Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Ratio and Proportion → Percentages ↓


Simple Interest Calculations in Percentages in Ratio and Proportion


Simple interest is a way to calculate how much interest you will earn or how much you will have to pay back on an amount of money over a certain period of time. This concept is important for students learning about financial math and ratios and proportions. This guide will show you the basics of simple interest calculations, explaining how percentages, ratios, and proportions work together in solving problems like this.

Understanding simple interest

Simple interest is calculated using the following formula:

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

Here, principal (P) is the initial amount, rate (R) is the interest rate per period as a percentage, and time (T) is the period for which the principal is borrowed or invested.

Explanation of key terms

  • Principal: The initial amount borrowed or invested.
  • Rate: The percentage of the principal charged as interest each period.
  • Time: The period for which money is borrowed or invested, usually in years.
  • Simple Interest: The amount earned or paid as interest on the principal over a period of time.

Visual example of simple interest

Let's consider an example to explain simple interest. Suppose you borrow $1,000 at an interest rate of 5% per annum for 3 years. Here's how you can calculate simple interest:

Step-by-step calculation:

P = $1,000 (Principal) R = 5% per year T = 3 years

Plugging these values into the formula gives:

SI = P × R × T SI = 1000 × (5/100) × 3 SI = $150

Therefore, the simple interest for three years is $150.

    
        
        principal
        
        Interest 1
        
        Interest 2
        
        Interest 3

In this visual example, the light blue rectangle represents the principal. Each rectangle after that represents the interest for each year.

Working with percentages

In simple interest problems, the interest rate is given as a percentage. A percentage is a way of expressing a number as a fraction of 100. So, when we talk about an interest rate of 5%, we mean 5 out of 100, or 0.05 in decimal form.

Rate of 5% = 5/100 = 0.05

To calculate interest, convert the percentage to a decimal and then multiply it by the principal and time.

Understanding ratio and proportion

A ratio is a way to compare two quantities. For example, if you have 3 apples and 6 oranges, the ratio of apples to oranges is 3 to 6, which can be simplified to 1 to 2.

A ratio is an equation that states that two ratios are equal. For example, if there is a ratio that 1/2 = 3/6, then this ratio is true because both fractions simplify to the same value.

Ratio and proportion in simple interest

Ratios and proportions can help in understanding the relationship between principal, interest, rate and time. If two loans have equal interest charged over time, then the ratio of their interest will be equal to the ratio of their principals, provided the rate and time are constant.

Practical examples with ratios

Imagine you have two sums of money: $500 and $1000, both invested at an interest rate of 10% for a period of 2 years.

Interest for $500 = 500 × (10/100) × 2 = $100 Interest for $1000 = 1000 × (10/100) × 2 = $200

Let us calculate the ratio of their interests:

Ratio of Interests = $100 : $200 = 1 : 2

The ratio of the principal amount is also:

Ratio of Principals = $500 : $1000 = 1 : 2

Therefore, the ratio of interest is equal to the ratio of principal, which shows direct proportion.

Example problem with solution

Now, let's solve another example using the calculation of simple interest as a percentage, and relate it to ratio and proportion:

Problem: John and Mary both save money in their bank accounts at the same interest rate of 6% per year. If John saves $1,200 for 3 years, and Mary saves $1,500 for the same period, who earns more interest, and by how much?

Solution:

Calculate John's interest:

John's Interest = $1,200 × (6/100) × 3 = $216

Calculate Mary's interest:

Mary's Interest = $1,500 × (6/100) × 3 = $270

Who earns more interest?

Mary earns more interest than John. Now calculate how much more interest she will earn:

Difference = $270 - $216 = $54

Therefore, Mary earns $54 more interest than John.

Interactive exercises

Let's ask some simple questions to practice what we've learned:

  1. If you invest $800 at 4% for 5 years, what will be the simple interest?
  2. Calculate the simple interest for $2,000 at 7% for 2 years.
  3. If A invests $600 and B $900, then what will be the ratio of the simple interest earned by the two at 5% rate for 4 years?

Please give your answers in the comments.

Conclusion

The concept of simple interest is fundamental and connects well with percentages, ratios, and proportions. Understanding each part can help you not only solve problems on paper, but also apply these concepts to real-world financial situations, whether you're saving or borrowing money. Through practice and examples, you become comfortable with these calculations and concepts, preparing you for more advanced math in the future.


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