#FinancialMathematics #Year12 #Standard >[!info]- [Investment and loans | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-standard-11-12-2024/content/n12-tba2/fac80cab35) >- MST-12-S2-02 models financial situations and solves problems involving interest, depreciation and borrowing money ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | --------------------------- | ------------------------------------------------ | -------------------------------------- | | [[Financial Mathematics A]] | - simple interest | - *repeated content* | | [[Financial Mathematics B]] | - future value formula<br>- depreciation formula | - *repeated content*<br>- credit cards | ## 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