What is the ci on rs 6400 for 2 years compounded annually at 7½% pa

Question 36 Compound Interest Exercise 14.2

Next

Answer:

Given,

Time = 2 years

Rate = 7.5 % per annum

Let principal = Rs P

Compound Interest (CI) – Simple Interest (SI) = Rs 360

C.I – S.I = Rs 360

By using the formula,

P [(1 + R/100)^n - 1] – (PTR)/100 = 360

P [(1 + 7.5/100)^2 - 1] – (P(2)(7.5))/100 = 360

P[249/1600] – (3P)/20 = 360

249/1600P – 3/20P = 360

(249P-240P)/1600 = 360

9P = 360 × 1600

P = 576000/9

= 64000

∴ The sum is Rs 64000

Video transcript

hello everybody welcome to leader learning my name is rajna chaudhary and we have to write this statement in the equation form it is written that write equation for the statements for these statements so statement is one fourth of a number x minus g minus four gives four so one fourth of a number x would be one fourth of x that mean the value of this part is 1 by 4 of x then we have to minus 4 from it so let's minus 4 from it so minus 4 and gives gives means is equal to 4 so this is the equation for the statement we can write it like that at the place of off we can write multiply then minus 4 is equal to 4. we can also write it like x upon 4 minus 4 is equal to 4. so this is the form of equation for the statement i hope you understand the method see you in my next video don't forget to like comment and subscribe leader learning channel thank you for watching

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1. Find the amount of $ 8000 for 3 years, compounded annually at 5% per annum. Also, find the compound interest.

Solution: Here, P = $ 8000, R = 5 % per annum and n = 3 years. Using the formula A = $ P(1 + R/ 100)ⁿ amount after 3 years = $ {8000 × (1 + 5/100)³} = $ (8000 × 21/20 × 21/20 × 21/20) = $ 9261. Thus, amount after 3 years = $ 9261. And, compound interest = $ (9261 - 8000)

Therefore, compound interest = $ 1261.

2. Find the compound interest on $ 6400 for 2 years, compounded annually at 7¹/₂ % per annum.

Solution: Here, P = $ 6400, R % p. a. and n = 2 years. Using the formula A = P (1 + R/100)ⁿ Amount after 2 years = [6400 × {1 + 15/(2 × 100)}²] = $ (6400 × 43/40 × 43/40) =$ 7396. Thus, amount = $ 7396 and compound interest = $ (7396 - 6400)

Therefore, compound interest = $ 996.

Case 2: Let principal = $ P, time = 2 years, and let the rates of interest be p % p.a. during the first year and q % p.a. during the second year.

1. Find the amount of $ 12000 after 2 years, compounded annually; the rate of interest being 5 % p.a. during the first year and 6 % p.a. during the second year. Also, find the compound interest.

Solution: Here, P = $12000, p = 5 % p.a. and q = 6 % p.a. Using the formula A = {P × (1 + P/100) × (1 + q/100)} amount after 2 years = $ {12000 × (1 + 5/100) × (1 + 6/100)} = $ (12000 × 21/20 × 53/50) =$ 13356 Thus, amount after 2 years = $ 13356 And, compound interest = $ (13356 – 12000)

Therefore, compound interest = $ 1356.

Case 3: For example suppose time is 2³/₅ years then,

1. Find the compound interest on $ 31250 at 8 % per annum for 2 years. Solution Amount after 2³/₄ years

Solution: Amount after 2³/₄ years = $ [31250 × (1 + 8/100)² × (1 + (3/4 × 8)/100)] = ${31250 × (27/25)² × (53/50)} = $ (31250 × 27/25 × 27/25 × 53/50) = $ 38637. Therefore, Amount = $ 38637, Hence, compound interest = $ (38637 - 31250) = $ 7387.

Let principal = $ P, rate = R% per annum, time = a years.

Then,

rate = (R/2) % per half-year, time = (2n) half-years, and amount = P × (1 + R/(2 × 100))²ⁿ

Compound interest = (amount) - (principal).

1. Find the compound interest on $ 15625 for 1¹/₂ years at 8 % per annum when compounded half-yearly.

Solution: Here, principal = $ 15625, rate = 8 % per annum = 4% per half-year, time = 1¹/₂ years = 3 half-years. Amount = $ [15625 × (1 + 4/100)³] =$ (15625 × 26/25 × 26/25 × 26/25)= $ 17576. Compound interest = $ (17576 - 15625) = $ 1951.

2. Find the compound interest on $ 160000 for 2 years at 10% per annum when compounded semi-annually.

Solution: Here, principal = $ 160000, rate = 10 % per annum = 5% per half-year, time = 2 years = 4 half-years. Amount = $ {160000 × (1 + 5/100)⁴} =$ (160000 × 21/20 × 21/20 × 21/20 × 21/20) compound interest = $ (194481- 160000) = $ 34481.

Compound Interest by Using Formula, when it is calculated Quarterly

Interest Compounded Quarterly

Then,

rate = (R/4) % Per quarter, time = (4n) quarters, and amount = P × (1 + R/(4 × 100))⁴ⁿ

Compound interest = (amount) - (principal).

Page 2

In 8th grade math practice you will get all types of examples on different topics along with the solutions. 8th grade math worksheets are arranged in such a way that students can learn math while practicing it step by step.

Keeping in mind the mental level of child in 8th grade, every efforts has been made to introduce new concepts in a simple language, so that the child understands them easily. The difficulty level of the problems has been reduced and mathematical concepts have been explained in the simplest possible way. Each topic contains a large number of examples to understand the applications of concepts.

In 8th grade math test we need to learn Rational Numbers, Exponents, Square and Square Roots, Cubes and Cube roots, Operations on Algebraic Expressions, Factorization, Linear Equations, Profit and Loss, Compound Interest, Ratio and Proportion, Time and Work and in geometry we learn Quadrilaterals, Parallelograms, Construction of Quadrilaterals, Three-Dimensional Figures, Area of a Trapezium and a Polygon, Volume and Surface Area of Solids, Data Handling, Constructing and Interpreting Bar Graphs, Pie Charts, Probability, Graphs, etc……

If student follow math-only-math they can improve their knowledge by practicing the worksheets for 8th graders which will them to score in their exam.

● Set Theory

Sets Theory: Brief description on set theory and the important sets used in mathematics.

Representation of a Set: Definition with examples of statement form, roster form or tabular form, set builder form cardinal number of a set and the standard sets of numbers.

Types of Sets: Definition with examples of empty set or null set, singleton set, finite set, infinite set, cardinal number of a set, equivalent set and equal sets.

Finite Sets and Infinite Sets: Learn how to distinguish between finite set and infinite set with examples.

Power Set: Explanation on power sets will help us to get the basic concepts if sets with examples.

Problems on Union of Sets: Learn how to find the union of two or more sets and worked-out examples of operations on union of sets.

Problems on Intersection of Sets: Learn how to find the intersection of two or more sets and worked-out examples of operations on intersection of sets.

Difference of two Sets: Learn how to find the difference between the two sets and worked-out examples.

Complement of a Set: Definition of complement of a set and their properties with some worked-out examples.

Problems on Complement of a Set: Learn how to find the complement of two or more sets and worked-out examples of operations on complement of sets.

Problems on Operation on Sets: Learn how to find the union and intersection of two or more sets and worked-out examples of the two basic operations of sets.

Word Problems on Sets: Apply set operations to solve word problems involving the properties of union and intersection of sets.

Venn Diagrams in Different Situations: Learn how to use the Venn diagrams in different situations to find the different sets.

Relationship in Sets using Venn Diagram: Learn how to find the relationship of the union, intersection and difference of the two sets using Venn-diagram.

Union of Sets using Venn Diagram: Diagrammatic representation to find the union of two sets and their properties, worked-out examples.

Intersection of Sets using Venn Diagram: Diagrammatic representation to find the intersection of two sets and their properties, worked-out examples.

Disjoint of Sets using Venn Diagram: Learn how to represent the disjoint sets of union and intersection using Venn-Diagram.

Difference of Sets using Venn Diagram: Learn how to represent the difference between two sets using Venn-Diagram.

Examples on Venn Diagram: Learn how to use the basic concepts of sets for solving the different types of problems on Venn diagram.

● Relations and Mapping

Ordered Pair

Cartesian Product of Two Sets

Relation

Domain and Range of a Relation

Practice Test on Math Relation

Functions or Mapping

Domain Co-domain and Range of Function

Math Practice Test on Function

● Relations and Mapping - Worksheets

Worksheet on Math Relation

Worksheet on Functions or Mapping

● Cube and Cube Roots

Cube

To Find if the Given Number is a Perfect Cube

Cube Root

Method for Finding the Cube of a Two-Digit Number

Table of Cube Roots

● Cube and Cube Roots - Worksheets

Worksheet on Cube

Worksheet on Cube and Cube Root

Worksheet on Cube Root

● Rational Numbers

Introduction of Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Rational Numbers in Descending Order

Representation of Rational Numbers on the Number Line

Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Addition of Rational Numbers

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Same Denominator

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Rational Expressions Involving Addition and Subtraction

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Product of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational  Number

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

To Find Rational Numbers

● Rational Numbers - Worksheets

Worksheet on Rational Numbers

Worksheet on Equivalent Rational Numbers

Worksheet on Lowest form of a Rational Number

Worksheet on Standard form of a Rational Number

Worksheet on Equality of Rational Numbers

Worksheet on Comparison of Rational Numbers

Worksheet on Representation of Rational Number on a Number Line

Worksheet on Adding Rational Numbers

Worksheet on Properties of Addition of Rational Numbers

Worksheet on Subtracting Rational Numbers

Worksheet on Addition and Subtraction of Rational Number

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Properties of Multiplication of Rational Numbers

Worksheet on Division of Rational Numbers

Worksheet on Properties of Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

Worksheet on Operations on Rational Expressions

Objective Questions on Rational Numbers

● Ratio and Proportion

What is Ratio and Proportion?

Practice Test on Ratio and Proportion

Worked out Problems on Ratio and Proportion

● Ratio and Proportion - Worksheets

Worksheet on Ratio and Proportion

● Significant Figures

Significant Figures

● Significant Figures - Worksheets

Worksheet on Significant Figures

● Fun with Numbers

Playing with Numbers

Test of Divisibility

Number Puzzles and Games

● Fun with Numbers - Worksheets

Worksheet on Number Puzzles and Games

● Exponents

Exponents

Laws of Exponents

Rational Exponent

Integral Exponents of a Rational Numbers

Solved Examples on Exponents

Practice Test on Exponents

● Exponents - Worksheets

Worksheet on Exponents

● Square

Square

Perfect Square or Square Number

Properties of Perfect Squares

● Square - Worksheets

Worksheet on Squares

● Square Root

Square Root

Square Root of a Perfect Square by using the Prime Factorization Method

Square Root of a Perfect Square by Using the Long Division Method

Square Root of Numbers in the Decimal Form

Square Root of Number in the Fraction Form

Square Root of Numbers that are Not Perfect Squares

Table of Square Roots

Practice Test on Square and Square Roots

● Square Root- Worksheets

Worksheet on Square Root using Prime Factorization Method

Worksheet on Square Root using Long Division Method

Worksheet on Square Root of Numbers in Decimal and Fraction Form

● Algebraic Expression

Algebraic Expression

Addition of Algebraic Expressions

Subtraction of Algebraic Expressions

Multiplication of Algebraic Expression

Division of Algebraic Expressions

● Formula

Formula and Framing the Formula

Change the Subject of a Formula

Changing the Subject in an Equation or Formula

Practice Test on Framing the Formula

● Formula - Worksheets

Worksheet on Framing the Formula

Worksheet on Changing the Subject of a Formula

Worksheet on Changing the Subject in an Equation or Formula

● Factorization

Factorization

Factors of Algebraic Expressions

Monomial is a Common Factor

Factorization when Monomial is Common

Binomial is a Common Factor

Factorization when Binomial is Common

Factorization by Grouping

Factorize by Grouping The Terms

Factoring Terms by Grouping

Factorization by Regrouping

Factorize by Regrouping The Terms

Factoring Terms by Regrouping

Factorization by Using Identities

Factorization of Perfect Square

Factorization of Perfect Square Trinomials

Difference of Two Squares

Factoring Differences of Squares

Factorize the Difference of Two Squares

Evaluate the Difference of Two Squares

Factorize the Trinomial x^2 + px + q

Factorize the Trinomial ax^2 + bx + c

Factorization of Quadratic Trinomials

● Factorization - Worksheet

Worksheet on Factoring Algebraic Expression

Worksheet on Factoring Binomials

Worksheet on Factoring by Grouping

Worksheet on Factorization by Regrouping

Worksheet on Factoring out a Common Binomial Factor

Worksheet on Factoring Identities

Worksheet on Factoring the Differences of Two Squares

Worksheet on Factorization using Formula

Worksheet on Factoring Trinomials

Worksheet on Factoring Simple Quadratics

Worksheet on Factoring Quadratic Trinomials

Worksheet on Factoring Trinomials by Substitution

Worksheet on Factorization

● Simplification  of Algebraic Fractions

Algebraic Fractions

Arithmetic Fraction and Algebraic Fraction

Highest Common Factor of Monomials

Highest Common Factor of Monomials by Factorization

Lowest Common Multiple of Monomials

Lowest Common Multiple of Monomials by Factorization

Highest Common Factor of Polynomials

Lowest Common Multiple of Polynomials

H.C.F. of Polynomials by Factorization

Highest Common Factor of Polynomials by Factorization

L.C.M. of Polynomials by Factorization

Lowest common multiple of Polynomials by Factorization

H.C.F. of Polynomials by Division Method

H.C.F. of Polynomials by Long Division Method

Relation Between H.C.F. and L.C.M. of Two Polynomials

Reduce Algebraic Fractions to its Lowest Term

Simplification of Algebraic Fractions

Rule of Separation of Division

Sum and Difference of Algebraic Fractions

Problems on Algebraic Fractions

Solving Algebraic Fractions

Multiplication of Algebraic Fractions

Division of Algebraic Fractions

● Simplification  of Algebraic Fractions - Worksheets

Worksheet on H.C.F. of Monomials

Worksheet on L.C.M. of Monomials

Worksheet on H.C.F. and L.C.M. of Monomials

Worksheet on H.C.F. of Polynomials

Worksheet on L.C.M. of Polynomials

Worksheet on H.C.F. and L.C.M. of Polynomials

Worksheet on Reducing Algebraic Fractions

Worksheet on Algebraic Expressions to the Lowest Terms

Worksheet on Algebraic Fractions

Worksheet on Simplifying Algebraic Fractions

● Equations

What is an Equation?

What is a Linear Equation?

How to Solve Linear Equations?

Solving Linear Equations

Problems on Linear Equations in One Variable

Word Problems on Linear Equations in One Variable

Practice Test on Linear Equations

Practice Test on Word Problems on Linear Equations

● Equations - Worksheets

Worksheet on Linear Equations

Worksheet on Word Problems on Linear Equation

● Simultaneous Linear Equations

Simultaneous Linear Equations

Comparison Method

Elimination Method

Substitution Method

Cross-Multiplication Method

Solvability of Linear Simultaneous Equations

Pairs of Equations

Word Problems on Simultaneous Linear Equations

Word Problems on Simultaneous Linear Equations

Practice Test on Word Problems Involving Simultaneous Linear Equations

● Simultaneous Linear Equations - Worksheets

Worksheet on Simultaneous Linear Equations

Worksheet on Problems on Simultaneous Linear Equations

● Linear Inequations

What are Linear Inequality?

What are Linear Inequations?

Properties of Inequation or Inequalities

Representation of the Solution Set of an Inequation

Practice Test on Linear Inequation

● Linear Inequations - Worksheets

Worksheet on Linear Inequations

● Quadratic Equations

Quadratic Equations

● Quadratic Equations - Worksheets

Worksheet on Quadratic Equations

● Percentage

Fraction into Percentage

Percentage into Fraction

Percentage into Ratio

Ratio into Percentage

Percentage into Decimal

Decimal into Percentage

Percentage of the given Quantity

How much Percentage One Quantity is of Another?

Percentage of a Number

Increase Percentage

Decrease Percentage

Basic Problems on Percentage

Solved Examples on Percentage

Problems on Percentage

Real Life Problems on Percentage

Word Problems on Percentage

Application of Percentage

● Percentage - Worksheets

Worksheet on Fraction into Percentage

Worksheet on Percentage into Fraction

Worksheet on Percentage into Ratio

Worksheet on Ratio into Percentage

Worksheet on Percentage into Decimal

Worksheet on Percentage of a Number

Worksheet on Finding Percent

Worksheet on Finding Value of a Percentage

Worksheet on Percentage of a Given Quantity

Worksheet on Word Problems on Percentage

Worksheet on Increase Percentage

Worksheet on Decrease Percentage

Worksheet on increase and Decrease Percentage

Worksheet on Expressing Percent

Worksheet on Percent Problems

Worksheet on Finding Percentage

● Profit, Loss and Discount

Calculating Profit Percent and Loss Percent

Word Problems on Profit and Loss

Examples on Calculating Profit or Loss

Practice Test on Profit and Loss

Discount

Practice Test on Profit Loss and Discount

● Profit, Loss and Discount - Worksheets

Worksheet to Find Profit and Loss

Worksheets on Profit and Loss Percentage

Worksheet on Gain and Loss Percentage

Worksheet on Discounts

● Time and Work

Time and Work

Pipes and Cistern

Practice Test on Time and Work

● Time and Work - Worksheets

Worksheet on Time and Work

● Time and Distance

Speed of Train

Relationship between Speed, Distance and Time

Conversion of Units of Speed

Problems on Calculating Speed

Problems on Calculating Distance

Problems on Calculating Time

Two Objects Move in Same Direction

Two Objects Move in Opposite Direction

Train Passes a Moving Object in the Same Direction

Train Passes a Moving Object in the Opposite Direction

Train Passes through a Pole

Train Passes through a Bridge

Two Trains Passes in the Same Direction

Two Trains Passes in the Opposite Direction

● Time and Distance - Worksheets

Worksheet on Conversion of Units of Speed

Worksheet on Calculating Time

Worksheet on Calculating Speed

Worksheet on Calculating Distance

Worksheet on Train Passes through a Pole

Worksheet on Train Passes through a Bridge 

Worksheet on Relative Speed

Worksheet on Decimal into Percentage

● Simple Interest

What is Simple Interest?

Calculate Simple Interest

Practice Test on Simple Interest

● Simple Interest - Worksheets

Simple Interest Worksheet

● Compound Interest

Compound Interest

Compound Interest with Growing Principal

Compound Interest with Periodic Deductions

Compound Interest by Using Formula

Compound Interest when Interest is Compounded Yearly

Compound Interest when Interest is Compounded Half-Yearly

Compound Interest when Interest is Compounded Quarterly

Problems on Compound Interest

Variable Rate of Compound Interest

Difference of Compound Interest and Simple Interest

Practice Test on Compound Interest

Uniform Rate of Growth

Uniform Rate of Depreciation

Uniform Rate of Growth and Depreciation

● Compound Interest - Worksheet

Worksheet on Compound Interest

Worksheet on Compound Interest when Interest is Compounded Half-Yearly

Worksheet on Compound Interest with Growing Principal

Worksheet on Compound Interest with Periodic Deductions

Worksheet on Variable Rate of Compound Interest

Worksheet on Difference of Compound Interest and Simple Interest

Worksheet on Uniform Rate of Growth

Worksheet on Uniform Rate of Depreciation

Worksheet on Uniform Rate of Growth and Depreciation

● Ratio and Proportion (Direct & Inverse Variation)

Direct Variation

Inverse Variation

Practice Test on Direct Variation and Inverse Variation

● Ratio and Proportion - Worksheets

Worksheet on Direct Variation

Worksheet on Inverse Variation

● Probability

Probability

● Probability - Worksheets

Worksheet on Probability

Geometry

● Lines and Angles

Basic Geometrical Concepts

Angles

Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Supplementary Angles

Complementary and Supplementary Angles

Adjacent Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines

● Parallelogram

Parallelogram

Properties of a Rectangle Rhombus and Square

Problems on Parallelogram

Practice Test on Parallelogram

● Parallelogram - Worksheet

Worksheet on Parallelogram

● Quadrilateral

What is Quadrilateral?

Different Types of Quadrilaterals

Construction of Quadrilaterals

Construct Different Types of Quadrilaterals

● Quadrilateral - Worksheets

Quadrilateral Worksheet

Worksheet on Construction on Quadrilateral

Worksheet on Different Types of Quadrilaterals

● Three-Dimensional Figures

Three-Dimensional Figures

● Three-Dimensional Figures - Worksheets

Worksheet on Three Dimensional Figures

● Mensuration

Area and Perimeter

Perimeter and Area of Rectangle

Perimeter and Area of Square

Area of the Path

Area and Perimeter of the Triangle

Area and Perimeter of the Parallelogram

Area and Perimeter of Rhombus

Area of Trapezium

Circumference and Area of Circle

Units of Area Conversion

Practice Test on Area and Perimeter of Rectangle

Practice Test on Area and Perimeter of Square

● Mensuration - Worksheets

Worksheet on Area and Perimeter of Rectangles

Worksheet on Area and Perimeter of Squares

Worksheet on Area of the Path

Worksheet on Circumference and Area of Circle

Worksheet on Area and Perimeter of Triangle

● Volume and Surface Area of Solids

Volume of Cubes and Cuboids

Worked-out Problems on Volume of a Cuboid

● Area of a Trapezium

Area of a Trapezium

Area of a Polygon

● Area of a Trapezium - Worksheet

Worksheet on Trapezium

Worksheet on Area of a Polygon

● Area Proposition

Figure on Same Base and between Same Parallels

Parallelograms on Same Base and between Same Parallels

Parallelograms and Rectangles on Same Base and between Same Parallels

Triangle and Parallelogram on Same Base and between Same Parallels

Triangle on Same Base and between Same Parallels

● Area Proposition - Worksheets

Worksheet on Same Base and Same Parallels

● Data Handling

Data Handling

Frequency Distribution

Grouping of Data

● Data Handling - Worksheet

Worksheet on Data Handling

● Constructing and Interpreting Bar Graphs or Column Graphs

Bar Graph or Column Graph

● Bar Graphs or Column Graphs - Worksheets

Worksheet on Bar Graphs or Column Graphs

● Pie Charts or Pie Graphs

Pie Chart

● Pie Charts or Pie Graphs - Worksheets

Worksheet on Pie Chart

● Coordinate Geometry

Coordinate Graph

Ordered pair of a Coordinate System

Plot Ordered Pairs

Coordinates of a Point

All Four Quadrants

Signs of Coordinates

Find the Coordinates of a Point

Coordinates of a Point in a Plane

Plot Points on Co-ordinate Graph

Graph of Linear Equation

Simultaneous Equations Graphically

Graphs of Simple Function

Graph of Perimeter vs. Length of the Side of a Square

Graph of Area vs. Side of a Square

Graph of Simple Interest vs. Number of Years

Graph of Distance vs. Time

● Coordinate Geometry - Worksheet

Worksheet on Coordinate Graph

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