Standard Financial Mathematics – Investments and loans

This lesson comprises three (3) master classes focusing on:

• Simple and compound interest
• Appreciation and depreciation of assets
• Shares and dividends
• Loans and credit cards

Content:

MS-F4.1

• Calculate the future value (FV) or present value (PV) and the interest rate (r) of a compound interest investment using the formula \( FV=PV(1+r)^n \)
  • compare the growth of simple interest and compound interest investments numerically and graphically, linking graphs to linear and exponential modelling using technology
  • investigate the effect of varying the interest rate, the term or the compounding period on the future value of an investment, using technology
  • compare and contrast different investment strategies performing appropriate calculations when needed
• Solve practical problems involving compounding, for example determine the impact of inflation on prices and wages
• Work with shares and calculate the appreciated value of items, for example antiques
  • record and graph the price of a share over time
  • calculate the dividend paid on a portfolio of shares, and the dividend yield (excluding franked dividends)

MS-F4.2

• Calculate the depreciation of an asset using the declining-balance method using the formula \( S=V_0(1−r)^n \), where \( S \) is the salvage value of the asset after \( n \) periods, \( V_0 \) is the initial value of the asset, \( r \) is the depreciation rate per period, expressed as a decimal, and \( n \) is the number of periods, as an application of the compound interest formula
• Solve practical problems involving reducing balance loans, for example, determining the total loan amount and monthly repayments
• Recognise credit cards as an example of a reducing balance loan and solve practical problems relating to credit cards
  • identify the various fees and charges associated with credit card usage
  • compare credit card interest rates with interest rates for other loan types
  • interpret credit card statements, recognising the implications of only making the minimum payment
  • understand what is meant by an interest-free period
  • calculate the compounding interest charged on a retail purchase, transaction or the outstanding balance for a given number of days, using technology or otherwise