Investment and Loans

financialmathematics year12 standard

Investment and loans | NSW Curriculum Website

• MST-12-S2-02 models financial situations and solves problems involving interest, depreciation and borrowing money

📖 Prior Knowledge

Content	Prerequisite relationships
Fractions Decimals Percentages	- Find a percentage of a quantity → Calculate simple interest - Find a percentage of a quantity → Calculate dividends and dividend yield - Find a percentage of a quantity → Calculate brokerage and share costs - Use multipliers for percentage change → Calculate compound interest by repeated multiplication
Algebraic Techniques	- Substitute values into algebraic expressions → Calculate simple interest - Substitute values into algebraic expressions → Apply the compound interest formula - Substitute values into algebraic expressions → Apply straight-line depreciation
Indices	- Apply index laws with numerical bases → Apply the compound interest formula
Equations	- Solve equations from formulas → Calculate simple interest
Linear Relationships	- Graph a linear relationship → Compare simple and compound interest
Financial Mathematics A	- Calculate simple interest (revisited content)
Financial Mathematics B	- Calculate compound interest by repeated multiplication (revisited content) - Apply the compound interest formula (revisited content) - Adjust for compounding frequency (revisited content) - Solve depreciation problems (revisited content) - Compare simple and compound interest (revisited content)
Managing Money	- Use a loan repayment table (revisited content)

Investment

• Calculate simple interest for different rates and time periods using the formula $I=Prn$ where $I$ = simple interest, $P$ = principal, $r$ = interest rate per time period and $n$ = number of time periods
• Solve problems involving simple interest in a variety of contexts
• Compare simple interest graphs for different interest rates and time periods, with and without using digital tools
• Calculate the future value, present value or interest rate of a compound interest investment using the formula $FV=PV{\left(1+r\right)}^n$ where $FV$ = future value of the investment, $PV$ = present value of the investment, $r$ = interest rate per time period and $n$ = number of time periods
• Solve problems involving compound interest in a variety of contexts, including inflation and appreciation
• Examine the effect of varying the interest rate, the term or the compounding period on the future value of an investment, with and without using digital tools
• Compare the growth of simple interest and compound interest investments numerically and graphically, with and without using digital tools
• Recognise that simple interest graphs are linear and compound interest graphs are exponential
• Use a spreadsheet to numerically and graphically model investments using both simple and compound interest
• Interpret and analyse tables and graphs about the value of share
• Graph and interpret the value of a share over time, with and without using digital tools
• Calculate the dividend paid and the dividend yield on shares (excluding franked dividends)
• Solve problems involving calculation of brokerage costs and total costs of purchasing shares
• Compare and contrast savings accounts, term deposits, shares and buying property as investment strategies

Depreciation

• Apply the straight-line depreciation method to calculate the depreciation of an asset using the formula $S=V_0-Dn$ where $S$ = salvage value, $V_0$ = initial value of the asset, $D$ = depreciation amount per time period and $n$ = number of time periods
• Apply the declining balance method to calculate the depreciation of an asset using the formula $S=V_0{\left(1-r\right)}^n$ where $S$ = salvage value, $V_0$ = initial value of the asset, $r$ = depreciation rate per time period and $n$ = number of time periods
• Compare straight-line depreciation and declining balance depreciation both numerically and graphically, with and without using digital tools
• Use a spreadsheet to numerically and graphically model depreciation using the straight-line and declining balance methods

Loans

• Compare and analyse the costs associated with buy now, pay later, short term and long term loans
• Model a reducing balance loan as an application of compound interest with periodic repayments in tabular form for up to four time periods, with and without using digital tools