Advanced Financial Mathematics – Modelling financial situations

This lesson comprises two (2) master classes focusing on:

• Financial decisions involving a home loan, a savings account, a car loan or superannuation
• Simple and compound interest
• Appreciation and depreciation of assets

Content:

MA-M1.1

• Solve compound interest problems involving financial decisions, including a home loan, a savings account, a car loan or superannuation
  • identify an annuity (present or future value) as an investment account with regular, equal contributions and interest compounding at the end of each period, or a single-sum investment from which regular, equal withdrawals are made
  • use technology to model an annuity as a recurrence relation and investigate (numerically or graphically) the effect of varying the interest rate or the amount and frequency of each contribution or a withdrawal on the duration and/or future or present value of the annuity
  • use a table of interest factors to perform annuity calculations, eg calculating the present or future value of an annuity, the contribution amount required to achieve a given future value or the single sum that would produce the same future value as a given annuity

MA-M1.4

• Use geometric sequences to model and analyse practical problems involving exponential growth and decay
  • calculate the effective annual rate of interest and use results to compare investment returns and cost of loans when interest is paid or charged daily, monthly, quarterly or six-monthly
  • solve problems involving compound interest loans or investments, eg determining the future value of an investment or loan, the number of compounding periods for an investment to exceed a given value and/or the interest rate needed for an investment to exceed a given value
  • recognise a reducing balance loan as a compound interest loan with periodic repayments, and solve problems including the amount owing on a reducing balance loan after each payment is made
• Solve problems involving financial decisions, including a home loan, a savings account, a car loan or superannuation
  • calculate the future value or present value of an annuity by developing an expression for the sum of the calculated compounded values of each contribution and using the formula for the sum of the first n terms of a geometric sequence
  • verify entries in tables of future values or annuities by using geometric series