Solver Calculations, Direct Solutions | HP 17bII manual

may be additional positive or negative answers, or no true solution at all. You can continue searching for other solutions by halting the calculation and entering a different guess.

One way to obtain a good guess for IRR% is to calculate NPV for various interest rates (I%). Since IRR% is the interest rate at which NPV equals zero, the best estimate of IRR% is the interest rate that yields the value for NPV closest to zero.

To find a good estimate for IRR%, key in a guess for IRR% and press Then, press to calculate NPV for that value. Repeat the calculation of NPV for several values of I%, and look for trends in the results. Choose as your guess for IRR% a value of I% that produces an NPV close to zero.

Solver Calculations

As noted in chapter12, the Solver uses two methods to find solutions, depending on the complexity of the equation: direct and iterative (an indirect). To use all the calculating power included in the Solver, it would help to understand, in a general way, how it works.

Direct Solutions

When you start a calculation (by pressing a menu key), the Solver first tries to find a direct solution by “isolating” the variable you are solving for (the unknown). Isolating a variable involves rearranging the equation so that the unknown variable is by itself on the left-hand side of the equation. For example, suppose you enter the equation:

P R O F I T = P R I C E － C O S T

If you’ve stored values for PROFIT and PRICE, pressing causes the Solver to internally rearrange the equation algebraically to solve for COST (COST is the unknown):

C O S T = P R I C E － P R O F I T

Answers calculated this way are called direct solutions.

240 B: More About Calculations

File name : English-M02-1-040308(Print).doc Print data : 2004/3/9

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HP 17bII manual Solver Calculations, Direct Solutions, O F I T = P R I C E － C O S T, S T = P R I C E － P R O F I T

Contents

Hp 17bII+ Financial Calculator Printing History Edition June January Welcome to the hp 17bII+ Welcome to the hp17bII+ Contents Error Messages Using Parentheses in CalculationsPower Function Exponentiation Saving and Reusing Numbers Time Value of Money Interest Rate ConversionsCash Flow Calculations Bonds Depreciation10 121 Running Total and Statistics 11 141 Time, Appointments, and Date Arithmetic 12 153 The Equation Solver 14 190 Additional Examples Assistance, Batteries, Memory, and Service More About Calculations Menu Maps RPN Summary RPN The Stack RPN Selected Examples Error Messages Index List of Examples List of ExamplesGeneral Business Calculations Currency Exchange Calculations Interest Rate Conversions Time, Alarms, and Date Arithmetic How to Use the Equation SolverBonds and Notes Running Total and Statistical Calculations Important Information Important Information Power On and Off Continuous Memory Adjusting the Display ContrastGetting Started Getting Started Setting the Language What You See in the DisplayKeys for language Key Description 18 1 Getting Started Shift Key @ Backspacing and Clearing Keys for Clearing Keys Display Description20 1 Getting Started Doing Arithmetic Keys DisplayDescription Using the Menu Keys Keying in Negative Numbers22 1 Getting Started Main Menu Menu Labels Menu Keys Main Menu Menu Label Operations Done Covered This Category 24 1 Getting Started Choosing Menus and Reading Menu Maps Using the MU%C menu 26 1 Getting StartedDisplaying the MU%C menu Calculations Using Menus Exiting Menus e Clearing Values in Menus28 1 Getting Started Solving Your Own Equations Solve = Cost Typing Words and Characters the ALPHAbetic Menu 30 1 Getting Started Editing ALPHAbetic Text Keys      Characters Calculating the Answer Calc Alphabetic Editing Operation Label or Key to PressKeyboard 32 1 Getting Started KeysDisplayDescription Controlling the Display Format Decimal PlacesInternal Precision Temporarily SHOWing ALL Rounding a Number Exchanging Periods and Commas in Numbers Error Messages Modes36 1 Getting Started Double Space. Press Calculator Memory @M Number of bytes Percentage of total Memory still free Arithmetic Calculator LineVDoing Calculations 38 2 Arithmetic VUsing Parentheses in Calculations Keys DisplayArithmetic VThe Percent Key Mathematical Functions40 2 Arithmetic VThe Power Function Exponentiation Shifted Math FunctionsKey Math Menu Math Menu Labels42 2 Arithmetic Description Saving and Reusing Numbers History Stack of Numbers VReusing the Last Result @L VKeys Display44 2 Arithmetic Storing and Recalling Numbers VKeys Display Description Keys New Register Contents Doing Arithmetic Inside Registers and VariablesArithmetic in Registers Scientific Notation Range of Numbers 48 2 Arithmetic Percentage Calculations Business Business Percentages BUS Menus Description Using the BUS Menus Examples Using the BUS MenusPercent Change %CHG 50 3 Percentage Calculations in Business Percent of Total %TOTL Markup as a Percent of Cost MU%C Markup as a Percent of Price MU%P52 3 Percentage Calculations in Business Sharing Variables Between Menus Currency Exchange Calculations Currx Menu54 4 Currency Exchange Calculation Selecting a Set of Currencies Currx MenuCurrency Exchange Calculation Menu Key Currencies United States Conversion Chart in US$ Entering a RateCurrency Rate Select CAN$ as currency 58 4 Currency Exchange Calculation Select HK$ as currency Converting Between Two Currencies Storing and Recalling Sets of CurrenciesExample Converting between Hong Kong and U.S Dollars Clearing the Currency Variables 60 4 Currency Exchange Calculation Time Value of Money TVM MenuTime Value of Money First Level of TVM Second Level of TVM TVM Menu Labels First LevelSecond Level Shortcut for N Multiplies the number in the display by Cash Flow Diagrams and Signs of Numbers 64 5 Time Value of Money FV is Using the TVM Menu 66 5 Time Value of Money Loan Calculations 68 5 Time Value of Money Figures and stores number @c  70 5 Time Value of Money Figures and stores Savings Calculations 000 72 5 Time Value of Money Figures and stores number Leasing Calculations 74 5 Time Value of Money  76 5 Time Value of Money Amortization Amrt Displaying an Amortization Schedule Amrt Menu LabelsLabel 78 5 Time Value of Money Time Value of Money 80 5 Time Value of Money Next successive set of payments authorized First year Printing an Amortization Table Table 82 5 Time Value of Money Calculates and prints Interest Rate Conversions 84 6 Interest Rate Conversions Icnv Menu Converting Interest RatesInterest Rate Conversions 86 6 Interest Rate Conversions Compounding Periods Different from Payment Periods 88 6 Interest Rate Conversions  90 6 Interest Rate Conversions Cash Flow Calculations Cflo menuCash Flow Calculations Cflo Menu Labels 92 7 Cash Flow Calculations Cash Flows Ungrouped Creating a Cash-Flow List 94 7 Cash Flow Calculations Entering Cash Flows For grouped cash flows The display now shows Prompting for #TIMES #T?. When the calculator displays 96 7 Cash Flow Calculations Viewing and Correcting the List Display Description Copying a Number from a List to the Calculator Line Naming and Renaming a Cash-Flow List98 7 Cash Flow Calculations Deleting Cash Flows from List. Pressing Clearing a Cash-Flow List and Its Name Starting or GETting Another ListViewing the Name of the Current List. Press , then e Cash-Flow Calculations IRR, NPV, NUS, NFV 100 7 Cash Flow Calculations Calc Menu for Cflo Lists Menu Label 102 7 Cash Flow Calculations Calculates NPV Group Number Amount 104 7 Cash Flow Calculations Prompts for next cash 106 7 Cash Flow Calculations Doing Other Calculations with Cflo Data Bonds Bond Menu108 8 Bonds Bond Menu Labels Menu Description LabelBonds Doing Bond Calculations 110 8 BondsTo calculate the price or yield of a bond Since there is no call on 112 8 Bonds MM.DDYYYY format Depreciation Deprc Menu114 9 Depreciation Deprc Menu Labels Depreciation Doing Depreciation Calculations DB, SOYD, and SL Methods116 9 Depreciation To calculate the depreciation for an asset Basis Salv 4,000 Acrs Method Year Percentage Deductible Keys Display Description118 9 Depreciation Partial-Year Depreciation Calendar Year Depreciation Value 120 9 Depreciation Running Total and Statistics Running Total and Statistics SUM Menu SUM Menu Labels122 10 Running Total and Statistics Creating a SUM List Entering Numbers and Viewing the Total 124 10 Running Total and Statistics Date Amount DateTransaction Naming and Renaming a SUM List 126 10 Running Total and Statistics Clearing a SUM List and Its Name Doing Statistical Calculations Calc Calculations with One Variable Calc Menu for SUM Lists Menu Key128 10 Running Total and Statistics Month Phone Expense Calculations with Two Variables Frcst 130 10 Running Total and Statistics Calc Total Mean Medn Stdev Range More MIN MAX Sort Frcst Frcst Menu Labels 132 10 Running Total and Statistics Curve Fitting and Forecasting Logarithmic Curve Fit 134 10 Running Total and Statistics To do curve fitting and forecasting Number of Minutes Dollar Sales RadioAdvertising Values 136 10 Running Total and Statistics Minutes Minutes Weighted Mean and Grouped Standard Deviation 138 10 Running Total and Statistics Summation Statistics Rent Doing Other Calculations with SUM Data 140 10 Running Total and Statistics Time, Appointments, Date Arithmetic Viewing the Time and DateTime, Appointments, and Date Arithmetic Time Menu Time Menu Labels142 11 Time, Appointments, and Date Arithmetic Setting the Time and Date SET SET Menu LabelsMenu Label Description Or DD.MMYYYY Adjusting the Clock Setting Adjst Changing the Time and Date Formats SET144 11 Time, Appointments, and Date Arithmetic Viewing or Setting an Appointment APT1-APT10 Menu Labels for Setting Appointments DescriptionAppointments Appt To set an appointment or view its current setting 146 11 Time, Appointments, and Date Arithmetic Acknowledging an Appointment Unacknowledged Appointments Clearing Appointments148 11 Time, Appointments, and Date Arithmetic To acknowledge a past-due appointment Date Arithmetic Calc Determining the Day of the Week for Any Date Calculating the Number of Days between DatesCalc Menu Labels for Date Arithmetic 150 11 Time, Appointments, and Date Arithmetic Calculating Past or Future Dates 152 11 Time, Appointments, and Date Arithmetic DATE2 Equation Solver Solver Example Sales ForecastsEquation Solver 154 12 The Equation Solver Next =OLD   Menu Label Solve Menu 156 12 The Equation SolverKeys Entering Equations Solve Menu LabelsTo make an entry into the Solver list Calculating Using Solver Menus Calc To do a calculation using a Solver menu158 12 The Equation Solver Rmenu label 160 12 The Equation Solver Eqty Editing an Equation Edit Naming an Equation Finding an Equation in the Solver List Shared VariablesClearing Variables 162 12 The Equation Solver Deleting Variables and Equations Deleting a variable is quite different from clearing it Writing Equations Deleting One Equation or Its Variables DeletDeleting All Equations or All Variables in the Solver @c 164 12 The Equation Solver 100 ⋅ C⋅ E What Can Appear in an Equation 166 12 The Equation Solver+ 5 ⋅ E Using the Alpha Menu Using a Typing Aid Solver Functions168 12 The Equation Solver Solver Functions for Equations Description DDAYSd1d2cal 170 12 The Equation Solver HH.MMSS formatIFcond expr 1 expr Svariable name Cfr c 1 c 2 s expr SIZECCFLO-listnameSIZESSUM-listname #TCFLO-listnameflow# 172 12 The Equation Solver Days Conditional Expressions with if OperatorKeys≥ = ≤ = ≠  174 12 The Equation Solver Rating Examples of Conditional EquationsVALUE＝FIRST＋1 ⎟ FIRST. If FIRST＝0, then VALUE＝FIRST Percent Salary Increase Summation Function ∑ 176 12 The Equation Solver Accessing Cflo and SUM Lists from the Solver Creating Menus for Multiple Equations S Function 178 12 The Equation Solver How the Solver Works Halting and Restarting the Iterative Search 180 12 The Equation Solver Entering Guesses 182 12 The Equation Solver  Printing 184 13 Printing Printer’s Power Source Double-Space PrintingPrinting the DisplayP Printing Printing Other Information @p Printing Variables, Lists, and Appointments ListPrinter Menu Labels 186 13 Printing    Printing Descriptive Messages MSG Trace Printing Trace188 13 Printing How to Interrupt the Printer Keys Print-out Additional Examples LoansSimple Annual Interest 190 14 Additional Examples Yield of a Discounted or Premium Mortgage Additional Examples 192 14 Additional Examples Figures and stores total Annual Percentage Rate for a Loan with Fees See appendix F for RPN keystrokes for the next two examples 11.5  194 14 Additional Examples @c e Loan with an Odd Partial First Period 196 14 Additional Examples Solver Equation for Odd-Period Calculations Canadian Mortgages 198 14 Additional Examples Solver Equation for Canadian Mortgages Advance Payments Leasing Solver Equation for Advance Payments Savings Value of a Fund with Regular Withdrawals200 14 Additional Examples Displays periodic Deposits Needed for a Child’s College Account 202 14 Additional Examples Additional Examples Flow of Withdrawals 204 14 Additional Examples For FLOW1 Value of a Tax-Free Account 206 14 Additional Examples 35  Value of a Taxable Retirement Account 208 14 Additional Examples Modified Internal Rate of Return 210 14 Additional Examples Group No. of Months Cash Flow, $ Flow no V8 /12 180000FLOW0 200000 I V13 /12 212 14 Additional Examples Price of an Insurance Policy Solver Equation for Insurance Price 214 14 Additional Examples Bonds Discounted Notes 216 14 Additional Examples Statistics Moving Average 218 14 Additional Examples Solver Equation for Moving Averages Chi-Squared χ2 Statistics UseIf necessary 220 14 Additional Examples If the expected values vary Keystroke Display Description Number Assistance, Batteries Memory, and Service Assistance, Batteries, Memory, and ServiceAnswers to Common Questions Obtaining Help in Operating the Calculator Assistance, Batteries, Memory, and Service Power and Batteries Low-Power IndicationsDo not use rechargeable batteries Installing Batteries Assistance, Batteries, Memory, and Service Managing Calculator Memory Resetting the Calculator Reset hole Erasing Continuous Memory For English languageFor the other languages Determining If the Calculator Requires Service Clock AccuracyEnvironmental Limits „ If the calculator won’t turn on Assistance, Batteries, Memory, and Service Confirming Calculator Operation Self-Test Warranty Assistance, Batteries, Memory, and Service Service Europe Country Telephone numbersAsia Pacific Country Telephone numbers America Country Telephone numbers HP Invent Regulatory information CanadaJapan More About Calculations IRR% CalculationsPossible Outcomes of Calculating IRR% More About Calculations Halting and Restarting the IRR% Calculation Storing a Guess for IRR% Direct Solutions Solver CalculationsO F I T = P R I C E － C O S T S T = P R I C E － P R O F I T E a ＝ L x W ＝ a R E a ⎟ W Iterative Solutions More About Calculations More About Calculations More About Calculations Equations Used by Built-in Menus Actuarial Functions Percentage Calculations in Business BUS Time Value of Money TVMAmortization Interest Rate Conversions Cash-Flow CalculationsNOM %  P NPV ＝ CF0 + ∑CFj x Uspv i% nj x Sppv i% Nj Bond Calculations NUS ＝ Uspv i% N Total ＝ ∑nj ⋅ CFj Depreciation Calculations DB ＝ Basis ⋅ Fact % /100 Sum and Statistics ForecastingModel Transformation Equations Used in Chapter SXY = Σ X− M SX 2 ⋅ SY Odd-Period Calculations Advance PaymentsModified Internal Rate of Return Menu Maps Menu Maps Figure C-2. Currx Menu Figure C-3. FIN Menu Figure C-3 . FIN Menu Figure C-4. SUM Menu Figure C-5. Time Menu Figure C-6. Solve Menu RPN Summary About RPNAbout RPN on the hp 17bII+ RPN Summary Setting RPN Mode To select RPN mode Press @  Where the RPN Functions Are Function Definition Key to Use Name~ same as Same as Arithmetic Topics Affected by RPN Mode Doing Calculations in RPNSimple Arithmetic ↓. Except in Cflo and SUM lists, Efunction and the key also 27 % To Calculate Press Display RPN Mode ALG Mode Calculations with STO and RCLChain Calculations－No Parentheses To Calculate Press Display RPN The Stack What the Stack IsRPN The Stack Reviewing the Stack Roll Down Exchanging the X- and Y-Registers in the Stack Arithmetic－How the Stack Does It How Enter Works Lost Clearing Numbers Reusing Numbers Last X RegisterRetrieving Numbers from Last Chain Calculations Solution 23 @w13 E9 *-7@t+ Exercises RPN Selected Examples RPN Selected Examples KeysDisplay   Calculates annual interest For E, press =, not #TIMES1 for FLOW1 I11 I  Annual payment deposit    Error Messages Error Messages Error Messages Error Messages                 Error Messages Index Special CharactersIndex 169 147 156 166 ,  31-32 174-76 145 149144 162-64 116 181-83 229Examples 133 168-71 138-39 ,  72-73213-15 239 242-46 , 132 , 109 , 49, 53 , 52, 128 , 128 , 128 , 128  Memory. See also Continuous Memory 143-44 , 101 , 101 , 101 , 157 , 56 , 56 , 56 , 42  92-94175 164-67 , 56 , 42 , 18 @p, 186 P PMT. See also Payments in TVM, 63 rounded amortization Repeating appointments past-due, 148 setting Using 128146-47 243-46 176 171 148 178 133-34 This regulation applies only to The Netherlands