Interest

Interest is a fee paid on borrowed assets. It is the price paid for the use of borrowed money,[1] or, money earned by deposited funds.

Interest is the cost of someone pays for the temporary exercise. The interest may be calculated by the calculator depends on the principal amount.

Types of Interest:

Following are the types of Interest:

• Simple Earned Interest.
• Compound Earned Interest.

Simple Earned Interest: When we need money, we borrow money from individuals or banks or finance companies. At the time of returning the money, we have to pay some additional money for the benefit of using the money borrowed for a specified period.Simple interest topic is easy to understand and that makes sense to the students.

Principal is the sum of money borrowed.
Interest is the additional money to be given.
Hence the formula to calculate Simple Interest is as follows:

Amount = Principal + Interest

A = P + I

Let us understand this form the following problem on Simple Interest.

Problem 1

Rashmi invested Rs. 10000 for 4 years at the rate of 12% per annum. Find the Simple Interest and the amount received by her after 5 years.

Solution:

Here:
Principal P = Rs 10000
Number of Years, n = 4 years
Rate of Interest, r = 12%
Simple Interest, I = (p*n*r)/100
= 10000*4*(12/100)
= Rs. 4800.

Amount, A = Principal + Interest

=10000 + 4800
= 14800
Therefore:

The Simple Interest = Rs. 4800.

Amount = Rs. 14800.

Compound Earned Interest: Compound interest arises when interest added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding (for example the interest is compounded).

Problem 1

Find the compound amount and compound interest by using compound interest calculator where the principal 60,000 borrowed at 10% compounded annually for 4 years.

Solution:

Here:

Principal P = 60000

Rate r = 10%

Number of Years n = 4

The Formula for Compound Interest A = (1+r)ⁿ.

= 60000 (1+0.1)⁴

⁼ 60000*1.4641

= 87846

The Compound amount = 87846

Compound Interest = Compound Amount - Principal

= 87846 - 60000
= 27846
The Compound Interest is 27846

For more problems on Simple Interest and Compound Interest click here

Linear Equation

A linear equation is defined as an algebraic equation in which every expression is either a stable (constant) or the product of a stable and a single variable. Linear equations can have one or more than one variables. It’s happening with great reliability in applied mathematics. A linear function is one whose diagram (graph) is a straight line.

Format of Linear equations:

Below are some forms of Linear Equations.

Linear equations:

A general type of a linear equation in the two variables x and y is

y =mx+b

Here ‘m’ and ‘b’ assign constants. Here the term linear is derived from a graphical line of diagram. That is straight line is occurring at a graph.

General form:

Ax+By+C=0

Where A and B are not both equal to zero.

Standard form:

Ax+By=C

Where A, B, and C are integers.

Slope–intercept form:

y=mx+b

Where m is the slope of the line and b is the y-intercept.

More to come....................................

Set Theory

What is a Set??

A well-defined collection of distinct objects is called a set.Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.

Below is the Notation of Sets

Capital letters are usually used to denote or represent a set.
viz., A, B, C, D, . . . .

The elements of sets are usually represented by lower case letters.
viz., a, b, c, x, y

There are two methods by which a set is represented.

• Roster Method
• Set builder form.

Roster Method: Here, a set is represented by listing all the elements of the set, the elements being separated by commas and are enclosed within flower brackets { }. It is also called as Tabular Method.

Example: A set containing 3,5,7,9,11 is written as {3,5,7,9,11} in Roster Method.

Set Builder Form: In set builder form, a set is represented by stating all the properties which are satisfied by the elements of the set and not by any other element. It is also called as Property Method.
If A contains all values of 'x' for which the condition P(x) is true, then we write A = {x: P(x)}.
Example: If A is a set of all positive factors of 36, then in Set builder method it is written as

A = {x : x is a factor of 36, x Î N}

Sub Set:
If all the members of set A are also members of set B, then A is a subset of B, denoted A ⊆ B.
For problems on Subsets please click here.

Probability Equations

Math was so hard for me until I found some simple ways to solve problems. Probability was one thing that I never understood in my school days, but yes now I found some easier ways to solve problems in Probability

A way of expressing facts or belief that an event will occur or occur is known as probability. Probability can be defined either in objective or subjective manner. The number of times something will occur probably to the total number of event occurred is known as probability. It is widely used in study areas like mathematics, statistics, finance, and in other areas such as science and philosophy.

Below are some simple examples of Equations in Probability.

Example 1: In a class of 80 students, 20 are in the fun committee and 30 are in the sports committee. If a Student is selected randomly, what is the probability that the selected student is:

a) in the Fun committee
b) in the Sports committee

Probability Equations Solution:

The total number of students in the class = 80

Number of students in the Fun committee = 20

Number of students in the Sports committee = 30

The probability of solving that the selected student in the Fun committee is,

P ( Students in Fun Committee) = 20/80
= 1/4
= 0.25

The probability of solving that the selected student in the Sports committee is,
P ( Students in sports committee) = 30/80
= 6/16
= 0.375

Permutation and Combination

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.

Let us understand Permutations and combination which is one of the topics under Discrete maths.

Permutations:

The different arrangements that can be made with a given number of things taking some or all of them at a time are called permutations.

The symbol ⁿP_r or P(n,r) is used to denote the number of permutations of n things taken r at a time.

Below is one solved example on Permutation.

Example 1: If nP₄ = 360, find the value of n.

Combination:

The selection of a number of things taking some or all of them at a time are called Combination.

The number of ways of selecting r things out of n dissimilar things is denoted by C(n, r) or ⁿC_r.

Below is one solved example on Combination.

There are 17 yellow balls, 17 green balls, and 17 purple balls in a bag. Select the fraction that expresses the probability of selecting a yellow ball from the bag.

Solution
1 There are 51 possible outcomes.
[17 + 17 + 17 = 51.]

2 Number of favorable outcomes = Number of yellow balls in a bag = 17

3 Probability (event) = amount of favorable outcomes Number of possible outcomes = 17 / 51 = 1 / 3

4 so, the probability of selecting a yellow ball from the bag is 1 / 3.

Multiplication Rule of Probability

Multiplication Rule in Probability

Events are said to be independent if the occurrence of one event does not affect the occurrence of others. If A and B are two independent events,
then
P(AΩB) = P(A)*P(B)

This is known as Multiplication Rule of Probability. The converse is also true, that is if two events A and B associated with a random experiment are such that

P(AΩB) = P(A)*P(B) then the two events are Independent Events.

If the occurrence of one event affects the other event,such that
P(AΩB) ≠ P(A).P(B)

then the two events are Dependent Events.

Probability Problems

Probability Problem 1: In a class of 60 students, 10 are in the drawing club and 15 are in the games club. If a student is selected randomly, what is the probability that the selected student is:

a) In the drawing club?

b) In the games club?

Solution:

The total number of students in the class = 60

Number of students in the drawing club = 10

Number of students in the games club = 15

The probability of solving that the selected student in the drawing club is,

P (students in drawing club) = 10 / 60

= 1/6

= 0.17

The probability of solving that the selected student in the games club is,

P (students in games club) = 15 / 60

= 1/4

= 0.25

Probability Problem 2: A card is drawn from an ordinary deck and we are told that it is red, what is the probability that the card is greater than 2 but less than 9.

Solution:

Let A be the event of getting a card greater than 2 but less than 9.

B be the event of getting a red card. We have to find the probability of A given that B has occurred. That is, we have to find P (A/B).

In a deck of cards, there are 26 red cards and 26 black cards.

\ n(B) = 26

Among the red cards, the number of outcomes which are favorable

To A are 12. That is n(AΩB) = 12

P(A/B) = n(AΩB)/n(B)

= 12/26

=6/13

FREQUENCY DISTRIBUTION

Introduction:

A Frequency Distribution defines us a summarized accumulation of data divided into commonly exclusive classes and the number of appearance in a class. Example: To show election result, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc. Some of the graphs can be used with frequency distributions are histograms, line graphs, bar charts and pie charts.

Types of Frequency Distribution:

• Categorial
• Ungrouped
• Grouped

Categorical frequency distributions represent data that can be placed in specific categories, such as gender, hair color, or religious affiliation.

An ungrouped frequency distribution simply lists the data values with the corresponding number of times or frequency count with which each value occurs.

A grouped frequency distribution is obtained by constructing classes (or intervals) for the data, and then listing the corresponding number of values (frequency count) in each interval.