Topics
Rational Numbers
- Rational Numbers
- Closure Property of Rational Numbers
- Commutative Property of Rational Numbers
- Associative Property of Rational Numbers
- Distributive Property of Multiplication Over Addition for Rational Numbers
- Identity of Addition and Multiplication of Rational Numbers
- Negative Or Additive Inverse of Rational Numbers
- Concept of Reciprocal or Multiplicative Inverse
- Rational Numbers on a Number Line
- Rational Numbers Between Two Rational Numbers
Linear Equations in One Variable
- Variable of Equation
- Concept of Equation
- Expressions with Variables
- Balancing an Equation
- The Solution of an Equation
- Linear Equation in One Variable
- Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Some Applications Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Solving Equations Having the Variable on Both Sides
- Some More Applications on the Basis of Solving Equations Having the Variable on Both Sides
- Reducing Equations to Simpler Form
- Equations Reducible to the Linear Form
Understanding Quadrilaterals
- Concept of Curves
- Different Types of Curves - Closed Curve, Open Curve, Simple Curve.
- Concept of Polygons
- Classification of Polygons
- Properties of a Quadrilateral
- Interior Angles of a Polygon
- Exterior Angles of a Polygon and Its Property
- Concept of Quadrilaterals
- Properties of Trapezium
- Properties of Kite
- Properties of a Parallelogram
- Properties of Rhombus
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Property: The adjacent angles in a parallelogram are supplementary.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Property: The diagonals of a rhombus are perpendicular bisectors of one another.
- Property: The Diagonals of a Rectangle Are of Equal Length.
- Properties of Rectangle
- Properties of a Square
- Property: The diagonals of a square are perpendicular bisectors of each other.
Practical Geometry
- Introduction to Geometric Tool
- Constructing a Quadrilateral When the Lengths of Four Sides and a Diagonal Are Given
- Constructing a Quadrilateral When Two Diagonals and Three Sides Are Given
- Constructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known
- Constructing a Quadrilateral When Three Sides and Two Included Angles Are Given
- Some Special Cases
Data Handling
- Concept of Data Handling
- Interpretation of a Pictograph
- Interpretation of Bar Graphs
- Drawing a Bar Graph
- Interpretation of a Double Bar Graph
- Drawing a Double Bar Graph
- Organisation of Data
- Frequency Distribution Table
- Graphical Representation of Data as Histograms
- Concept of Pie Graph (Or a Circle-graph)
- Interpretation of Pie Diagram
- Chance and Probability - Chance
- Basic Ideas of Probability
Squares and Square Roots
- Concept of Square Number
- Properties of Square Numbers
- Some More Interesting Patterns of Square Number
- Finding the Square of a Number
- Concept of Square Roots
- Finding Square Root Through Repeated Subtraction
- Finding Square Root Through Prime Factorisation
- Finding Square Root by Division Method
- Square Root of Decimal Numbers
- Estimating Square Root
Cubes and Cube Roots
Comparing Quantities
- Concept of Ratio
- Basic Concept of Percentage
- Increase Or Decrease as Percent
- Concept of Discount
- Estimation in Percentages
- Basic Concepts of Profit and Loss
- Sales Tax, Value Added Tax, and Good and Services Tax
- Calculation of Interest
- Concept of Compound Interest
- Deducing a Formula for Compound Interest
- Rate Compounded Annually Or Half Yearly (Semi Annually)
- Applications of Compound Interest Formula
Algebraic Expressions and Identities
- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Types of Algebraic Expressions as Monomials, Binomials, Trinomials, and Polynomials
- Like and Unlike Terms
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Binomial
- Multiplying a Monomial by a Trinomial
- Multiplying a Binomial by a Binomial
- Multiplying a Binomial by a Trinomial
- Concept of Identity
- Expansion of (a + b)2 = a2 + 2ab + b2
- Expansion of (a - b)2 = a2 - 2ab + b2
- Expansion of (a + b)(a - b) = a2-b2
- Expansion of (x + a)(x + b)
Mensuration
Visualizing Solid Shapes
Exponents and Powers
Direct and Inverse Proportions
Factorization
- Factors and Multiples
- Factorising Algebraic Expressions
- Factorisation by Taking Out Common Factors
- Factorisation by Regrouping Terms
- Factorisation Using Identities
- Factors of the Form (x + a)(x + b)
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial
- Dividing a Polynomial by a Polynomial
- Concept of Find the Error
Introduction to Graphs
- Concept of Bar Graph
- Interpretation of Bar Graphs
- Drawing a Bar Graph
- Concept of Double Bar Graph
- Interpretation of a Double Bar Graph
- Drawing a Double Bar Graph
- Concept of Pie Graph (Or a Circle-graph)
- Graphical Representation of Data as Histograms
- Concept of a Line Graph
- Linear Graphs
- Some Application of Linear Graphs
Playing with Numbers
Definition
- Conversion Period: Time period and rate when interest not compounded annually The time period after which the interest is added each time to form a new principal is called the conversion period.
Notes
Rate Compounded Annually Or Half Yearly (Semi-Annually):
Time period and rate when interest not compounded annually The time period after which the interest is added each time to form a new principal is called the conversion period.
i) When compound interest is compounded annually,
Amount when interest is compounded annually = `"P"( 1 + "R"/100)^n`;
P is principal, R is rate of interest, n is time period
P = Rs. 100 at 10% per annum compounded annually
The time period taken is 1 year
I = ₹ `(100 xx 10 xx 1)/100` = Rs. 10
A = Rs. 100 + Rs. 10
A = Rs. 110.
ii) When compound interest is compounded Semi-annually,
When the interest is compounded half-yearly, there are two conversion periods in a year each after 6 months. In such situations, the half-yearly rate will be half of the annual rate.
Amount when interest is compounded half-yearly
= `"P"( 1 + "R"/200)^(2n) .......{"R"/2 "is half-yearly rate and"
, 2n = "number of half-years"`
iii) When compound interest is compounded quarterly,
In this case, there are 4 conversion periods in a year and the quarterly rate will be one-fourth of the annual rate.
Amount when interest is compounded quarterly,
= `"P"(1 + "R"/400)^(4n) ........{ "R"/4 "is half-yearly rate and, 4n = number of half-years"’`
Example
Find CI paid when a sum of Rs. 10,000 is invested for 1 year and 3 months at `8 1/2%` per annum compounded annually.
1 year 3 months = `1 3/12 "year" = 1 1/4 "years"`
A = ₹ `10000(1 + 17/200)^(1 1/4)`
Find the amount for the whole part, i.e., 1 year in this case.
A = ₹ `10000(1 + 17/200)`
A = ₹ `10000 xx 217/200 ` = ₹ 10,850
Now this would act as principal for the next `1/4` year.
SI = ₹ `(10850 xx 1/4 xx 17)/(100 xx 2)`
SI = ₹ `(10850 xx 1 xx 17)/(800)` = Rs. 230.56
Interest for first year = ₹ 10850 - ₹ 10000 = ₹ 850
And, interest for the next `1/4` year = ₹ 230.56
Therefore, total compound Interest = 850 + 230.56 = ₹ 1080.56.
If you would like to contribute notes or other learning material, please submit them using the button below.
Shaalaa.com | What is Conversion Period in Compound Interest?
to track your progress
Series: Rate Compounded Annually Or Half Yearly (Semi Annually)
0%
What is Conversion Period in Compound Interest?
00:12:26 undefined
00:12:26 undefined
Formula of Compound Interest & Total Amount when the Interest is Compounded Annually
00:13:33 undefined
00:13:33 undefined
Formula of Compound Interest & Total Amount when the Interest is Calculated Semi-annually
00:17:24 undefined
00:17:24 undefined
Formula of Compound Interest & Total Amount when the Interested is Calculated Quarterly
00:17:50 undefined
00:17:50 undefined
Problems on Compound Interest - Part 1
00:08:26 undefined
00:08:26 undefined
