Podcast
Questions and Answers
In finance, ______ is calculated on the original principal only.
In finance, ______ is calculated on the original principal only.
Simple Interest
The ______ is used to express a relationship between two quantities.
The ______ is used to express a relationship between two quantities.
Ratio
When interest is calculated on the accumulated amount, it is referred to as ______ interest.
When interest is calculated on the accumulated amount, it is referred to as ______ interest.
Compound
A ______ factor is a multiplier that relates measurements on a drawing to actual measurements.
A ______ factor is a multiplier that relates measurements on a drawing to actual measurements.
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A ______ is a way of expressing a number as a fraction of 100.
A ______ is a way of expressing a number as a fraction of 100.
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In finance, the formula for ______ is used to calculate the total interest earned over time.
In finance, the formula for ______ is used to calculate the total interest earned over time.
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A ______ can help compare two quantities, such as distance to time.
A ______ can help compare two quantities, such as distance to time.
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To find the total amount after interest is applied, you would add ______ to the principal amount.
To find the total amount after interest is applied, you would add ______ to the principal amount.
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A scale factor of 2 means that the drawing is ______ times larger than the actual size.
A scale factor of 2 means that the drawing is ______ times larger than the actual size.
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Expressing a part of the whole in terms of ______ allows for easy comparison with other quantities.
Expressing a part of the whole in terms of ______ allows for easy comparison with other quantities.
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Study Notes
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.
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Description
This quiz covers key concepts in the Western Australian Year 9 curriculum related to financial literacy. Students will explore simple interest, compound interest, ratios and rates, percentages, and scale factors. It's designed to help reinforce understanding of these essential mathematical principles.
