This topic covers the use of first-order linear recurrence relations and technology to model and analyse a range of financial situations, and solve related problems involving interest, appreciation and depreciation, loans, annuities and perpetuities.

Depreciation of assets, including:

- review of the use of a first-order linear recurrence relation to generate the terms of a sequence
- use of a recurrence relation to model and compare (numerically and graphically) flat rate, unit cost and reducing balance depreciation of the value of an asset with time, including the use of a recurrence relation to determine the depreciating value of an asset after n depreciation periods, including from first principles for \( n \le 5 \)
- use of the rules for the future value of an asset after n depreciation periods for flat rate, unit cost and reducing balance depreciation and their application.

Compound interest investments and loans, including:

- review of the concepts of simple and compound interest
- use of a recurrence relation to model and analyse (numerically and graphically) a compound interest investment or loan, including the use of a recurrence relation to determine the value of the compound interest loan or investment after \( n \) compounding periods, including from first principles for \( n \le 5 \)
- difference between nominal and effective interest rates and the use of effective interest rates to compare investment returns and the cost of loans when interest is paid or charged, for example, daily, monthly, quarterly
- rule for the future value of a compound interest investment or loan after n compounding periods and its use to solve practical problems.

Reducing balance loans (compound interest loans with periodic repayments), including:

- use of a first-order linear recurrence relation to model and analyse (numerically and graphically) the amortisation of a reducing balance loan, including the use of a recurrence relation to determine the value of the loan or investment after n payments, including from first principles for \( n \le 5 \)
- use of a table to investigate and analyse the amortisation of a reducing balance loan on a step-by-step basis, the payment made, the amount of interest paid, the reduction in the principal and the balance of the loan
- use of technology with financial modelling functionality to solve problems involving reducing balance loans, such as repaying a personal loan or a mortgage, including the impact of a change in interest rate on repayment amount, time to repay the loan, total interest paid and the total cost of the loan.

Annuities and perpetuities (compound interest investments with periodic payments made from the investment), including:

- use of a first-order linear recurrence relation to model and analyse (numerically and graphically) the amortisation of an annuity, including the use of a recurrence relation to determine the value of the annuity after n payments, including from first principles for \( n \le 5 \)
- use of a table to investigate and analyse the amortisation of an annuity on a step-by-step basis, the payment made, the interest earned, the reduction in the principal and the balance of the annuity
- use of technology to solve problems involving annuities including determining the amount to be invested in an annuity to provide a regular income paid, for example, monthly, quarterly
- simple perpetuity as a special case of an annuity that lasts indefinitely.

Compound interest investment with periodic and equal additions to the principal (an annuity investment), including:

- use of a first-order linear recurrence relation to model and analyse (numerically and graphically) annuity investment, including the use of a recurrence relation to determining the value of the investment after n payments have been made, including from first principles for \( n \le 5 \)
- use of a table to investigate and analyse the growth of an annuity investment on a step-by-step basis after each payment is made, the payment made, the interest earned and the balance of the investment
- use of technology with financial modelling functionality to solve problems involving annuity investments, including determining the future value of an investment after a number of compounding periods, the number of compounding periods for the investment to exceed a given value and the interest rate or payment amount needed for an investment to exceed a given value in a given time.

*source – VCE Mathematics Study Design*

#### Simple Interest or Flat Rate Interest

- Video - Understanding Simple Interest (3:07)
- Video - Calculating Simple Interest (3:20)
- Video - Total Amount including Simple Interest in Years (2:14)
- Video - Total Amount including Simple Interest in Months (2:18)
- Video - Total Amount including Simple Interest in Quarters (2:10)
- Video - Finding the Period of Simple Interest (5:00)
- Video - Finding the Principal of Simple Interest (4:38)
- Video - Finding the Rate of Simple Interest (4:52)
- Video - Applications of Simple Interest (5:45)
- Topic - Calculating Simple Interest for Years
- Topic - Calculating Simple Interest for Years and Months
- Topic - Finding Periods
- Topic - Finding Simple Interest Rates
- Topic - Finding Principals
- Topic - Finding Monthly Instalment given Simple Interest

#### Simple Interest Applications

- Video - Theory of Total Amount to be Paid (2:53)
- Video - Total Amount to be Paid by Annual Simple Interest (3:25)
- Video - Total Amount to be Paid by Quarterly Simple Interest (1:30)
- Video - Understanding Repayments upon Simple Interest (3:10)
- Video - Repayments Monthly upon Simple Interest (3:12)
- Video - Repayments Fortnightly upon Simple Interest (0:55)
- Video - Repayments Quarterly upon Simple Interest (1:08)
- Video - Borrowing Money and Repay in Monthly Instalments (2:12)

#### Compound Interest Applications

- Video - Investments by Compound Interest (4:32)
- Video - Amount of Interest Earned by Compound Interest (2:17)
- Topic - Compound Interest Applications: Compounded Annually
- Topic - Compound Interest Applications: Compounded Monthly
- Topic - Compound Interest Applications: Interest Earned
- Topic - Compound Interest Applications: Principal Amount

#### Nominal and Effective Interest Rates

- Video - Understanding Effective Interest Rate (4:09)
- Video - Effective Interest Rates: Annual, Half-Yearly, Quarterly, Monthly (5:55)
- Video - Effective Interest Rates: Fortnightly, Weekly, Daily (4:27)
- Video - Application of Effective Interest Rate (2:12)
- Video - Effective Interest Rate and Flat-Rate Interest (4:58)
- Video - Comparison of Interest Rates using Effective Interest Rates (3:53)

#### Manipulation of Simple Interest Formula

- Video - Understanding Flat-Rate Interest (3:20)
- Video - Flat-Rate Interest Annually (4:04)
- Video - Flat-Rate Interest Quarterly (4:05)
- Video - Theory of Finding Principals (3:44)
- Video - Finding Principals from Annual Interest (2:24)
- Video - Finding Principals from Quarterly Interest (2:37)
- Video - Theory of Finding Interest Rate (2:20)
- Video - Finding Annual Interest Rate (2:41)
- Video - Finding Quarterly Interest Rate (2:27)
- Video - Theory of Finding Periods (2:13)
- Video - Finding Periods upon Annual Simple Interest (2:32)
- Video - Finding Periods upon Quarterly Simple Interest (2:20)

#### Personal Loans in Compound Interest

- Topic - Monthly Repayments of Reducing Balance Personal Loans
- Topic - Weekly Repayments of Reducing Balance Personal Loans
- Topic - Total Interest Charged on Personal Loans in Monthly Repayments
- Topic - Total Interest Charged on Personal Loans in Weekly Repayments
- Topic - Outstanding Balance on Personal Loans in Monthly Repayments
- Topic - Outstanding Balance on Personal Loans in Weekly Repayments

#### Home Loans in Compound Interest

- Topic - Monthly Repayments of Reducing Balance Home Loans
- Topic - Weekly Repayments of Reducing Balance Home Loans
- Topic - Total Interest Charged on Home Loans in Monthly Repayments
- Topic - Total Interest Charged on Home Loans in Weekly Repayments
- Topic - Outstanding Balance on Home Loans in Monthly Repayments
- Topic - Outstanding Balance on Home Loans in Weekly Repayments

#### Loan Repayments in Borrowing Money

- Video - Understanding Loan Repayments using Loan Balance Due (4:28)
- Video - Calculating the Values of Loan Repayments (4:27)
- Video - Loan Balance Sheet (4:33)
- Video - Understanding of Calculating Repayments in a Table (3:30)
- Video - Calculating Monthly Repayments in a Table (4:13)
- Video - Calculating Fortnightly Repayments in a Table (3:21)
- Topic - Understanding Loan Repayments using Loan Balance Due
- Topic - Calculating the Values of Loan Repayments
- Topic - Loan Balance Sheet
- Topic - Understanding of Calculating Repayments in a Table
- Topic - Calculating Monthly Repayments in a Table

#### Reducing Balance Loans

- Video - Reading a Table Reducing Balance Loan (2:56)
- Video - Reducible Balance Loan using Period-Loan Table (1:04)
- Video - Reducible Balance Loan using Interest-Loan Table (3:33)
- Video - Table for Reducing Balance Loan based on the Loan Amount (5:16)
- Video - Table for Reducing Balance Loan based on Interest Rates (3:45)
- Video - Graphs of Reducing Balance Loan (6:33)
- Video - Comparisons Monthly and Fortnightly Repayments using Graphs (2:53)
- Video - Monthly Instalments by Borrowing Table (8:47)

#### Loan Repayments using Present Value

- Video - Understanding Loan Repayments (6:20)
- Video - Annual Loan Repayments (1:03)
- Video - Monthly Loan Repayments (1:00)
- Video - Fortnightly Loan Repayments (3:32)
- Topic - Finding Annual Repayments using Present Value Formula
- Topic - Finding Quarterly Repayments using Present Value Formula
- Topic - Finding Monthly Repayments using Present Value Formula
- Topic - Finding Present Value by Annual Repayments
- Topic - Finding Present Value by Quarterly Repayments
- Topic - Finding Present Value by Monthly Repayments
- Topic - Finding Total Interest Paid

#### Loan Repayments using Reducible Interest and Balance

- Video - Reducible Interest using Tables (4:34)
- Video - Reducible Interest Monthly (3:49)
- Video - Repayment Table of Reducible Interest Loans (4:38)
- Video - Repayment Table of Reducible Interest Loans: Interest Paid (4:38)
- Video - Completing Repayment Table of Reducible Interest Loans (5:24)
- Video - Repayment Table of Reducible Interest Loans: P + I - R (3:30)
- Video - Payout of Reducible Interest Loans (4:23)
- Video - Loan Statement of Reducible Interest Loans (5:01)
- Video - Hire Purchase or Buy Outright (3:11)
- Video - Flat Rate Loans and Reducing Balance Loans (6:23)

#### Annuities Formula

- Topic - Amount Owing in Monthly Repayments at Monthly Interest Rate
- Topic - Amount Owing in Quarterly Repayments at Quarterly Interest Rate
- Topic - Amount Owing in Weekly Repayments at Weekly Interest Rate
- Topic - Amount Owing in Fortnightly Repayments at Fortnightly Interest Rate
- Topic - Amount Owing in Monthly Repayments at Annual Interest Rate
- Topic - Amount Owing in Quarterly Repayments at Annual Interest Rate
- Topic - Amount Owing in Weekly Repayments at Annual Interest Rate
- Topic - Amount Owing in Fortnightly Repayments at Annual Interest Rate
- Topic - Amount of Monthly Repayment by Annuity Formula
- Topic - Amount of Quarterly Repayment by Annuity Formula
- Topic - Amount of Weekly Repayment by Annuity Formula
- Topic - Amount of Fortnightly Repayment by Annuity Formula
- Topic - Total Interest of Monthly Repayments by Annuity Formula
- Topic - Total Interest of Quarterly Repayments by Annuity Formula
- Topic - Total Interest of Weekly Repayments by Annuity Formula
- Topic - Total Interest of Fortnightly Repayments by Annuity Formula

#### Future Value of an Annuity

- Video - Understanding Annuity (3:09)
- Video - Annuity Example (4:34)
- Video - Annuity Question (3:04)
- Video - Future Value of an Annuity Compounded Annually (3:34)
- Video - Future Value of an Annuity Compounded Half Yearly (1:37)
- Video - Future Value of an Annuity Compounded Quarterly (1:04)
- Video - Future Value of an Annuity Compounded Monthly (1:00)
- Video - Future Value of an Annuity Compounded Weekly (1:09)
- Video - Future Value of an Annuity Compounded Fortnightly (1:34)

#### Application of Future Value of an Annuity

- Video - Interests Earned from an Annuity Compounded Annually (4:22)
- Video - Interests Earned from an Annuity Compounded Quarterly (2:23)
- Video - Understanding Contributions Needed for Annuity (5:28)
- Video - Contributions Needed for Annuity Compounded Annually (1:13)
- Video - Contributions Needed for Annuity Compounded Quarterly (1:37)
- Video - Contributions Needed for Annuity Compounded Monthly (1:47)
- Video - Future Value using $1 Annuity Table (2:37)
- Video - Annuity Values by $1 Annuity Table (2:43)
- Video - Interest Earned by Annuity (2:19)

#### Present Value of an Annuity

- Video - Present Value using Future Value Compounded Annually (4:01)
- Video - Present Value using Future Value Compounded Half Yearly (1:48)
- Video - Present Value using Future Value Compounded Quarterly (0:54)
- Video - Present Value using Future Value Compounded Monthly (3:20)
- Video - Present Value using Future Value Compounded Weekly (0:57)
- Video - Present Value using Contributions Compounded Annually (8:31)
- Video - Present Value using Contributions Compounded Monthly (1:20)
- Video - Present Value using Contributions Compounded Quarterly (2:22)

#### Annuity Investments

- Topic - Superannuation Compounded Annually Deposit Annually 1
- Topic - Superannuation Compounded Annually Deposit Annually 2
- Topic - Superannuation Compounded Monthly Deposit Monthly 1
- Topic - Superannuation Compounded Monthly Deposit Monthly 2
- Topic - Superannuation at Annual Interest Rate Deposit Monthly 1
- Topic - Superannuation at Annual Interest Rate Deposit Monthly 2