Grade 8
  1. Number Systems  1.1. Rational Numbers  1.2. Irrational Numbers  1.3. Real Numbers  1.4. Properties of Real Numbers  1.4.1. Commutative Property  1.4.2. Associative Property  1.4.3. Distributive Property  1.5. Representation on the Number Line  1.6. Operations on Real Numbers  1.6.1. Addition and Subtraction  1.6.2. Multiplication and Division  1.7. Rationalization  1.8. Exponents and Powers  1.9. Square Roots and Cube Roots
  2. Algebra  2.1. Algebraic Expressions  2.2. Identities and Simplification  2.2.1. Multiplying Binomials  2.2.2. Using Algebraic Identities  2.3. Factorization  2.3.1. Common Factors  2.3.2. Factorization by Grouping  2.3.3. Factorization of Trinomials  2.3.4. Special Products  2.4. Linear Equations in One Variable  2.4.1. Solving Linear Equations  2.4.2. Word Problems on Linear Equations
  3. Geometry  3.1. Understanding Quadrilaterals  3.1.1. Properties of Quadrilaterals  3.1.2. Types of Quadrilaterals  3.1.2.1. Parallelogram  3.1.2.2. Rectangle  3.1.2.3. Square  3.1.2.4. Rhombus  3.1.2.5. Trapezium  3.2. Constructions  3.2.1. Constructing Quadrilaterals  3.2.2. Constructing Bisectors  3.2.3. Constructing Angles  3.2.4. Constructing Triangles  3.3. Symmetry and Transformations  3.3.1. Reflection  3.3.2. Rotation  3.3.3. Translation  3.3.4. Symmetry in Patterns
  4. Mensuration  4.1. Area and Perimeter  4.1.1. Perimeter of Polygons  4.1.2. Area of Triangles  4.1.3. Area of Quadrilaterals  4.1.4. Area of Circles  4.2. Surface Area and Volume  4.2.1. Cubes  4.2.2. Cuboids  4.2.3. Cylinders  4.2.4. Cones  4.2.5. Spheres
  5. Data Handling  5.1. Organizing Data  5.2. Frequency Distribution Tables  5.3. Graphical Representation of Data  5.3.1. Bar Graphs  5.3.2. Histograms  5.3.3. Pie Charts  5.3.4. Line Graphs (added)  5.4. Probability  5.4.1. Introduction to Probability  5.4.2. Experimental Probability
  6. Coordinate Geometry  6.1. Cartesian Plane  6.2. Plotting Points  6.3. Coordinate System  6.4. Distance Between Points  6.5. Applications of Coordinate Geometry
  7. Introduction to Graphs  7.1. Linear Graphs  7.2. Applications of Graphs  7.3. Distance-Time Graphs  7.4. Speed-Time Graphs
  8. Comparing Quantities  8.1. Ratio and Proportion  8.2. Percentage  8.2.1. Increase and Decrease Percent  8.2.2. Discount in Percentage  8.2.3. Profit and Loss in Percentage  8.2.4. Simple Interest  8.2.5. Compound Interest
  9. Exponents and Powers  9.1. Laws of Exponents  9.2. Negative Exponents  9.3. Standard Form  9.4. Applications of Exponents
  10. Introduction to Squares and Square Roots  10.1. Properties of Square Numbers  10.2. Finding Square Roots  10.2.1. Prime Factorization Method  10.2.2. Division Method  10.3. Estimating Square Roots
  11. Introduction to Cubes and Cube Roots  11.1. Properties of Cube Numbers  11.2. Finding Cube Roots  11.2.1. Prime Factorization Method in Finding Cube Roots

Grade 8 → Comparing Quantities → Percentage ↓


Simple Interest


Simple interest is a concept used in finance and mathematics to calculate the interest earned or charged on a principal amount over time. It is called "simple" because it is simple to calculate and is not compounded, meaning it is based only on the principal amount. Let's understand this concept in depth.

What is simple interest?

Simple interest is calculated using a formula that relies on three major components:

  • Principal (P): It is the initial amount of money that is either invested or borrowed.
  • Rate of Interest (R): It is the percentage of the principal amount charged as interest for a specific period.
  • Time (T): It is the period for which money is borrowed or invested, usually expressed in years.

The formula for simple interest is given as:

Simple Interest (SI) = (P × R × T) / 100

This formula will help you figure out the additional money, called "interest," either earned on an investment or paid on a loan.

Analysis of the formula

Principal

The principal amount is the initial value, and it depends on whether you are dealing with a loan or an investment. For example, if you deposit $1000 in a bank account, $1000 will be your principal amount.

Interest rate

The interest rate is expressed as a percentage. If the interest rate is 5%, it means that 5% of the principal amount will be charged as interest for each time period (usually annually).

Time

Time is the period for which money is invested or borrowed. It is usually measured in years. If the time is given in months or days, you need to convert it to years.

Example calculation

Let's put this into practice with some examples:

Example 1: Calculation of simple interest

Suppose you deposit $2000 in a savings account with a 4% annual interest rate for a period of 3 years. How much interest will you earn?

Using the simple Interest Formula:

P = $2000, R = 4%, T = 3 years
SI = (2000 × 4 × 3) / 100
SI = 240

The interest earned would be $240.

Example 2: Using different time frames

If you borrow $1500 at an interest rate of 6% for 1 year and 6 months, how will you calculate the interest?

Convert 1 year and 6 months to years:

T = 1 + 6/12 = 1.5 years

Now use the formula:

P = $1500, R = 6%, T = 1.5 years
SI = (1500 × 6 × 1.5) / 100
SI = 135

The interest to be paid is $135.

Visual representation

year 1 Year 2 season 3 $20 $40 $60

This diagram shows the growth of simple interest over three years. Every year the same amount of interest is added to the principal.

Why use simple interest?

Simple interest is useful for quick calculations and is used when interest is not accrued on interest already earned. It is commonly used in short-term loans and to teach basic financial concepts.

Real life applications of simple interest

Understanding simple interest is important in many real-life scenarios. Here are some examples:

  • Car loans: Many car loans use simple interest to determine how much finance charge you'll pay.
  • Savings accounts: Some savings accounts may use simple interest to calculate interest earned, particularly if compound interest is not specified.
  • Short-term personal loans: Small personal loans of short duration often use simple interest calculations.

More examples

Example 3: Finding the principal

If the simple interest earned at 5% in 3 years is $450, what was the principal amount?

You can rearrange the simple interest formula to solve for the principal:

SI = (P × R × T) / 100
450 = (P × 5 × 3) / 100
P = (450 × 100) / (5 × 3)
P = $3000

The principal was $3000.

Example 4: Scheduling time

How long will it take for an investment of $1000 to earn $200 in simple interest at 4% per annum?

Rearrange the formula to solve for time:

SI = (P × R × T) / 100
200 = (1000 × 4 × T) / 100
T = (200 × 100) / (1000 × 4)
T = 5 years

It will take 5 years to earn $200.

Limitations of simple interest

While simple interest is easy to calculate, it does not take into account interest on interest earned, which is a limitation in scenarios where compound interest is used. For long-term financial products such as retirement accounts or long-term loans, compound interest provides a more accurate picture of financial income or fees over time.

Key takeaways

  • Calculation of simple interest is simple and easy.
  • It is useful for teaching short term loans and basic financial concepts.
  • It depends on the principal amount, interest rate and time period.
  • This does not take into account the compounding effect of interest.

Understanding simple interest is a fundamental step to understanding more complex financial concepts such as compound interest and other investment instruments.


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Simple Interest

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