Mathematics Number-Alteration Functions, 100 | HP 12C Financial 12C

Section 7

Mathematics and

Number-Alteration Functions

The hp 12c platinum provides several keys for mathematical functions and for altering numbers. These functions are useful for specialized financial calculations as well as for general mathematics calculations.

One-Number Functions

Most of the mathematics functions require that only one number be in the calculator (that is, the number in the display) before the function key is pressed. Pressing the function key then replaces the number in the display by the result.

Reciprocal. Pressing ycalculates the reciprocal of the number in the display — that is, it divides 1 by the number in the display.

Square. Pressing g¡calculates the square of the number in the display.

Square Root. Pressing gr calculates the square root of the number in the display.

Logarithm. Pressing g° calculates the natural logarithm (that is, the logarithm to the base e) of the number in the display. To calculate the common logarithm (that is, the logarithm to the base 10) of the number in the display,

calculate the natural logarithm, then press 10g°zin RPN mode and z10g°}in ALG mode.

Exponential. Pressing g> calculates the exponential of the number in the display — that is, it raises the base e to the number in the display.

Factorial. Pressing ge calculates the factorial of the number in the display — that is, it calculates the product of the integers from 1 to n, where n is the number in the display.

Round. The display format specifies to how many decimal places a number inside the calculator is rounded when it appears in the display; but the display format alone does not affect the number itself inside the calculator. Pressing fB, however, changes the number inside the calculator to match its displayed version. Thus, to round a number in the display to a given number of decimal places, temporarily set the display format (as described on page 87) to show the desired number of decimal places, then press fB.

100
File name: hp 12c pt_user's guide_English_HDPMF123E27	Page: 100 of 275
Printed Date: 2005/8/1	Dimension: 14.8 cm x 21 cm

Image 100

HP 12C Financial 12C manual Mathematics Number-Alteration Functions, One-Number Functions, 100

Contents

Hp 12c platinum financial calculator Printing History Introduction About This Handbook Financial Calculations in the United Kingdom For More Solutions to Financial ProblemsIntroduction Contents Contents Section Part II Programming 103 Part III Solutions 155 227 Appendix E Formulas Used 250 267 Making Financial Calculations Easy 48.00 500.0021,396.61 14.00 10,371.79 168.0011,024.82 42.03 Part Problem Solving Power On and Off Low-Power IndicationAdjusting the Display Contrast Getting Started Getting Started Keying in NumbersDigit Separators Negative Numbers Keying in Large Numbers 7814Backspacing 123.63 KeystrokesDisplay ALG mode 63+Clear Keys Keys Clears RPN mode ALG mode Undo OperationRPN and ALG Keys Example Keystrokes RPN mode Display Simple Arithmetic Calculations in RPN Mode13.00 Simple Arithmetic Calculations in ALG Mode Chain Calculations in RPN Mode Keystrokes RPN mode22.95 35.38 10.14 1053+ 30.00 42.00 Chain Calculations in ALG Mode Parentheses Calculations Storage Registers Keystrokes ALG mode 8zgØ5 1gÙ DisplayStoring and Recalling Numbers Later that same day … Keystrokes Display RPN mode 250.00Keystrokes Display 1250?0 500?2 Storage Register Arithmetic Clearing Storage Registers58.33 13.70 10.14053.00 064.54 Percentages in RPN Mode Percentage and Calendar FunctionsPercentage Functions 300 Percentages in ALG Mode Percentage and Calendar Functions 860.00 21,390.00283.40 22,673.40 Keystrokes ALG mode Display Percent Difference58.50 53.25 Percent of Total in RPN Mode 29.69 Percent of Total in ALG Mode Calendar Functions Date Format Future or Past Dates 14.05 11,09,2004 Number of Days Between Dates 11.09498.00 491.00 Basic Financial Functions Financial RegistersStoring Numbers into the Financial Registers Displaying Numbers in the Financial Registers Basic Financial Functions Simple Interest CalculationsClearing the Financial Registers 60.00 450.00455.25 455.18 Financial Calculations and the Cash Flow Diagram Basic Financial Functions Payment Mode Cash Flow Sign Convention Generalized Cash Flow Diagrams Basic Financial Functions Compound Interest Calculations Calculating the Number of Payments or Compounding Periods 35,000.00 Stores PV Sets the payment mode to End325.00 328.00 27.33181.89 143.11 327.00 141.87466.87 Recalls payment amount GÂ n Keystrokes ALG mode 775.0050.00 Stores FV 58.00 29.0050.00 977.27 4000 Keystrokes Display ALG mode 4000 22.73Calculating the Periodic and Annual Interest Rates 10,000.00 Stores FV Keystrokes RPN mode Keystrokes ALG mode Calculating the Present Value 9gC 450ÞP 1500+ 12.00 17,500.00540,000.00 369,494.09 243,400.00 Stores PV 200.00 60,000.00717.44 Calculating the Future Value Sets payment mode to End 5gA243400$ 243,400.00 1363.29ÞP -1,363.29 222,975.98 Amount of balloon payment 24.00 281.3432,000.00 28,346.96 Odd-Period Calculations Basic Financial Functions 135.17 0120045gC Z30+ 950.00 120.00GÒ z30+ §12 Basic Financial Functions 250,000.00 AmortizationKeystrokes Display FCLEAR G Enters 25 gC 250000 $ 498.12 970.91245,029.09 238.26 093.75 404.37360.00 380.51 Additional Financial Functions Discounted Cash Flow Analysis NPV and IRR Additional Financial Functions Calculating Net Present Value NPV Negative cash flow 130,000.00 212.18 Year Cash Flow 79,000.00 14,000.0011,000.00 10,000.00 Calculating Internal Rate of Return IRR 13.72 Reviewing Cash Flow Entries 100,000.00 500.00 14,000.00 79,000.00 Changing Cash Flow Entries 644.75 857.21 Bond Calculations Bond Price042018 120.38 122.13 Bond YieldTotal price, including accrued Depreciation Calculations 400.001f# 2f# 660.00 440.003f# Additional Operating Features Continuous Memory Additional Operating Features Status IndicatorsDisplay Number Display Formats 14.8746 14.9 14.87456320 Scientific Notation Display Format 487456 1487456320 Key in RPN Mode Special Displays Arithmetic Calculations With Constants Recovering From Errors in Digit Entry 429,000.00 Statistics Functions Accumulating Statistics Correcting Accumulated Statistics MeanStatistics Functions Register Statistic 32.00 40.0038.00 35.00 820.59 Standard Deviation463.00 Linear Estimation 28,818.93Keystrokes Display 48 gQ Estimated sales for a 48 hour Keystrokes RPN mode 0gR Display Keystrokes ALG mode 0gR 1gR~d-~ Display001 GR~d~ Weighted Mean One-Number Functions Mathematics Number-Alteration Functions100 258 Mathematics and Number-Alteration Functions3880000000 Power Function in ALG Mode Power Function in RPN ModeKeystrokes To CalculateDisplay ALG mode Part Programming Why Use Programs? Programming BasicsCreating a Program 104 Programming Basics 200150.00 155.00 Running a Program 001 002 003 004 005 006 007 625 473.75159 124.25 Program Memory Identifying Instructions in Program Lines Nnn Nnn, 44 Nnn,43,33,000Displaying Program Lines Instruction Keycode Mode and displays current line Pressing gÜdoes the reverse Keystrokes Display RPN modeSets calculator to Program Program memory Keystrokes Display 008,43,33,000 Program line 000 Instruction and Program Line Expanding Program Memory Programming Basics Setting the Calculator to a Particular Program Line Executing a Program One Line at a Time Program line 002 Program line 003Program line 004 b Program line 006 Program line 005 + Pausing During Program Execution Interrupting Program Execution 68.5 119 Keystrokes RPN mode ?+1 ?+2 ?+3 Keystrokes ALG mode?+1 ?+2 ?+3 001 002 004 005 006008 001 002 003 004 012, 44 40 950.61890.50 60.11 402.82 370.52Stopping Program Execution 003,44 004 005 006 FCLEAR² 13\68.5 18\72.9 24\85 Fourth item Simple Branching Branching and Looping125 Looping Branching and Looping 150,000.00 007,43,33,002782.47 593.75 593.75 005188.72 188.72 007,43,33,002 592.25 Conditional Branching190.22 Branching and Looping Recalls test value into X-register 006,43,33,008 004,43,33,007Stores income into register R9 006,43,33,009 008,43,33,010010 20,000.00 15,000.00 15,000.00 004,43,33,00715,000.00 007 20,000 20,000.00 007 25,00025,000.00 25,000.00 005 15,000 15,000.00 00515,000.00 006,43,33,009 15,000.00 009 012,43,33,000 Line 012 gi000 000.00 005, 43 34 Line 005 go 20,000.0020,000.00 009 Line 009 25,000.00 007 25.00 010 Changing the Instruction in a Program Line Program Editing139 Adding Instructions at the End of a Program Keystrokes RPN mode Keystrokes ALG mode Fs gi.006 DisplayProgram Editing 12,000.00 012013 014 Adding Instructions by Replacement Adding Instructions within a Program Fs 15000t 016 Adding Instructions by Branching Keystrokes RPN mode Fs gi.000 001,43,33,012011,43,33,000 Gi.010 014 015,43,33,000 016 012 013017,43,33,002 018 019 017,43,33,000020 021,43,33,000 022 Program Editing Storing Another Program Multiple Programs149 018,43,33,000 019 020 021 022023 024 025 026 027,43,33,019 029 030 031 032 025 026 027 028033,43,33,025 028 029 030 031 032 033 034,43,33,029034 035 036 037 038 039 040,43 33,035 Running Another Program Page Part Solutions Annual Percentage Rate Calculations With Fees Real Estate and Lending156 Real Estate and Lending 160,000.00908.46 156,800.00 159,250.00 156,050.00 Keystrokes Display RPN mode ALG mode 12§ §12³ Keystrokes Display RPN mode ALG mode FCLEARGPrice of a Mortgage Traded at a Discount or Premium 72.00 137.17 777.61312.00 657.97 252.00 Yield of a Mortgage Traded at a Discount or Premium300,000.00 096.57 210.00 Rent or Buy Decision 258,377.2418.00 12.11 000 001 002 003 004,44 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 RPN mode Registers Real Estate and Lending 165.00 700.00900.00 270,000.00 Keystrokes Display RPN mode ALG mode Yield Deferred Annuities46,048.61 15,218.35 750.00 600.0012,831.75 Investment Analysis Partial-Year DepreciationStraight-Line Depreciation 000 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025,43 026 027 028 029 030 031032,44 033,44 036 037 038 039 040 041,43,33036,44 037,43,33 Investment Analysis 125,000.00 666.67123,333.33 118,333.33 730.00 504.75Declining-Balance Depreciation 000 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021,43 022 023 024 025 026 027028,44 029,44 034 035 036 034 035 036 037 038 039 040 50,000.00 11,458.33 Sum-of-the-Years-Digits Depreciation 018 019 020 021 022 023 024 025,43,33026 027 028 029 030 031 035 036 037 038 039 040 042 043 044 500M Keystrokes Display RPN mode ALG mode FCLEARG 12000$25n Full- and Partial-Year Depreciation with Crossover 008 009 010 011 012 013 014 008 009 010 011?-0 032,43,33 033 034 035 036 037 038 039040,44 041,44 042 057,43,33 058 059 060 061 062063,44 064,43,33 080,44 081 082 083 084 085,43,33086 087 088 089 090 091 092 093 094,43,33 Keystrokes Display RPN mode ALG mode FCLEAR H 11000 $ 375.00 125.00406.25 804.69 Excess Depreciation 10,500.00312.50 531.25 Modified Internal Rate of Return Group # of Months Cash Flow $ 200,000.00657,152.37 775,797.83 Black-Scholes Formula for Valuing European Options Keystrokes Display Keystrokes Display 065 066 067 068 069 070 071,43,33,077073,44 074 075,44 076 077 078 089 090 091 092,44 093 094 095096,44 097 098 099 089,44 090 199 113 114,44 115 116 117118,43,33 Program Instructions 52.00 20.5414.22 71.15 10.00 20.00 Leasing Advance PaymentsSolving for Payment 202 Leasing 11.6464.45 000 001 008 009 010 011 012 013 014 015 016 017 008 009 010 011 012 013 014 015 016 017 018 019 65.43 66.86 Solving for Yield 57.0023,200.00 600 P 17.33 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016Annual yield as a Percentage Keystrokes ALG mode 017,45,4319.48 ? t Advance Payments With Residual 018 019 020 021 022 023 024 025 026 027 028 029 030 15.00 22,000.00487.29 520.81 34.00 710.0018.10 Keystrokes Display RPN mode ALG mode FCLEARG 25\ 25z 4nz¼ SavingsNominal Rate Converted to Effective Rate 213 002 003 004 005 006 007 008 Savings002 003 004 005 006 007 008 009 010 Effective Rate Converted to Nominal Rate ³ÞM¼ Keystrokes Display RPN mode ALG mode FCLEAR G N100 $ Continuous Rate Converted to Effective Rate105.35 35 +Þ +5.35 ³Þ Bonds 30/360 Day Basis Bonds001 002 003 004 005 006 007 008 009 010 011 012 013 217 014 015 016 017 018 019 020 021 022 023 024 025 026 027 029 030 031 032 033 034 035 036 037038,43,33 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 039 040 041 042 043 044 045 046 Bonds 219040,43,33 041 042 043 044 045 046 047 048 049 102.55 103.41 104.74 Annual Coupon Bonds 223 20 ?0 12.01 94.75Page Appendices RPN and the Stack 228 Getting Numbers Into the Stack The Key Appendix a RPN and the Stack Rearranging Numbers in the Stack Termination of Digit EntryStack Lift Key Two-Number Functions and the Stack One-Number Functions and the StackMathematics Functions Percentage Functions Calendar and Financial Functions Register Last X Register and the Key Arithmetic Calculations with Constants + 5 6 + 84,000 168,000.00336,000.00 672,000.00 Algebraic Mode ALG 237 Keying in Negative Numbers Appendix B Algebraic Mode ALG532.50 Key in ALG Mode History Stack in ALG Mode400.43 737.07 18.5 § 8zgØ 1250+7b To Calculate Keystrokes Display ALG mode Power FunctionPercent of Total More About L 243 Appendix C More About L Error 0 Mathematics Error Conditions245 Error 1 Storage Register Overflow Error 2 StatisticsError 3 IRR Error 4 Memory Error 5 Compound Interest OperationCondition Error 7 IRR Error 6 Storage RegistersOperation Condition Error 9 Service Error 8 CalendarPr Error Formulas Used PercentageInterest Simple Interest Appendix E Formulas Used Compound Interest Discounted Cash Flow Analysis Calendar Bonds 200 Depreciation DPN J Finite Compounding Interest Rate ConversionsContinuous Compounding Weighted Mean StatisticsLinear Estimation Standard Deviation Rent or Buy Decision Battery, Warranty, Service Information BatteryLow-Power Indication 259 Appendix F Battery, Warranty, and Service Information Installing a New Battery Verifying Proper Operation Self-Tests Appendix F Battery, Warranty, and Service Information Warranty Service Regulatory Information USA Temperature Specifications Noise DeclarationCanada Japan Mortgages United Kingdom Calculations267 Annual Percentage Rate APR Calculations Appendix G United Kingdom Calculations 269 Financial Function Key IndexStatistics Modes MathematicsNumber Alteration Stack Rearrangement 272 Programming Key Index Run Mode Active KeysPressed from Keyboard Subject Index 274 Subject Index Subject Index Subject Index Subject Index