation table for annuities

• #### Periodic Payments to CI Investment 4 concepts

1. Read and interpret an amortisation table for compound interest investments with regualr additions to the principal

2. Modelling compound interest investments with regular additions to the principal

3. Using a recurrence relation to analyse compound interest investments with additions to the principal

4. Using a financial solver to analyse a compound interest investment with regular additions to the principal

### What you'll get

Learning Content

• A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
• All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

• We match you to a private, expert tutor who is right for your needs and goals
• Our tutors are talented, tested, top ATAR achievers and subject experts
• During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Loans, Investments and Annuities

Reporting

• Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
• You and your parents receive a comprehensive feedback report after every session
• Every session is recorded and available for you to watch at any time, allowing you to review what was covered

### Ready to start this program?

Simply pick a time that works for you

We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime