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7: Statistical Calculations 89

Contents

user’s guide Notice REGISTER YOUR PRODUCT AT: www.register.hp.com Welcome to the HP 10BII Hewlett-PackardQuality Features Contents Page Page Page Page Page At a Glance Basics—Ata Glance Percentages—Ata Glance Memory Keys—Ata Glance… Time Value of Money (TVM)—Ata Glance… TVM What if…—Ata Glance… Amortization—Ata Glance… Interest Rate Conversion—Ata Glance… IRR/YR and NPV—Ata Glance… Statistics—Ata Glance… QXPEHU0 QXPEHUA 0A 0A *4 –10.00 1,420.00 Keyboard Map Page Getting Started Power On and Off Adjusting the Display Contrast Simple Arithmetic Calculations QXPEHUNH\VWDUWVDQHZFDOFXODWLRQ "d 3UHVVLQJ GLVSOD\V ï &DOFXODWHï $GGV Understanding the Display and Keyboard Cursor Clearing the Calculator Clearing Memory Annunciators Shift Key Statistics Key INPUT Key SWAP Key Math Functions QXPEHU Display Format of Numbers Specifying Displayed Decimal Places Scientific Notation Displaying the Full Precision of Numbers Interchanging the Period and Comma Rounding Numbers Messages Business Percentages Percent Key Finding a Percent Adding or Subtracting a Percent Percent Change Margin and Markup Calculations Margin Calculations Markup on Cost Calculations Using Margin and Markup Together Number Storage and Arithmetic Using Stored Numbers in Calculations Using Constants Operation 6WRUHV´QXPEHUµDVFRQVWDQW 6WRUHV´²QXPEHUµDVFRQVWDQW 6WRUHV´ïQXPEHUµDVFRQVWDQW 6WRUHV´¸QXPEHUµDVFRQVWDQW Using the M Register Using Numbered Registers Doing Arithmetic Inside Registers *!"UHJLVWHUQXPEHU *!dUHJLVWHUQXPEHU Doing Arithmetic Power Operator Using Parentheses in Calculations µ d* 1RFDOFXODWLRQ\HW &DOFXODWHV² &DOFXODWHV Picturing Financial Problems How to approach a Financial Problem Signs of Cash Flows Periods and Cash Flows Simple and Compound Interest Simple Interest Compound Interest Interest Rates Two Types of Financial Problems Recognizing a TVM Problem PV = 150,000.00 I/YR = 7.5% N = 360 (30 × 12) PMT = -1,041.40 FV = -10,000.00 Recognizing a Cash Flow Problem Page Time Value of Money Calculations Using the TVM Application Clearing TVM Begin and End Modes Loan Calculations *b "P 6WRUHVQXPEHURI SHULRGVLQORDQ 13,000.00 \HDUV .7.50 (2 –930.00 6WRUHVLQWHUHVWUDWH 133,006.39 Example: A Mortgage With a Balloon Payment. <RX·YHREWDLQHGD 6ROYHWKLVSUREOHPXVLQJWZRVWHSV &DOFXODWHWKHORDQSD\PHQWXVLQJD\HDUWHUP &DOFXODWHWKHUHPDLQLQJEDODQFHDIWHU\HDUV Step 1. )LUVWFDOFXODWHWKHORDQSD\PHQWXVLQJD\HDUWHUP WKHQVWRUHV P 48.006WRUHV\HDUWHUP P / –163,388.39 2 –164,812.45 Savings Calculations 6HWVPWR\HDUV 3,035.28 \HDUV I/YR = 6.3% N = 360 (15 years × 24 half-months) FV SHU\HDU (2 –80.00 6WRUHVUHJXODU GHSRVLWV Lease Calculations FV = 7,500.00 Money received by lessor is positive I/YR = 10% PV I/YR = 9% N PMT = -2,400.00 (48th payment due up front) (2 –2,400.00 6WRUHVPRQWKO\ 95,477.55 YDOXHRIPRQWKO\ Amortization PER 180,000.00 6WRUHVIXWXUHYDOXH –1,289.54 0 12 –1,579.82 $PRUWL]HWKHVHFRQG\HDU –1,706.69 –13,767.79 176,713.49 'LVSOD\V35,1DQGWKH 25– –220.21 –90.21 9,193.28 54– Interest Rate Conversions Investments With Different Compounding Periods Compounding and Payment Periods Differ Step 1. &DOFXODWHWKHHTXLYDOHQWUDWHZLWKPRQWKO\FRPSRXQGLQJ SHULRGVSHU\HDU Step 2. &DOFXODWHWKHIXWXUHYDOXH 6WRUHVSUHVHQWYDOXH 6WRUHVSD\PHQW 2,519.61 Cash Flow Calculations How to Use the Cash Flow Application 11,765.29 Flows received are positive -2,000.00 Flows paid out 11,765.29 QRPLQDO\LHOG 0RQWKO\\LHOG 76 6: Cash Flow Calculations NPV and IRR/YR: Discontinuing Cash Flows Organizing Cash Flows Entering Cash Flows Viewing and Replacing Cash Flows Calculating Net Present Value I/YR = 15% 10,000 5,000 7,500 WKH,NH\ RFFXUUHQFHV 5,000.00 IORZ FDOFXODWHWKHQHWSUHVHQWYDOXH 27,199.92 H[DPSOHRQSDJH 7KLVUHVXOWVKRZVWKDWLI\RXZDQWD\LHOGRISHU\HDU\RXVKRXOGSD\ NPV = 27,199.92 Calculating Internal Rate of Return Automatic Storage of IRR/YR and NPV Statistical Calculations Clearing Statistical Data Entering Statistical Data One-VariableStatistics Two-VariableStatistics and Weighted Mean Correcting Statistical Data Correcting One-VariableData Correcting Two-VariableData Summary of Statistical Calculations Mean, Standard Deviations, and Summation Statistics A A d)+ *T 'LVSOD\VΣ[ 'LVSOD\VQ Linear Regression and Estimation (QWHUWKH[\GDWDXVLQJWKHLQVWUXFWLRQVRQSDJH (QWHUWKHNQRZQ[YDOXHRU\YDOXH Week Minutes of Advertising Sales 0A IRUFRQVHFXWLYHZHHNV 0A *4 'LVSOD\VVORSH Weighted Mean Page Additional Examples Business Applications Setting a Sales Price Forecasting Based on History Cost of Not Taking a Cash Discount Loans and Mortgages Simple Annual Interest Continuous Compounding Yield of a Discounted (or Premium) Mortgage Step 1. &DOFXODWH3070DNHVXUH)9 ( –100,000.00 6WRUHVRULJLQDODPRXQWRI PRUWJDJH DIWHU\HDUV Annual Percentage Rate for a Loan With Fees 7KHORDQZLOOEH –1,230.26 &DOFXODWHVSD\PHQW 156,800 6XEWUDFWVSRLQWV &DOFXODWHV$35 Loan With a Partial (Odd) First Period Automobile Loan Canadian Mortgages What if … TVM Calculations –3,555.00 (QWHUVQHZSD\PHQW IRUHYHU\WZRZHHNV ELZHHNO\SD\PHQWV WRSD\RIIORDQ Savings Saving for College Costs DQQXDOUDWH 2 15,000.00 DQQXQFLDWRULVQRWGLVSOD\HG 6WRUHVDQQXDO ZLWKGUDZDO Gains That Go Untaxed Until Withdrawal 6HWWR%HJLQPRGH3UHVV*OLIBEGINDQQXQFLDWRULVQRWGLVSOD\HG P VWDUWZLWK DQQXDOSD\PHQW 387,640.45 2"P Value of a Taxable Retirement Account Cash Flow Examples Wrap-AroundMortgages 1 1 ² CF0 –35,000.00 2(, CF1 Net Future Value CF6 –29,203.14 YDOXH139 39 34,800.58 Assistance, Batteries, and Service Answers to Common Questions Environmental Limits Power and Batteries Low Power Annunciator Battery Specifications Installing Batteries Accessing the battery compartment LQFRUUHFWO\UHSODFHG Warning 5HSODFHRQO\ZLWKWKHVDPHW\SHRIEDWWHU\RUZLWK KD]DUGRXVFKHPLFDOV ,QVHUWWKHQHZEDWWHULHVPDNLQJVXUHWKDWWKHSRVLWLYHVLJQ RQHDFKEDWWHU\LVIDFLQJRXWZDUG Determining if the Calculator Requires Service Limited One-YearWarranty What Is Covered What Is Not Covered Consumer Transactions in the United Kingdom If the Calculator Requires Service Obtaining Service Service Charge Shipping Instructions Warranty on Service Service Agreements Regulatory Information End-userterms and conditions HP 10B II Calculator Warranty period: 12 months HP warrants to you, the Hewlett-Packard For consumer transactions in Australia and New Zealand Page More About Calculations IRR/YR Calculations Possible Outcomes of Calculating IRR/YR Halting and Restarting IRR/YR Entering a Guess for IRR/YR Effect of Using Σ– to Correct Data Range of Numbers Equations Margin and Markup Calculations Time Value of Money (TVM) Amortization Interest Rate Conversions Cash-FlowCalculations Statistics Page Messages running 5XQQLQJ$FDOFXODWLRQLVLQSURFHVV UFLO 8QGHUIORZ$QLQWHUPHGLDWHUHVXOWLQ790LVWRRVPDOOIRUWKH+3 138 C: Messages Index Special Keys O BEGIN , %X\RXWYDOXH &DQDGLDQPRUWJDJHV H[DPSOHV *XDUDQWHH *XHVVLQJ,55<5 ,QLWLDOFDVKIORZ 0 INT 139 URXQGLQJ VWRULQJ 2GGILUVWSD\PHQW W 6KLIWNH\ 6LJQFKDQJLQJ 6LPSOHLQWHUHVW 6ORSH 6TXDUHURRW 6TXDUHV 6WDQGDUGGHYLDWLRQ , SRSXODWLRQ VDPSOH 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