selects appropriate notations and conventions to communicate mathematical ideas and solutions
interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems
solves financial problems involving compound interest
Related Life Skills outcomes: MALS-12NA, MALS-13NA, MALS-14NA, MALS-15NA, MALS-16NA, MALS-17NA
- Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (ACMNA229)
establish and use the formula to find compound interest:
\( A = P \left( 1+R \right) ^n \) where \(A\) is the total amount, \(P\) is the principal, \(R\) is the interest rate per compounding period as a decimal, and \(n\) is the number of compounding periods
- calculate and compare investments for different compounding periods, eg calculate and compare the value of an investment of $3000 at an interest rate of 6% per annum after 5 years when the interest is compounded annually, as opposed to the interest being compounded monthly (Problem Solving)
- use a spreadsheet to graph the value of an investment of a particular amount at various compound interest rates over time (Problem Solving)
- solve problems involving compound interest
- calculate the principal or interest rate needed to obtain a particular total amount for a compound interest investment (Problem Solving)
- use a 'guess and refine' strategy to determine the number of time periods required to obtain a particular total amount for a compound interest investment (Problem Solving)
- compare the total amounts obtained for a particular investment when the interest is calculated as compound interest and as simple interest, eg compare the total amount obtained when $10,000 is invested at an interest rate of 6% per annum compounded monthly for 5 years, with the total amount obtained when the interest is calculated as simple interest (Problem Solving)
- use the compound interest formula to calculate depreciation
Internet sites may be used to find commercial rates for home loans and to provide 'home-loan calculators'.
National Numeracy Learning Progression links to this Mathematics outcome
When working towards the outcome MA5.2-4NA the sub-elements (and levels) of Operating with percentages (OwP6) and Number patterns and algebraic thinking (NPA7-NPA8) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.
The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.