MTH Virtual University of Pakistan. Knowledge beyond the boundaries Modules Statistics. Details of modules are given in handout for lecture Business Mathematics & Statistics (MTH). Handouts (pdf) / Powerpoint Slides (PPTs) Course Codes. Select a course code for Handouts (pdf/PPTs). MTH Complete Handouts 1 to 45 lectures in single pdf file.

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Optional Resources Handouts supplied by the professor. Instructor's Slides Online or CD based learning materials. Prerequisites The students. Download VU Business Mathematics & Statistics - MTH Handouts. Business Mathematics & Statistics - MTH VUTube. Administrator. Business Mathematics & Statistics - MTH VU Video Lectures, Handouts, Power Point Slides, Solved Assignments, Solved Quizzes, Past Papers and.

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Drag the mouse to cell with value 40 reference: F34 and drop the mouse. Excel Formula for Subtraction Excel formulas for subtraction are similar to those of addition but with the minus sign. Let us go through the steps for subtracting 15 from Enter values in row 50 as follows: Click on cell with value 25 reference: Click on cell with value 15 reference B Press enter key.

If you enter 15 first and 25 later, then the question will be to find result of subtraction Only the sign of multiplication will be used.

Business Mathematics & Statistics - MTH302 VU Video Lectures

Let us look at the multiplication of two numbers 25 and The entries will be made in row Enter values as under: Click on cell with number 25 reference: Click on cell with number 15 reference: Press Enter key. The answer is in cell C Let us divide by 15using Excel formula for division.

Let us enter numbers in row 75 as follows: Click the cell A Enter in cell A Click cell B Enter Click cell C Click on cell with value reference: Click cell with number 15 reference: The answer 16 will be displayed in cell C Enter 2o in cell A Click on cell A The answer 0. Let us calculate 16 raised to the power 2 by Excel formula for exponentiation. The values will be entered in row The steps are: Select Cell A Enter 16 in this cell. Select cell B85 Enter 2 in this cell.

Select cell C Select cell with value 16 reference: Select number 2 reference: B85 Press Enter key. The result is displayed in cell C Change values to see change in results. Set up new worksheets for each Excel operator with different values.

Set up worksheets with combinations of operations. You are advised to carry out discussions with other students on different topics. It will be in your own interest to prepare your own solutions to Assignments. The lectures will be delivered in a mixture of Urdu and Englis. The slides available on the VU website before the actual lecture is televised. Students are encouraged to carry out preparatory reading before the lecture.

There are lecture slides as well as other supporting material available on the web site. Links to a web-based discussion and bulletin board will also been provided. Teaching assistants will be assigned by VU to provide various forms of assistance such as grading, answering questions posted by students and preparation of slides Text and Reference Material This course is based on material from different sources.

A list of reference books to be posted and updated on course web site. You are encouraged to regularly visit the course web site for latest guidelines for text and reference material.

Any allowances that exceed this amount are considered taxable both for the employee as well as the company. Example 1 The salary of an employee is as follows: Is any add back to the income of the company? What is the taxable income of employee? Hence Rs. Structure of Allowances The common structure of allowances is as under: An equal amount, i. The company can invest the savings in Provident Fund in Government Approved securities such as defense saving Certificates.

Interest earned on investments in Provident Fund is credited to the account of the employees in proportion to their share in the Provident Fund. Example 4 The salary of an employee is as follows: What is the contribution of the company? What is the total saving of the employee per month on account of Provident Trust Fund? Gratuity Fund According to local laws, a company can establish a Gratuity Trust Fund for the benefit of the employees.

The company can invest the savings in Gratuity Fund in Government Approved securities such as defence saving Certificates. Interest earned on investments in Gratuity Fund is credited to the account of the employees in proportion to their share in the Gratuity Fund. Example 5 The salary of an employee is as follows: What is the contribution of the company on account of gratuity to the Gratuity Trust Fund? Leaves All companies have a clear leaves policy. The number of leaves allowed varies from company to company.

Typical leaves allowed may be as under: What is the cost on account of casual, earned and sick leaves per year if normal working days per month is 22? What is the total cost of leaves as percent of gross salary?

Such benefits may be about 5. Leaves are Other companies may have more social benefits. Example 7 The salary of an employee is as follows: What is the cost of the company on account of leaves It includes.

Basic Salary 2. House rent allowance 3.

Conveyance allowance 4. Utilities 5. Provident fund 6. Gratuity fund 7. Leaves 8. Group insurance medical etc 9. Miscellaneous social charges. Benefits can also include more factors and are not limited to the above list. The purpose of the benefits is to increase the economic security of employees Example 8 The salary of an employee is as follows: There is mistake in calculating gross remuneration in example given below.

Total amount of leaves are which is the amount for 1 year not 1 month. So divide the amount of leaves by 12 and then calculate gross remuneration. Converting fraction to percent Calculate percent by multiplying fraction by Any number written in the form: For example 2. Converting percent into decimal fraction Review Lecture 3 Calculating simple or weighted averages Using Microsoft Excel Gross Remuneration The following slide shows worksheet calculation of Gross remuneration on the basis of Rs, basic salary.

Conveyance and Utilities Allowance are both 2. The arithmetic formulas are as follows: Excel formulas are within brackets. Excel formula: This feature can be used for quick and correct calculation of all allowances and benefits.

In our case we used the value after the semicolon to indicate that no decimal is required. If you want 1 decimal use the value 1. If the formula in cell D93 is copied to cell E93 say , the cell reference B93 in formula changes to C Add numbers in a cell 2. Add all contiguous numbers in a row or column 3.


Add noncontiguous numbers 4. Add numbers based on one condition 5. Add numbers based on multiple conditions 6. Add numbers based on criteria stored in a separate range 7. Add numbers based on multiple conditions with the Conditional Sum Wizard 1.

See Example 2 2. See Example 3. Add numbers based on one condition Use the SUMIF function to create a total value for one range, based on a value in another range. Add numbers based on criteria stored in a separate range Syntax DSUM database,field,criteria Database is the range of cells that makes up the list or database. Field indicates which column is used in the function.

Criteria is the range of cells that contains the conditions you specify. Number1, number2, Calculate the average of numbers in a contiguous row or column Calculate the average of numbers not in contiguous row or column Weighted average is one type of arithmetic mean of a set of data, in which some elements of the set carry more importance weight than others.

Grades are often computed using a weighted average. So first we convert them to fraction. Find the percent change.

First the entries of data were made as follows: In cell C7 the formula for percentage change was: Find the percentage change. Data entry Cell D Calculations using Excel are shown in the following slides. Data entry Cell C If you invested Rs. What will be the percent decrease in the interest rate on a given balance? As we learnt in lecture 5, the calculation will be as follows: Stock represents a claim on the company's assets and earnings.

As you acquire more stock, your ownership stake in the company becomes greater. Whether you say shares, equity, or stock, it all means the same thing. Stock yield With stocks, yield can refer to the rate of income generated from a stock in the form of regular dividends. This is often represented in percentage form, calculated as the annual dividend payments divided by the stock's current share price.

Price-earnings ratio A valuation ratio of a company's current share price compared to its per-share earnings. Calculated as: Outstanding shares Stock currently held by investors, including restricted shares owned by the company's officers and insiders, as well as those held by the public. Shares that have been redownloadd by the company are not considered outstanding stock. Current Assets The value of all assets that are reasonably expected to be converted into cash within one year in the normal course of business.

Current assets include cash, accounts receivable, inventory, marketable securities, prepaid expenses and other liquid assets that can be readily converted to cash. Market value The price at which investors download or sell a share of stock at a given time Face value Original cost of a share of stock which is shown on the certificate. Also referred to as "par value. Dividend Usually, a company distributes a part of the profit it earns as dividend.

For example: A company may have earned a profit of Rs 1 crore in It keeps half that amount within the company. This will be utilised on downloading new machinery or more raw materials or even to reduce its borrowing from the bank.

It distributes the other half as dividend. Assume that the capital of this company is divided into 10, shares. That would mean half the profit -- ie Rs 50 lakh Rs 5 million -- would be divided by 10, shares; each share would earn Rs The dividend would then be Rs per share. If you own shares of the company, you will get a cheque of Rs 50, shares x Rs from the company.

Sometimes, the dividend is given as a percentage -- i e the company says it has declared a dividend of 50 percent. It's important to remember that this dividend is a percentage of the share's face value.

MTH302 - Business Mathematics & Statistics Complete Handouts Lecture no.1 to 45

Face value of each share is 10Rs. What is your return on investment? Bought Calculation using Excel along with formula is given in the following slide: These are called annuities. Annuities are essentially series of fixed payments required from you or paid to you at a specified frequency over the course of a fixed period of time. An annuity is a type of investment that can provide a steady stream of income over a long period of time.

The most common payment frequencies are yearly once a year , semi-annually twice a year , quarterly four times a year and monthly once a month. Calculating the Future Value or accumulated value of an Annuity If you know how much you can invest per period for a certain time period, the future value of an ordinary annuity formula is useful for finding out how much you would have in the future by investing at your given interest rate.

If you are making payments on a loan, the future value is useful for determining the total cost of the loan. Let's now run through Example 1. Consider the following annuity cash flow schedule: The following diagram shows how much you would have at the end of the five- year period: Since we have to add the future value of each payment, you may have noticed that, if you have an annuity with many cash flows, it would take a long time to calculate all the future values and then add them together.

Fortunately, mathematics provides a formula that serves as a short cut for finding the accumulated value of all cash flows received from an annuity: Each of the values of the first calculation must be rounded to the nearest penny - the more you have to round numbers in a calculation the more likely rounding errors will occur. So, the above formula not only provides a short-cut to finding FV of an ordinary annuity but also gives a more accurate result. Calculating the Present Value or discounted value of an Annuity If you would like to determine today's value of a series of future payments, you need to use the formula that calculates the present value of an ordinary annuity.

For Example 2, we'll use the same annuity cash flow schedule as we did in Example 1. To obtain the total discounted value, we need to take the present value of each future payment and, as we did in Example 1, add the cash flows together. Again, calculating and adding all these values will take a considerable amount of time, especially if we expect many future payments. As such, there is a mathematical shortcut we can use for PV of ordinary annuity. Here is the calculation of the annuity represented in the diagram for Example 2: The formula for Accumulated Value S is as follows: As an example if we deposit rupees and get rupees i.

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Here will be future value of at the end of year 1. The amount , if invested again, can be Rs. This rate is called Discount Rate. The present worth of future payments is called Discounted Value. The components of an algebraic expression are separated by Addition and Subtraction. In algebraic expressions there are four types of terms: Multiplication is assumed when two factors are written beside each other. There are two steps for Division by a monomial. Identify factors in the numerator and denominator 2.

Cancel factors in the numerator and denominator Example: The result is: Here the steps are: Divide each term in the numerator by the denominator 2. How to multiply polynomials? Look at the example —x 2x2 — 3x Here each term in the trinomial 2x2 — 3x -1 is multiplied by —x. The steps in this calculation are: Simplify inside the brackets first. Square each factor 3. In the next step we take squares. The resulting expression is: To solve linear equations: Collect like terms 2.

Divide both sides by numerical coefficient. Step 1: If this function is not available, and returns the NAME? The syntax is as follows: In this example, in the first case the objective is to find total interest paid in the second year of payments for periods 13 to Please note there are 12 periods per year.

The second case is for the first payment period. The Years of the loan are given in cell A3. The Present value is in cell A4.

For the Start period the value 13 was entered. For the End period, the value 24 has been specified.

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The value of Type is 0, which means that the payment will be at the end of the period. Please note that the annual interest is first divided by 12 to arrive at monthly interest. Then the Years of the loan are multiplied by 12 to get total number of months in the Term of the loan.

The answer is In the second formula, which gives Interest paid in a single payment in the first month 1 was specified as the Start period. For the End period also the value 1 was entered. This is because only 1 period is under study.

All other inputs were the same. The syntax is as under: In this example, in the first case the objective is to find the total principal paid in the second year of payments, periods 13 through The second case is for the principal paid in a single payment in the first month. The Term in years 30 is given in cell A3. Please note that the interest is first divided by 12 to arrive at monthly interest.

Then the years of loan are multiplied by 12 to get total number of months in the term of the loan. In the second formula, which gives the principal paid in a single payment in the first month 1 was specified as the start period.The mean is larger than the median 50 The median is larger than the mean.

Please check your browser settings or contact your system administrator. Question No: 40 A single die is rolled. The y-intercept is the point where the line crosses the y-axis.

In cell C15, the cell reference B15 is written. Admin Team. Question No: 12 Prices are ,,, and Moving averages are , Now Actual- Trend are , 5 0, 0 10, , 10 Question No: 13 There are 6 flags to give signal, now use 3 flags and guess the no. Is it possible to multiply the given matrices in this order?

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