Year 9 Mathematics: Financial Literacy

Simple Interest

• Simple interest calculated using the formula: I = PRT, where I is interest, P is the principal amount, R is the rate of interest per year, and T is the time in years.
• Interest is a fixed percentage of the principal, making it straightforward to calculate over time.

Compound Interest

• Compound interest calculated using the formula: A = P (1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
• Interest is earned on both the initial principal and the accumulated interest from previous periods, leading to exponential growth over time.

Ratios and Rates

• Ratios represent a relationship between two quantities, showing how many times one value contains or is contained within another (e.g., 3:2).
• Rates express a ratio that compares two different units, such as speed (distance/time) or density (mass/volume), facilitating comparisons and calculations.

Percentage

• Percentage is a way to express a number as a fraction of 100, utilizing the symbol %.
• Commonly used to calculate discounts, tax, and interest rates, allowing for easier interpretation of changes in value concerning the whole.

Scale Factor

• Scale factor defines the ratio of the dimensions of a scaled object to the original object, critical in geometry for enlarging or reducing figures.
• To find the new dimensions, multiply each dimension of the original object by the scale factor, which is a positive number typically greater than or less than one.

Simple Interest

• Simple interest is calculated using the formula: ( I = P \times r \times t ), where ( I ) = interest, ( P ) = principal amount, ( r ) = rate of interest per period, and ( t ) = time the money is invested or borrowed.
• Interest remains constant over the period, making it easy to calculate for short-term investments or loans.

Compound Interest

• Compound interest is calculated on the initial principal, which also includes all accumulated interest from previous periods.
• The formula used is: ( A = P(1 + r)^n ), where ( A ) = the amount of money accumulated after n periods, ( P ) = principal amount, ( r ) = annual interest rate, and ( n ) = number of compounding periods.
• Compound interest grows faster than simple interest due to the reinvestment of earned interest.

Ratios and Rates

• A ratio is a comparison of two quantities, expressed as a fraction, proportion, or with a colon (e.g., 3:2).
• Rates are a specific kind of ratio that compares two quantities of different units, such as speed (e.g., kilometers per hour).
• Understanding ratios and rates is essential in solving real-world problems involving proportions, such as recipes or budgets.

Percentage

• Percentage represents a fraction out of 100, commonly used to express how much one quantity is of another.
• The formula to calculate percentage is: ( \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 ).
• Percentages are widely used in financial calculations, statistics, and to compare quantities effectively.

Scale Factor

• Scale factor is a number that scales or multiplies a certain dimension or quantity in a proportional manner.
• Applied in concepts such as maps, models, and similar figures, it determines how much larger or smaller a figure is compared to the original.
• The scale factor is crucial for resizing objects accurately in mathematics and geometry.