How do you find the simple interest rate when given a fraction?

Simple interest is used when a company borrows money for a loan. Usually this amount will be on a monthly basis. The formula for simple interest is principal times the interest rate times the period. Usually period is expressed as a fraction of 12. For example, one month of interest will be 1/12. As an example, Firm A borrows $10,000 from bank. The bank charges 4 percent interest annually and Firm A needs to compute the interest to pay for the first month.

Determine the terms of the interest calculations. In the example, the terms are $10,000, 4 percent interest and one month.
Multiply the interest rate by the principal. In the example, $10,000 times 4 percent equals $400.
Multiply the number calculated in Step 2 by the term. In the example, $400 times 1/12 equals $33.34 of interest for the month.

The interest rate is a percent of the principal to be paid . With this, the lender can compensate from lending his/her money and paid for a certain period of time.

Here are the scenarios to be considered,when solving the rate of interest:

1. Principal, time and interest are given

Steps:

a. Divide the interest by the product of the principal and time.

b. Time should be in years.

where,

P is Principal

I is Interest

2. Future amount, time and principal are given

Steps:

a. Divide the future amount by the principal.

b. Subtract the quotient by 1.

c. Divide the difference by the time.

d. Time should be in years.

Let's have a look at the derivation of the formula, Using the formula of Future Amount,Time is denoted by 'T' and Principal by 'P'

Future Amount=P x [1+(Rate x T)]

`(Future Amount)/P=[1+(Rate*T)]`

`(Future Amount)/P-1=(Rate*T)`

`[(Future Amount)/P-1]/T=Rate `

`Rate= ( (Future Amount)/P- 1)/T`

3. Future amount, time and interest are given

Steps:

1. Subtract the future amount by the interest. The result is the principal.

2. Divide the interest by the product of the principal and time.

3. Time should be in years.

Let's have a look at the derivation of the formula,

Using the formula of Future Amount

`Interest=P*Rate*Time`

where,

P means Principal

`Rate=Interest/(Time*P)-------(i)`

We know that,

Principal=Future Amount-Interest

So, we can write equation (i) as,

where,

T is Time

I is Interest

Harry paid an interest of $8 after he borrowed $160 from his brother. If the interest is for 1 year, what was the rate of interest?

Explanation:

Principal amount is $160.

Interest is $8.

Time to pay the principal with the interest is 1 year.

Using the formula for solving the rate of interest;

`Rate = I/(P x T)`

`Rate = 8/(160 x 1)`

`Rate = 0.05 or 5%`

Therefore, the rate of interest was 5%.

A man loaned $10,000 from the bank in order to build a small business. He was issued to pay a total of $12,100 for 2 years. Find the rate of interest.

Explanation:

Principal amount is $10,000.

Future amount is $12,100.

Time to pay the principal with the interest is 2 years.

Using the formula for solving the rate of interest;

`Rate = ((Future Amount)/P - 1)/T`

`Rate = ((12 100)/(10 000) - 1)/2`

`Rate = (1.21 - 1)/2`

`Rate = 0.21/`2

`Rate = 0.105 or 10.5%`

Therefore, the rate of interest was 10.5%.

Shane paid a total of $2472 to Peter after 6 months of borrowing.If he paid an interest of $72, what was the rate of interest?

Explanation:

Future amount is $2,472.

Interest is $72.

Time to pay the principal with the interest is 6 months.

Converting months into years;

`6 months X (1 year)/(12 months) = 1/2 years`

Using the formula for solving the rate of interest;

`Rate = ( Interest)/(Time x (Future Amount-Interest))`

`Rate = ( 72)/(1/2 x (2472-72))`

`Rate = ( 72)/(1/2 x 2400)`

`Rate = ( 72)/1200`

`Rate = 0.06 or 6%`

Therefore, the rate of interest was 6%.

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Simple Interest(S.I) :It is the interest is calculated uniformly on the original principal throughout the loan period .

When we need a large sum of money for buying house, car etc. We borrow money either by bank or by some agency . The money borrowed is called loan and we become borrower

When we borrow money in the from of loan that money we have to return in a specified period of time by giving them extra fees. This extra fees is called Interest(S.I)

Some Definitions :

Principal : Money borrowed.

Rate: is the percentage of the principal charged as interest each year. The rate is expressed as a decimal fraction, so percentages must be divided by 100.

Example : 5% = 5/100 = 0.05

Amount : The total money which the borrower pays back to the lender at the end of the specified period is called the amount.

Time : Time in years of the loan.

The simple-interest formula is often abbreviated in this form:
If the time is given in month then divide the given formula by 12. Interest = ( P x R x T ) / 12

If the time is given in days then divide the given formula by 365.

Interest = ( P x R x T ) / 365

Amount (A) = Principal (P) + Interest (S.I)

Simple Interest Calculator The following simple-interest calculator will help you determine how much interest you can earn when investing your money with a company.It is the interest is calculated uniformly on the original principal throughout the loan period . The loan period may be in years,months or in days.
Example : 1) Anita borrowed $800 for 2 years at the rate of 12% per annum. Find the interest.Also find the amount paid by her.

Solution :

Principal = ’P’ = $800, Rate = R = 12% = 0.12 , Time= 'T' = 2 years.

Interest : I = P x R x T I = 800 x 0.12 x 2 I = 192

Interest = $192

Amount: A = P + I A = 800 + 192

Amount = $992

Simple Interest (S.I)
• Finding rate when Principal and time are given

• Finding time when Principal and rate are given
• Solved examples on Simple-Interest

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7th grade math
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Welcome to 12 grade math!!!! 11th grade math is a foundation for 12th grade math. Some of the topics which you have studied in 11th grade the same topics are repeated in 12th grade-math but in details. ask-math describes the what the student are going to learn in this grade. Some topic introduction and to learn these topics step by step, there are links given at the bottom.

Relations : ask-math has already introduces this topic in 11th grade math. Now in the 12th grade, ask-math teaches you about the Cartesian products of the sets, different types of relations.

Functions: In this chapter ask-math explains you about various types of functions, composition of functions and inverse of a function.
Inverse trigonometric functions :In this chapter, you will learn the inverses of all trigonometric functions and to study their properties.
Algebra of matrices :In this section you will learn the operations on matrices such as addition, subtraction and multiplication of matrices.
Determinants Every square matrix can be associated to an expression or a number which is known as its determinant.
Continuity : Continuous function is a function for which sufficiently small changes in the input result in random small changes in the output if not then the function is said to be a discontinuous function.
Differentiability :Let f(x) be a real valued function whose derivative exists at each point in its domain.
Mean value theorems : Let f be a real valued function defined on the interval [a,b] such that the function is continuous at [a,b] , differentiable on (a,b) and f(a)= f(b).
Tangents and Normals : In this section you will learn how to find the gradient of the curve.
Application of derivatives: In this section you will learn Increasing and decreasing functions and Maxima and Minima.
Integrals : Under this section , you will learn indefinite and definite integrals.
Application of intergrals: Here you will learn how to find the area under the simple curve and area between the two curves.
• Relations
Cartesian product of sets
Domain
Relation
Void relation
Universal relation
Identity relation
Reflexive relation on set
Symmetric relations
Transitive relation Antisymmetric relation Equivalence relation

• Limits and continuity

Introduction to Limits

Finding limits numerically
finding limits graphically
Limits that fail to exist
Formal definition of Limits
Properties of Limits
Evaluate the limit by direct substitution
Limits of trigonometric functions
Finding limits by factorization method
Finding limits by rationalizing method
Calculus Squeeze theorem
Continuity of a function
Greatest integer function
Intermediate Value theorem
Infinite Limits

• Differentiation

Introduction of derivatives

Derivatives of a function
Differentiability and Continuity
Derivative of a constant function
Power rule for derivatives
Constant Multiple Rule for derivatives
Sum and difference rules for derivatives
Derivative of trigonometric function
Product rule for differentiation
Quotient rule for differentiation
Chain rule for differentiation
Implicit differentiation
Derivative of exponential function
Differentiation of logarithmic function
Derivative of bases other than e
Derivatives of inverse trigonometric functions
Finding Related rates
Extreme value theorem
Relative minimum and maximum
Critical points
Rolle's Theorem
Mean Value Theorem
Increasing and Decreasing functions
Second Order Derivatives
concavity of function
Point of inflection
Limits at Infinity
Analyzing Graph of function
Introduction to Optimization
Optimization Problems
Newon's method for approximating function
Tangent line approximation
Differentials
Antiderivatives(Indefinite Integral)
Power rule of Integration
Properties of Integration
Integration of trigonometric functions
Integration by U-substitution
Integration of Logarithmic function
Integration by parts

12th grade math

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In this section, I have given you the contents of 3rd grade . By the end of third grade , students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication, and division of whole numbers. Students estimate, measure, and describe objects in space. They use patterns to help solve problems. They represent number relationships and conduct simple probability experiments.

3rd grade Contents Number Sense

1) Students understand the place value of whole numbers. Whole numbers 2) Count, read, and write whole numbers to 10,000. 3) Compare and order whole numbers to 10,000. 4) Identify the place value for each digit in numbers to 10,000.
5) Round off numbers to 10,000 to the nearest ten, hundred, and thousand. Rounding
6) Use expanded notation to represent numbers
(Example: 3,206 = 3,000 + 200 + 6). Expanded notation
7) Students calculate and solve problems involving addition, subtraction, multiplication, and division: 8) Find the sum or difference of two whole numbers between 0 and 10,000.
9) Memorize to automaticity the multiplication table for numbers between 1 and 10. Tables
10) Understand the special properties of 0 and 1 in multiplication and division. 11) Determine the unit cost when given the total cost and number of units. 12) Solve problems that require two or more of the skills mentioned above.
13) Students understand the relationship between whole numbers, simple fractions, and decimals: Fractions Decimals
14) Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context. 15) Add and subtract simple fractions
(Example: determine that 1/8 + 3/8 is the same as 1/2). Add and subtract fractions

16) Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole-number multipliers and divisors. Multiplying fractions 17) Know and understand that fractions and decimals are two different representations of the same concept
(Example: 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a dollar). Fraction to percent
Algebra and Functions for 3rd grade

18) Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships: 19) Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities.
20) Solve problems involving numeric equations or inequalities. Algebra
21) Select appropriate operational and relational symbols to make an expression true (Example if 4 __ 3 = 12, what operational symbol (+,-,X and ÷ goes in the blank?). 22) Express simple unit conversions in symbolic form
(Example: __ inches = __ feet x 12). Unit conversion

23) Recognize and use the commutative and associative properties of multiplication Commutative Property
Measurement and Geometry for 3rd grade

24) Students choose and use appropriate units and measurement tools to quantify the properties of objects
25) Choose the appropriate tools and units (metric and U.S.) and estimate and measure the length, liquid volume, and weight/mass of given objects. Length,weight,capacity
26) Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them. Area and Volume 27) Find the perimeter of a polygon with integer sides.
28) Carry out simple unit conversions within a system of measurement (Example: centimeters and meters, hours and minutes). Length,weight,capacity
29) Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems. 30) Identify, describe, and classify polygons (including pentagons, hexagons, and octagons).
31) Identify attributes of triangles (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle). Isosceles, equilateral triangles

32) Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square). Parallelogram, Rectangle and Squares 33) Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle.
34) Identify, describe, and classify common three-dimensional geometric objects (Example: cube, rectangular solid, sphere, prism, pyramid, cone, cylinder). Cube,Sphere, Cone etc.

35) Identify common solid objects that are the components needed to make a more complex solid object.
Statistics, Data Analysis, and Probability

36) Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions. 37) Identify whether common events are certain, likely, unlikely, or improbable. 38) Record the possible outcomes for a simple event (Example: tossing a coin) and systematically keep track of the outcomes when the event is repeated many times. 39) Summarize and display the results of probability experiments in a clear and organized way (e.g., use a bar graph or a line plot). 40) Use the results of probability experiments to predict future events (Example: use a line plot to predict the temperature forecast for the next day).
41) Mathematical Reasoning

3rd grade curriculum
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By the end of 4th grade, students understand large numbers and addition, subtraction, multiplication, and division of whole numbers. They describe and compare simple fractions and decimals. They understand the properties of, and the relationships between, plane geometric figures. They collect, represent, and analyze data to answer questions.

Number Sense for 4th grade

1) Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers: Decimal relate to simple fractions.

2) Read and write whole numbers in the millions. Whole numbers in the millions

3) Order and compare whole numbers and decimals to two decimal places. Comparisons of decimal numbers

4) Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. Rounding numbers

5) Decide when a rounded solution is called for and explain why such a solution may be appropriate.

6) Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions. Equivalent fractions

7) Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (Example: 1/2 = 0.5 or 0.50 ) Notation of decimals

8) Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line. Represent fractions on number line

9) Use concepts of negative numbers. Introduction of negative numbers

10) Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places. 11) Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals. 12) Estimate and compute the sum or difference of whole numbers and positive decimals to two places. 13) Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer. 14) Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.

15) Understand that many whole numbers break down in different ways (Example: 18= 6 x 3 = 2 x 3 x 3) Factors of small numbers

16) Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers. Prime numbers

Algebra and Functions for 4th grade

17) Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences. Introduction to Algebra

18) Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (Example: demonstrate an understanding and the use of the concept of a variable). Variables

19) Interpret and evaluate mathematical expressions that now use parentheses. 20) Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations. 21) Use and interpret formulas (Example: area = length x width or A = lw) to answer questions about quantities and their relationships.

22) Understand that an equation such as y = 3 x + 5 is a prescription for determining a second number when a first number is given. Simple equations

23) Students learn addition of like terms. Addition and subtraction of like terms.

Measurement and Geometry for 4th grade
24) Students understand perimeter and area. Perimeter and Area

25) Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm2), square meter (m2), square kilometer (km2), square inch (in2), square yard (yd2), or square mile (mi2).

26) Area and perimeter of rectangle.

Area and perimeter of Rectangle

27) Use of formulas of area and perimeter and solved problems based on it. Problems based on area and perimeter of rectangle

28) Coordinate Geometry.

29) Parallel lines.Parallel lines

30) Understanding the radius and diameter of a circle. Circle

31) Congruent figures.

32) Symmetry. Symmetry

33) Definition of acute, right and obtuse angles. Types of angles

34) Geometric solids.(Prism, pyramid etc.)

35) Know the definitions of different triangles. Types of triangles

36) Know the definition of different quadrilaterals. Types of quadrilateral

Statistics and Probability (For US students)

37) All types of graphs and charts.(Example : Bar, Histogram etc.)
Bar graph, Histogram etc .

38) Median and Mode. Median and Mode

39) Probability. (tree diagram) 40) Mathematical Reasoning.

4th grade curriculum
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We are an educational site named ask-math.com and we provide good study stuff. This year is important as since students need to decide about the stream which will lead their career. The class 11th grade math syllabus covers the knowledge about the topics that are included in the mathematics. As we know that there is no limit of the course, and if all study is divided in different streams then definitely the limit of that streams for a particular class according to the capacity of the students is must. Thus, class 11th syllabus is necessary for the students to get to know what the topics are and they have to study in 11th standard so that the base of the 12th standard would be strong. In India. the 12th standard percentage have a lot importance in one's life and the admission in higher classes depends on this percentage and knowledge and the study of 12th standard could affected with the knowledge of the base of 11th grade . So it is very necessary to know the topics involved for 11th. Ask-math.com has organized each and every topics that are included in 11 th grade. To learn these topics step by step click on the links given at the bottom of this page. Here is a list of all of the topics students learn in 11th grade math.

Sets : The concept of set is basic in all branches of mathematics. It has proved to be of particular importance in the formations of relations and functions.

Relations and Functions : In mathematics, we come to across relations such as i) line l is parallel to line m ii) number m is less than number n . In all these we notice that a relation involves pairs of objects in certain order. This section is devoted to the study of relations and functions in mathematics.
Mathematical induction : The process of reasoning from general to particular and the other is known as the process of induction. In algebra or in other disciplines of mathematics, there are certain results or statements that are formulated in terms of n , where n is a positive integer. To prove such statements we use a specific technique, is known as the “Principle of Mathematical Induction”.
Logarithms : It is a specific process that reduces the amount of work involved in multiplying and dividing large numbers.
Complex Numbers : Complex number is a number of the form a + ib, where a and b are real numbers and i is the imaginary unit which has the property of i2 = -1
Linear Inequations : 13x <250 such equations are called linear inequations.The study of inequations is very useful in solving problems in the fields of science, mathematics, statistics, optimization problems, economics,psychology etc.
Quadratic Equations : In this section ask-math provides you the quadratic equations with real coefficients but having negative discriminant.
Sequences and series : In this section ask-math covers all types of sequences such as arithmetic progression (A.P), Geometric progression (G.P) and harmonic progression.
Trigonometric functions : In this section, ask-math provides the circular function and their properties. Such as conversion of angles from radian to degree, signs of trigonometric functions, domain and range of trigonometric functions, sum and difference of angles etc.
Cartesian system of rectangular co-ordinates : This section provides you the distance formula, section formula , area of triangle using coordinates , parametric equation of line etc.
Straight line and family of straight line: In this section, we shall derive the various forms of the equation of a line including the lines parallel to axes and the oblique ones. Sets :

• Sets

• Cartesian product of sets Functions :

• Circular function

• Composite functions
• Evaluate inverse cosine function
• Evaluate inverse sine function
• Even and odd function in trigonometry Graph of functions :

• Graph a rational function

• Graph of a trigonometric function
• Graph of y=sin(bx)
• Graph of y = cos(bx)
• Graph rational functions with holes
• Intercept of rational function
• Inverse tangent function
• One to one function
• Onto function
• Periodic function in trigonometry
• Trigonometric functions in different quadrants Mathematical Induction :

• Prove by mathematical induction

Logarithm :

• Common and natural logarithm

• Rules for logarithms
• Evaluating logarithm
• Logarithms change of base
• Application of logarithm Complex Numbers :

• Complex numbers

• Addition of complex numbers
• Subtraction of complex numbers
• Complex numbers polar form
• Complex roots of quadratic equation
• Conjugate complex number
• Division of complex numbers
• Modulus of a complex number
• Multiplication of complex numbers
• Perform operations with complex numbers Quadratic Functions :

• Introduction of quadratic equation

• Irrational roots of quadratic equation
• Nature of roots in quadratic equation
• Quadratic equations with real coefficients
• Show that quadratic equation cannot have more than two roots
• Quadratic equations with complex coefficients • Linear Inequalities :

• Graphing linear inequality

• Graphing systems of linear inequalities
• Linear inequalities
• Solve two step linear inequalities
• Solving linear equations inequalities algebra
• Solving one step equations and inequalities
• System linear inequalities word problems
• System of linear inequalities Sequence and Series

• Series and sequences

• What is an arithmetic means
• Arithmetic progression
• Find terms arithmetic progression
• Arithmetic sequence properties
• Sum of arithmetic progression
• Geometric progression
• Properties of geometric progression
• Find common ratio when sum of n terms of geometric progression is given
• General term of geometric progression
• Geometric progression problem
• Selection of terms in geometric progression
• Solved sums on geometric progression
• Sum of a geometric progression
• Sum of an infinite geometric progression
• Relation between Geometric and Arithmetic mean

11th grade math

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7th grade math curriculum summary : In seventh grade, students apply many concepts that they have learnt in 6th grade but in more detail. Students will learn real world problems which involves percentage,profit and loss,interest scale drawings etc. Based on integers which the students have already learnt in 6th grade will apply properties of operations to all rational numbers. Lastly the students will learn data handling which includes sample of a population and how to effectively compare different population. • Integers
• Fractions
• Decimals
• Rational Numbers
• Exponents
• Algebraic Expressions
• Linear Equations In One Variable
• Ratio and Proportion
• Percentage
• Profit And Loss
• Simple Interest
• Lines And Angles
• Properties of Triangles
• Congruence of Triangles
• Construction of Triangles (SSS)
• SAS Triangle Construction
• ASA Triangle Construction
• HL Triangle Construction
• Symmetry
• Area and Perimeter Rectangles and Square
• Area and Perimeter of Parallelogram
• Area and Perimeter of Rhombus
• Area and Perimeter of Triangle
• Circumference and area of Circle
• Data Handling