Math Prsntation (Autosaved)

7/31/2019 Math Prsntation (Autosaved)

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Mathematics is used in most aspects of daily life. Many ofthe top jobs such as business consultants, computer

consultants, company directors and a host of others

require a solid understanding of basic mathematics.

It also play important role in business, like Business

mathematics by commercial enterprises to record and

manage business operations. Mathematics typically used

in commerce includes elementary arithmetic, such as

fractions, decimals, and percentages, elementary algebra,

statistics and probability.

Business management can be made more effective in

some cases by use of more advanced mathematics such

as calculus, matrix algebra and linear programming.

Commercial organizations use mathematics in accounting,

inventory management, marketing, sales forecasting, and

financial analysis.

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LOGARITHM

Advanced tools to optimization and

planning in economic system.

Logarithms are simply the powers or the

indices to a given base. It is the clever

method of reducing long multiplicationsinto much simpler additions and

reduction divisions into subtraction


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The earliest records of mathematics

show it arising in response to particular

needs in business and industries. It is the

applications of advanced tools to

optimization and planning in.

Logarithm plays an important role of

business mathematics and decision

analysis. So, now describing logarithm as

a tool in business planning and decision

making.


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Practical implementation in

business decisional works

Calculating due date, interest, and maturity

value of simple interest when the loan is for

monthly, daily or yearly for a business.

Computing compound interest and resulting

compound amount at the maturity date for

saving and investment

Calculating salary, commission and annuity

Calculating the outstanding amount for

installment purchase


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Business firm must calculate its

depreciation to know the actualfinancial condition of that particular

firm by using logarithm.

Budgetary planning is the most

important planning. Without knowing

cost of salary, machinery cost,depreciation cost budget cant be

prepared

Calculating the amount of sinking fund,

pension, annuity, retain earning,

compound interest, accumulation are

easier and accurate with logarithm.


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MATHEMATICAL APPLICATION

An example is given below to show it that

how important logarithm is and what role itplays in proper planning and decision

making:-

A limited company at which intends to create a

depreciation fund to replace at the end of the

25th

year assets costing taka 100000. The

amount to be retained out of profits every year

if the interest rate is 3% is to be calculated.


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Solution :-

Here, m= a/I {(1+i)^n -1)}

m=100000, i =0.03, n =25

Where,

100000= a/0.03{(1+0.03)^25 -1)}

=a/0.03{(1.03)^25-1}

=a/0.03(20.089-1)

A=100000*0.03/1.089

=27755 (Ans)

X=(1.03)^25

log x=25 log (1.03)

=25*0.01288

=0.3200

X =antilog (0.3200)

X=2.089

Hence, the amount to be retained is Tk.27755.


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PERMUTATION

In mathematics, the notion of permutation is

used with several slightly different meanings,

all related to the act of permuting

(rearranging) objects or values.

A permutation of a set of objects is an

arrangement of those objects into a

particular order.

The number of permutations of n distinct

objects is n (n 1) (n 2)...21, which

number is called "n factorial" and written


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Permutation Formula

A formula for the number of possible permutations of

r objects from a set of n. This is usually written nPr

Formula: nPr = n!/(n-r)

p=number of permutation

n=number of items

r= number of items in each permutation

MATHEMATICAL IMPLEMENTATION

EXAMPLE:

Indicate how many 4 digit numbers greater than 7000

can be from the digits 3, 5,7,8,9

Solution: If the digits are to be greater than 7000

then the first digit can be only one of the 7, 8 and 9.

Now, the first digit can be chosen in 3 ways and theremaining three can be any of the 4 digits left, which

can be chosen in 4p3 ways

Therefore the total number of ways

=3 x 4P3 = 3 x 4 x3 x2 = 72 ways.


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APPLICABILITY IN ECONOMICAL WORKS

The Allocation of Country Telephone Codes

The allocation of country telephone code must be in specific

order. The emphasis on this allocation is in the word order.

For this reason, this implies the principle of permutation in

mathematics.

The Allocation of City/Area Codes

Telephone area codes of all countries in the world are usually

assigned by the countrys Ministry of Telecommunications.

Usually, these digits are 3, selected from the decimal number

system, 0.9.

In applied statistics

The use of permutation methods in applied statistics is

becoming increasingly widespread. Permutation methods

are employed for three reasons:

1. They provide exact significance levels rather than

approximation

2. Their significance levels are distribution free.

3. They yield more powerful statistics.


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COMBINATION

In mathematics combinations is a way of

selecting several things out of a large

group, where order does not matter.

However, repetition in each combination

is not allowed except otherwise stated.

Thus, the combination of 3 objects taken

all at a time.

FORMULA ANALYSIS

The mathematical formula for finding out

different combinations requires a slightanalysis than the formula used for

permutation.

ncr = n!/ {(n-r)! r! }


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MATHEMATICAL IMPLICATION

EXAMPLE:

If a manager of a shop of a readymade

garments wants to display 4 combinations

out of the total 6 colors of ladies suits

received in his store he can display in thefollowing ways:

Solution:

According to the rule,

6c4 = 6!/ {(6-4)!*4!}

=(6*5*4*3*2*1)/ {(2*1) (4*3*2*1)}

=15

Therefore, the manager can display his products in total 15ways.


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Mathematics for Finance

Use of mathematical formulae or models in

business finance or financial decision is

Mathematics for finance.

The financial decision making is based on

the core concepts of interest ,present value,

annuities, creation of sinking funds etc

SIMPLE INTEREST:

The amount earned only on the original initial

principal amount invested is called simple interest.

Formulae: Interest I=Principal/Amount ,

A = P(1+rn)


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Implementation on business:

A company wants to buy a land.If the person borrowed Tk.4000000 at

10% interest for 4 years, find the simple interest after 4 years.

Solution:

Given that, P=4000000

r=10%

n=4

Using the formula of interest, (I)=Pxrxn

=4000000x(10/100)x4

=TK.1600000

Compound interest:

Interest earned on both the initial principal and the

interest re-invested from the prior periods is

compound interest.

Formula: Interest (I) = P{(1+r)^n-1}


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Implementation on business:

A company invested TK. 50000 for 4 years at 12 % rate

of interest. What will be the compound rate of interest

after 4 years if the interest is paid yearly.

Solution:

Given that, P=50000, r=12%, n=4

Interest (I)= 500000{(1+r)^n-1}

=Tk.28676


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SINGKING FUND

Its a fund or account into which a person or company

deposits money on a regular basis in order to repay

some debt or liability of future.

A corporation might establish a sinking fund in order to

accumulate sufficient capital to replace obsolete

equipment.

For long term corporate bodies each years sinking fund

budget needs to allocate funding in accordance with

long term plan.


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Formula modification

Money deposited annually in order to accumulate by its

termination time, the capital amount needs to cover the

anticipated expenditure. The formula is as follows:

A=F*r/[(1+r)n-1]*1

Here,

A= Annual amount.

F=Future value of the sinking fund.

r= Interest rate earned each period.

n= Number of periods over the annual amount A is

deposited.


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Mathematicalimplementation

Example:

Lets consider that a companys major capital expenditure of

TK.100000 is anticipated in 10 years. What amount the company

needs to deposit in the next 10 years to fund such expenditure if

annual interest rate can be earned 5%?

Solution:

We estimate this by using the formula where

F=100000,

r=5% and

n=10

Putting the values according to the formula:

A=100000*0.05/[(1+0.05)10-1]

=TK.7950

Hence, the amount needed to be deposited annually by the

com an is TK.7950.


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Applicability of sinking fund

The opportunity costs of the sinking fund requirement

may be the inability to secure long term debt.

The accumulation of funds in a special account also

provides the issuer with security against future

business conditions that may be detrimental to its

ability.

The insurance provide by a sinking fund decreases

the interest rates, therefore the expenses.

The issuer can book capital gains on debt

retirement if it purchases bonds in the openmarket below book value.


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LINEAR EQUATION

The practical use of linear equation is in evolving certain

relations and finding out the value of the unknown.

The concept was first invented by the Russian

Mathematician L.V. Kantorovich and developed later by

George B. Dantzig

A system of simultaneous equations is helpful for

finding unique values for unknowns, where the

equations should be equal to the number of unknowns.

IMPLEMENTATION OF LINEAR EQUATION

IN BUSINESS DECISION


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The main theme of theory is to optimize the use of

scarce resources which include machine, man-

power, ware-house, raw- materials etc.

There are several theoretical tools to accomplish

this purpose but those are not adequate for

treating a complex economic problem.

For tackling such problems that are used for linear

programming has been found to be most useful.


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SYSTEM OF LINEAR EQUATION

IN-CONSISTENT CONSISTENT

LINEAR

EQUATION


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GRAPHICAL SOLUTION

There can be graphical solutions as well as

algebraic solutions of equations.

The former courses of graphical solution were

not prcised but easy to use in some cases.

The equations are consistent but dependent.


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QUADRATIC EQUATION

An equation having the highest index as 2 is called the

quadratic equation. For example:

x2+5x+6=0

The general form of quadratic equation is ax2+bx=0.But

another form of this equation is {-b(b2-4ac)}/2a

It is an equation which when reduced to the rational

integral form contains the square of the unknown

quantity.

MATHEMATICAL ANALYSIS

Demand for goods of an industry is given by the

equation pq=100, where p is the price and q is its

quantity, supply is given by the equation 20+3p.We

need to count the equilibrium price and quantity


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Solution:

The demand equation is pq=100 and----(1)

supply equation is 20+3p=q------------(2)

Substituting the value of q from (2) in (1), we get

P(20+3p)=100

3p2+20p-100=0

P = -20(400+1200)

Hence, the equilibrium price (p) =10/3 ,

Quantity exchanged (q) =30 (ans)

QUADRATIC EQUATION IN BUSINESS PLANNING AND

DECISION MAKING

It indicates the relationship between quantity of

goods and costs.

Indicates the relationship between order and

spending

Indicates relation between investment and income.

Sometimes complicated verbal statement when

translated in equation or inequalities can be solved

with great ease.


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Set theory

Applicability of set theory in making surveys

regarding decision making

A SET IS A COLLECTION OF WELL-DEFINED AND

WELL DISTINGUISHED OBJECTS.THE SETS IS OF MUCH WIDER APPLICATION,

ESPECIALLY THEY HELP IN PREPARING THE

PROGRAMME FOR FEEDING IN TO THE MACHINE.

Applying set theory

In sets we deal with a group of objects which can

be defined in terms of their distinctive feature,

magnitudes etc.

It is possible to tell whether a given object

belongs to a set or not.

The basic feature of a set is that it is well defined

and well-distinguished for easy recognition.


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In the view of the previous mentioned topics, each of the

respective parts discussed played a vital role in dealing with

business decision. Their impacts are mentioned viz:-

The compound interest, rate of interest, salary,

commission, depreciation etc are being calculated easily

with the help of log.

Permutation helps in allocating utility expenses as well

calculating all relates expenses.

Combination is the process of maintaining a selectiveorder while a company has a choice among a huge

amount of choices.

Decisional works are incomplete without the effect of

financial mathematics. It mainly decides the best type of

investment field.


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Another part of the financial math is the sinking fund

which declares itself the safest way of investment and

as a decision.

The role of equations in decisional works is

indescribable. The linear equation commits to

evolving certain relations and finding out the value ofthe unknown.

The quadratic equation plays a vital role in calculating

the relation between the demand, supply and

quantity of product of a company.

In sets we deal with a group of objects and find out

relation between elements and within the givenconditions.

In the perspective of the above mentioned topics

decisions regarding the success of the business we can

consider them and their prescribed rules needs to be

followed thoroughly.

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Math Prsntation (Autosaved)