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1、BUSINESS MATHEMATICS&STATISTICS,BUSINESS MATHEMATICS&STATISTICSLecture 2,COURSE MODULES8 ModulesModules 1-4:MathematicsModules 5-8:Statistics,Module 1Overview(Lecture 1)Applications of Basic Mathematics(Lectures 2-6),LECTURE 2Course OverviewArithmetic Operations&Using Microsoft Excel,ARITHMETIC OPER
2、ATIONSAdditionSubtractionMultiplicationDivisionExponent,BUSINESS MATHEMATICS&STATISTICS,BUSINESS MATHEMATICS&STATISTICSLECTURE 3,LECTURE 3EvaluationsCalculate Gross EarningsUsing Microsoft Excel,EvaluationIn order to successfully complete this course,the student is required to meet the evaluation cr
3、iteria,Evaluation Criterion 1Full participation is expected for this course,Evaluation Criterion 2All assignments must be completed by the closing date,Evaluation Criterion 3Overallgrade will be based on VU existing Grading Rules,Evaluation Criterion 4All requirements must be met in order to pass th
4、e course,GradingThere will be a term exam and one final exam;there will also be 4 assignments The final exam will be comprehensive,GradingThese will contribute the following percentages to the final grade:Mid Term Exam 35%Final 50%4 Assignments 15%,CollaborationDiscusPrepare own solutionsMake origin
5、al submissions,ETHICSNo copyingNo cheatingNo short cuts,MethodologyThere will be 45 lectures each of 50 minutes duration The lectures will be delivered in a mixture of Urdu and English,MethodologyHeavily supported by slide presentationsThe slides available on the VU website before the actual lecture
6、 is televised Students to carry out preparatory reading before the lecture,MethodologyOwn page on the VUs web site Lecture and other supporting material Link to a web-based discussion and bulletin board,MethodologyTeaching assistants will be assigned by VU to provide various forms of assistance such
7、 as grading,answering questions posted by students and preparation of slides,Text and Reference MaterialMaterial from different sources Topics for reading on course web site and in professors handoutsOn the course web site A list of reference books to be posted and updated on course web site,PROBLEM
8、SIf you have any problems with understanding of the courseContactbizmathvuedupk,SalaryBasic Salary+Allowances+Gratuity+Provident Fund+Social Charges,AllowancesHouse Rent 45%Conveyance 2.5%Utilities 2.5%,Gratuity1/11 th of Basic Salary About 9.09%of Basic,Provident Fund1/11 th of Basic SalaryAbout 9.
9、99%of Basic,Social Charges Casual Leave 18 DaysSick Leave 12 DaysMedical/Group Insurance 5%Total about 29%of Gross Salary,SummaryBasic salary 100%Allowances 50%Gratuity 9.99%Provident Fund 9.99%Social Charges 29%,EXAMPLE 1Basic Salary=6,000 Rs Calculate Remuneration Including Allowances,Gratuity,Pro
10、vident Fund and Social Charges,Decimal Fraction=0.5 10/100=0.1Common Fraction10/100=1/10,PercentFraction X 100Example0.1 X 100=10%,Converting%into Fraction20%=20/100=0.2,Rate Percent or FractionEarnings20%or 20/100=0.2,PercentagePercent of the BaseExample20%of 120In 20%of 120120 is Base20%is Rate,Pe
11、rcentage=Base x Rate20%x 12020/100 x 120Or 0.2 X 120=24,What Percentage is 6%of 40=Rate X Base=0.06 X 40=24,Base=Percentage/RateExampleRate=24.0%Percentage=96Base=96/0.24=400,BUSINESS MATHEMATICS&STATISTICS,BUSINESS MATHEMATICS&STATISTICS,LECTURE 4Review Lecture 3Calculating simple or weighted avera
12、gesUsing Microsoft Excel,Lecture 3 ReviewWORKSHEETRemuneration.xls,Average(Arithmetic Mean)=Sum/NSum=Total of numbersN=Number of numbers,EXAMPLE 1 Numbers:10,7,9,27,2Sum:=10+7+9+27+2=55Numbers=5Average=55/5=11,ADDING NUMBERS USING MICROSOFT EXCELAdd numbers as you type them Add all numbers in a cont
13、iguous row or columnAdd numbers that are not in a contiguous row or columnAdd numbers based on one condition Add numbers based on multiple conditions Add numbers based on criteria stored in a separate rangeAdd numbers based on multiple conditions with the Conditional Sum Wizard,Add numbersAdd number
14、s as you type themType=5+10 in a cellResult 15.See Example 2,Add all numbers in a contiguous row or column Click a cell below the column of numbers or to the right of the row of numbersClick AutoSum Press ENTER See Example 2,Add numbers that are not in a contiguous row or columnUse the SUM function
15、See Example 3,Add numbers based on one conditionUse the SUMIF function to create a total value for one range,based on a value in another rangeSimilar to Example 4,Add numbers based on multiple conditions Use the IF and SUM functions to do this task See Example 4,Add numbers based on criteria stored
16、in a separate range Use the DSUM function to do this task Study DSUM Example,DSUMAdds the numbers in a column of a list or database that match conditions you specify.SyntaxDSUM(database,field,criteria)Database is the range of cells that makes up the list or database.Field indicates which column is u
17、sed in the function.Criteria is the range of cells that contains the conditions you specify.,DSUMEXAMPLE=DSUM(A4:E10;Profit“;A1:F2)The total profit from apple trees with a height between 10 and 16(75),AVERAGE USING MICROSOFT EXCELCalculate the average of numbers in a contiguous row or columnCalculat
18、e the average of numbers not in a contiguous row or column,AVERAGEReturns the average(arithmetic mean)of the arguments.SyntaxAVERAGE(number1,number2,.)Number1,number2,.are 1 to 30 numeric arguments for which you want the average.,WEIGHTED AVERAGEAv.1 x weight 1+Av.2 x weight 2+.Av.N x weight nWeight
19、s in fractions,BUSINESS MATHEMATICS&STATISTICS,BUSINESS MATHEMATICS&STATISTICS,LECTURE 5Review of Lecture 4Basic calculations of percentages,salaries and investments using Microsoft Excel,Mondays Sales were Rs.1000 and grew to Rs.2500 the next day Find the percent change,CALCULATIONInitial Value=100
20、0Final Value=2500 Change=1500%Change=1500/1000 x 100=150,HOW many Percent is Next Days sale with refernce to Mondays Sale?Mondayss sale=1000Next days sale=2500Next days sale as%=2500/1000 x 100=250%=Two and a half times,reference,ow,ow,reference,In the making of dried fruit,15kg.of fruit shrinks to
21、3 kg Find the percent change.,CALCULATIONOriginal fruit=15 kgFinal fruit=3 kgChange=3-15=-12%change=-12/15 x 100=-80%Size was reduced by 80%,After mixing with water the weight of cotton increased from 3 kg to 15 kg Find the percent change.,CALCULATIONOriginal weight=3 kgFinal weight=15 kgChange=15-3
22、=12%change=12/3 x 100=400%Weight increased by 400%,A union signed a three year collective agreement that provided for wage increases of 3%,2%,and 1%in successive yearsAn employee is currently earning 5000 rupees per month What will be the salary per month at the end of the of the term of the contrac
23、t?,CALCULATION5000(1+3%)(1+2%)(1+1%)=5000 x 1.03 x 1.02 x 1.01,Investment for a period of 4 years Rates of return for each year are 4%,8%,-10%and 9%respectively.If you invested Rs.100,000 at the beginning of the term,how much will you have at the end of the last year?,BUSINESS MATHEMATICS&STATISTICS
24、,BUSINESS MATHEMATICS&STATISTICS,LECTURE 6Review Lecture 5DiscountSimple and compound interest Average due date,interest on drawings and calendar,Revision Lecture 5A chartered bank is lowering the interest rate on its loans from 9%to 7%.What will be the percent decrease in the interest rate on a giv
25、en balance?,A chartered bank is increasing the interest rate on its loans from 7%to 9%What will be the percent increase in the interest rate on a given balance?,Investors,Stock Quotation Calculations,Closing price per share,Annual dividend per share,=,10,41.125,=,.3%,Closing price per share,Annual e
26、arnings per share,=,41.125,1.11,Total#of shares outstanding,Annual earnings,=,100,000,1,000,000,=$0.10,BUYING SHARESIf you buy 100 shares at Rs.62.50 per share with a 2%commission,calculate your total cost,CALCULATION100*Rs.62.50=Rs.6,250.02*Rs.6,250=125 Rs.6,375,RETURN ON INVESTMENTSuppose you boug
27、ht 100 shares at Rs.52.25 and sold them 1 year later at Rs.68.With a 1%commission rate buying and selling the stock and a current Rs 10 dividend per share in effect,what was your return on investment?,Bought100 shares at Rs.52.25=5,225.00Commission at 1%=52.25Total Costs=5,277.25,Sold100 shares at R
28、s.68=6,800.00Commission at 1%=-68.00Total Costs=6,732.00,GainNet receipts=6,732.00Total cost=-5,277.25Net Gain=1,454.75Dividends(100*1)=100.00Total Gain=1,554.75Return on investment=1,554.75/5277.25*100=29.46%,DiscountRebate or reduction in priceExpressed as%,DiscountList price=2200Discount Rate=155
29、Discount?=2200 x 0.15=330,Net Cost Price=List price-DiscountList price=4,500 Rs.Discount=20%Net cost price=4,500 20%of 4,500=4,500 0.2 x4,500=4,500 900=3,600 Rs.,Simple InterestI=P.R.T/100P=PrincipalR=Rate percent per annumT=Time in yearsI=Simple interest,Find interestP=Rs.500T=4 yearsR=11%I=P x T x
30、 R/100=500 x 4 x 11/100=Rs.220,Compound InterestAlso attracts interestP=800Interest year 1=0.1 x 800=80New P=800+80=880Interest on 880=0.1 X 880=88New P=880+88=968,Compound Interest FormulaS=Money accrued after n yearsP=PrincipalR=RateN=Number of yearsS=P(1+r/100)n,ExampleCalculate interest on Rs.75
31、0 invested at 12%per annum for 8 years.S=P(1+r/100)8=750(1+12/100)8=1957,BUSINESS MATHEMATICS&STATISTICS,BUSINESS MATHEMATICS&STATISTICS,Module 2Exponents and RadicalsLinear Equations(Lectures 7)Investments(Lectures 8)Matrices(Lecture 9)Ratios&Proportions and Index Numbers(Lecture 10),LECTURE 7Revie
32、w of lecture 6Exponents and radicals Simplify algebraic expressions Solve linear equations in one variable Rearrange formulas to solve for any of its contained variables,AnnuityValue=4,000Down payment=1,000Rest in 20 installments of 200Sequence of payments at equal interval of timeTime=Payment Inter
33、val,NOTATIONSR=Amount of annuityN=Number of paymentsI=Interest rater per conversion periodS=Accumulated valueA=Discounted or present worth of an annuity,ACCUMULATED VALUES=r(1+i)n 1)/iA=r(1-1/(1+i)n)/i)Accumulated value=Payment x Accumulation factorDiscounted value=Payment x Discount factor,ACCUMULA
34、TION FACTOR(AF)i=4.25%n=18AF=(1+0.0425)18-1)=26.24R=10,000Accumulated value=10,000 x 26.24=260,240,DISCOUNTED VALUEValue of all payments at the beginning of term of annuity=Payment x Discount Factor(DF)DF=(1-1/(1+i)n)/i)=(1-1/(1+0.045)8)/0.045)=6.595,ACCUMULATED VALUE=2,000 x(1-1/(1+0.055)8)/0.055)=
35、2,000 x11.95=23,900.77,Algebraic Expression,indicates the mathematical operations to be carried out on a combination of NUMBERS and VARIABLES,Terms,the components of an Algebraic Expression that are separated by ADDITION or SUBTRACTION signs,x(2x2 3x 1),Terms,1 Term,2 Terms,3 Terms,any more than 1 T
36、erm!,3x2,3x2+xy,3x2+xy 6y2,Term,each one in an Expression consists of one or more FACTORS separated by MULTIPLICATION or DIVISION sign,xy=x*y,Also,assumed when one factor is written under an other!,Term,Numerical Coefficient,Literal Coefficient,FACTOR,3x2,Algebraic Expression,Terms,Division by a Mon
37、omial,Identify Factors in the numerator and denominator,36x2y,3(12)(x)(x)(y),60 xy2,5(12)(x)(y)(y),Cancel Factors in the numerator and denominator,=,Division by a Monomial,Divide each TERM in the numerator by the denominator,Cancel Factors in the numerator and denominator,48a2/8a 32ab/8a or,6,4,=,48
38、(a)(a),32ab,-,8a,8a,=6a,4b,Multiplying Polynomials,Multiply each term in the TRINOMIAL by(x),+,+,=,=,-2x3,+,3x2,+,The product of two negative quantities is positive.,x,Exponents Rule of,=32*4,34,Base,3,Exponent,4,3,i.e.3*3*3*3,Power,=81,32*33,=32+3,=3,5,=243,(32)4,=(1+i)20-8,=(1+i),12,=3,8,=6561,Exp
39、onents Rule of,X4,=,Z3*2,z6,Solving Linear Equations in one Unknown,Equality in Equations,A+9,Expressed as:A+9=137 A=137 9 A=128,Solving Linear Equations in one Unknown,Solve for x from the following:x=341.25+0.025x,x-0.025x=341.25,0.975x=341.25,x=341.25+0.025x,x=341.25 0.975,x=350,BUSINESS MATHEMAT
40、ICS&STATISTICS,Solving Word Problems,for the Unknown,Barbie and Ken sell cars at the Auto World.,Data,In April they sold 15 cars.,Barbie sold twice as many cars as Ken.,How many cars did each sell?,2C+C=15 3C=15,C=5,Barbie=2 C=10 Cars,Ken=C=5 Cars,Barbie sold twice as many cars as Ken.,In April they
41、 sold 15 cars.,Colleen,Heather and Marks partnership interests in Creative Crafts are in the ratio of their capital contributions of$7800,$5200 and$6500 respectively.,What is the ratio of Colleens to Heathers to Markss partnership interest?,Colleen,Heather and Marks partnership interests in Creative
42、 Crafts are in the ratio of their capital contributions of$7800,$5200 and$6500 respectively.,7800,5200,:,6500,:,Colleen,Heather,Mark,Equivalent ratio(each term divided by 100),78,52,65,:,:,Equivalent ratio with lowest terms,1.5:1:1.25,The ratio of the sales of Product X to the sales of Product Y is
43、4:3.The sales of product X in the next month are forecast to be$1800.,What will be the sales of product Y if the sales of the two products maintain the same ratio?,Expressinga Ratio inEquivalent Forms,A 560 bed hospital operates with 232 registered nurses and 185 other support staff.The hospital is
44、about to open a new 86-bed wing.,Assuming comparable staffing levels,how many more nurses and support staff will need to be hired?,Expressinga Ratio inEquivalent Forms,Since X:Y=4:3,then$1800:Y=4:3,Y,=,3,4Y=1800*3,Y=1800*3,=$1350,Expressinga Ratio inEquivalent Forms,A 560 bed hospital operates with
45、232 registered nurses and 185 other support staff.The hospital is about to open a new 86-bed wing.,560:232:185=86:RN:SS,=,232,RN,560RN=232*86,560RN=19952,RN=19952/560,Hire 35.63 or 36 RNs,=,185,SS,560SS=185*86,560SS=15910,SS=15910/560,Hire 28.41 or 29 SS,S,Expressinga Ratio inEquivalent Forms,A punc
46、h recipe calls for fruit juice,ginger ale and vodka in the ratio of 3:2:1.,If you are looking to make 2 litres of punch for a party,how much of each ingredient is needed?,Expressinga Ratio inEquivalent Forms,LO 2.&3.,A punch recipe calls for mango juice,ginger ale and orange juice in the ratio of 3:
47、2:1.,3+2+1=6,Total Shares,2 litres/6=333 ml per share,M J,G A,O,*3,*2,*1,=1 litre,=667 mls,=333 mls,333 ml per share,A punch recipe calls for mango juice,ginger ale and orange juice in the ratio of 3:2:1.,If you have 1.14 litres of orange juice,how much punch can you make?,Punch,6,=,Punch=6*1.14 lit
48、res,=6.84 litres,You check the frige and determine that someone has been drinking the orange juice.You have less than half a bottle,about 500 ml.,How much fruit juice and ginger ale do you use if you want to make more punch using the following new punch recipe?Mango juice:ginger ale:orange juice=3:2
49、:1.5,How much fruit juice and ginger ale do you use if you want to make more punch using the following new punch recipe?:Mango juice:ginger ale:Orange juice=3:2:1.5,M J,G A,1.5,=,0.5,Mango Juice=3*0.5/1.5,=1 litre,1.5,=,0.5,Ginger Ale=2*0.5/1.5,=.667 litre=667 ml.,BUSINESS MATHEMATICS&STATISTICS,LEC
50、TURE 8Compound Interest Calculate returns from investmentsAnnuitiesExcel Functions,CUMIPMTReturns the cumulative interest paid between two periodsCUMIPMT(rate,nper,pv,start_period,end_period,type)Rate interest rate.Nper total number of payment periodsPv present value.Start_period first period in the
