FINANCIAL MATHEMATICS
Use simple and compound decay formulae to solve problems (including straight line depreciation and depreciation on a reducing balance) (link to Learning Outcome 2).
Demonstrate an understanding of different periods of compounding growth and decay (including effective compounding growth and decay and including effective and nominal interest rates).
Clarification
- Understand the difference between nominal and effective interest rates and convert fluently between them for the following compounding periods:
· Monthly
· Quarterly
· Half-Yearly or semi-annually
NOTE:
Daily (365 days in a year) and biannually (every two years) could be tested in assignments or tutorials.
- If patterns and functions are linked, then simple interest can be seen as a straight line function and compound interest as an exponential function.
(a) Calculate the value of n in the formula A = P(1 ± i)^{n}
(b) Apply knowledge of geometric series to solving annuity, bond and sinking fund problems, with or without the use of the formulae:
Critically analyse investment and loan options and make informed decisions as to the best option(s) (including pyramid and micro-lenders’ schemes).
Solve non-routine, unseen problems.
Clarification
- Candidates are expected to calculate any of the following
· A
· P
· i (but not in the F_{v} and P_{v} formulae)
· n (by using logarithms)
· x
· F_{v}
· P_{v}
- Timelines are a useful strategy to solve problems in Financial Mathematics.
- Pyramid and micro-lenders’ schemes will not be examined in the examination but can be assessed by means of Grade 12 school-based assessment tasks.
Solve non-routine, unseen problems.
Clarification
- Questions of this nature are not specifically taught in class and do not have a direct route to the solution. Learners are required to use their knowledge of Mathematics in a creative way to solve problems of this nature.
- Learners should, however, be exposed to these types of problems in the teaching process so that they develop problem-solving strategies.