HP 12C Financial 12C 258 Appendix E: Formulas Used

PMT

258 Appendix E: Formulas Used

The Rent or Buy Decision

Market Value = PRICE(1 + I)n where:

I= appreciation per year (as decimal)

n= number of years

Net Cash Proceeds on Resale = Market Value – Mortgage Balance – Commission

The interest rate is obtained by solving the financial (compound interest) equation for i using:

= number of years house is owned = down payment + closing costs

= mortgage payment + taxes + maintenance – rent – (% tax) (interest + taxes)

FV = net cash proceeds on resale

Annual interest rate = 12 × i

File name: hp 12c pt_user's guide_English_HDPMF123E27	Page: 258 of 275
Printed Date: 2005/8/1	Dimension: 14.8 cm x 21 cm

Contents

Edition HP part number F2232-90001 Notice Introduction 4 Introduction Financial Calculations in the United Kingdom For More Solutions to Financial Problems Contents Part I: Problem Solving 6Contents Section 3: Basic Financial Functions Section 4: Additional Financial Functions Section 5: Part II: Programming Part III: Solutions Section 15: Savings Nominal Rate Converted to Effective Rate Effective Rate Converted to Nominal Rate Continuous Rate Converted to Effective Rate Appendices Appendix E: Formulas Used Appendix F: Battery, Warranty, and Service Information Appendix G: United Kingdom Calculations Function Key Index Programming Key Index Subject Index Example 1: zn: the number of compounding periods zi: the interest rate per compounding period zPV: the present value of a compounded amount zPMT: the periodic payment amount Making Financial Calculations Easy Note: running Display fCLEARHf2 14 Making Financial Calculations Easy 10,371.79 Example 3: Keystrokes Display 11,024.82 Part Problem Solving Getting Started Section 1: Getting Started Keying in Numbers Digit Separators Negative Numbers 18 Section 1: Getting Started Keying in Large Numbers Backspacing KeystrokesDisplay (RPN mode) gÚgÚ KeystrokesDisplay (ALG mode) .63+ The CLEAR Keys Key(s)Clears: 20 Section 1: Getting Started Undo Operation The RPN and ALG Keys To select RPN mode: RPN Simple Arithmetic Calculations in RPN Mode Keystrokes (RPN mode) 22 Section 1: Getting Started Simple Arithmetic Calculations in ALG Mode Keystrokes (ALG mode) (ALG mode) –13.54 gr§ Chain Calculations in RPN Mode Example: Solution: 24 Section 1: Getting Started 1,064.54 Your hp 12c platinum calculates the answer in just the same way in RPN mode: 3\4§ 12.00Step 1: Multiply the numbers in the first parentheses 5\6§ Step 2: Multiply the numbers in the Chain Calculations in ALG Mode 1,400.43 Parentheses Calculations (5 − 1) 8zgØ5 Storage Registers Storing and Recalling Numbers 28 Section 1: Getting Started 1,250.00 (RPN mode) 7,500.00 8,000.00 Clearing Storage Registers Storage Register Arithmetic 30 Section 1: Getting Started 1,053.00 Percentage and Calendar Functions 32 Section 2: Percentage and Calendar Functions Percentages in ALG Mode Section 2: Percentage and Calendar Functions Net Amount in RPN Mode 23,250.00 1,860.00 21,390.00 34 Section 2: Percentage and Calendar Functions Percent Difference –8.97 Percent of Total in RPN Mode 36 Section 2: Percentage and Calendar Functions Percent of Total in ALG Mode Calendar Functions Date Format Month-Day-Year 38 Section 2: Percentage and Calendar Functions For example, to key in April 7, 2004: Day-Month-Year 1.Key in the one or two digits of the day 3.Key in the two digits of the month 11,09,2004 40 Section 2: Percentage and Calendar Functions Number of Days Between Dates Basic Financial Functions 42 Section 3: Basic Financial Functions Clearing the Financial Registers Simple Interest Calculations 1.Key in or calculate the number of days, then press n 2.Key in the annual interest rate, then press ¼ 3.Key in the principal amount, then press Þ$ 4.Press fÏ to calculate and display the interest accrued on a 360-daybasis Section 3: Basic Financial Functions –450.00 fÏd 44 Section 3: Basic Financial Functions Financial Calculations and the Cash Flow Diagram Page 46 Section 3: Basic Financial Functions The Cash Flow Sign Convention The Cash Flow Sign Convention: The Payment Mode BEGIN Generalized Cash Flow Diagrams 48 Section 3: Basic Financial Functions Compound Interest Calculations Specifying the Number of Compounding Periods and the Periodic Interest Rate Calculating the Number of Payments or Compounding Periods 50 Section 3: Basic Financial Functions total n equal fCLEARG 10.5gC 35000$ Number of payments required 12z Twenty-sevenyears and four months z12} Twenty-sevenyears and four months 52 Section 3: Basic Financial Functions +:P –141.87 –466.87 gÂ n –775.00 –50.00 4,000.00 4,000.00 Stores FV 54 Section 3: Basic Financial Functions z2} 4,027.27 Calculates FV – which equals the balance in the account if 58 full deposits were made –22.73 Calculating the Periodic and Annual Interest Rates 8\4§w –6,000.00 10,000.00 Stores FV 56 Section 3: Basic Financial Functions §4} Calculating the Present Value 19,198.60 20,698.60 58 Section 3: Basic Financial Functions 17,500.00 540,000.00 –369,494.09 Calculating the Payment Amount 243,400.00 Stores PV 243,400.00 –1,363.29 60 Section 3: Basic Financial Functions –3,200.00 60,000.00 –717.44 Calculating the Future Value 5gA 243400$ 243,400.00 1363.29ÞP –1,363.29 –222,975.98 62 Section 3: Basic Financial Functions 2gA 1,281.34 2Þ¼ –2.00 Odd-PeriodCalculations 64 Section 3: Basic Financial Functions noninteger n Page: 64 of 5gC 4,500.00 –135.17 66 Section 3: Basic Financial Functions z30+ gÒ z30+ §12} 3,950.00 –120.00 68 Section 3: Basic Financial Functions To obtain an amortization schedule: 3.Enter the amount of the loan (the principal), using $ Key in the periodic payment, then press 5.Press g× or (for most direct reduction loans) gÂ to set the payment mode 6.Key in the number of payments to be amortized 70 Section 3: Basic Financial Functions –1,498.12 –13,006.53 –4,970.91 245,029.09 1f –1,093.75 –404.37 –1,091.98 –406.14 Additional Financial Page Page Page Page Page Page Page Page Page Page Page Page Page Additional Operating Features Section 5: Additional Operating Features The Display Status Indicators Number Display Formats 88 Section 5: Additional Operating Features Standard Display Format Scientific Notation Display Format Mantissa Display Format 90 Section 5: Additional Operating Features Special Displays Running Overflow and Underflow The Key in RPN Mode Arithmetic Calculations With Constants 1,095.00 92 Section 5: Additional Operating Features Recovering From Errors in Digit Entry 429,000.00 9,987 9,987.00 Statistics Functions 94 Section 6: Statistics Functions Register Statistic Correcting Accumulated Statistics Mean Section 6: Statistics Functions Salesperson Hours/Week Sales/Month 21,714.29 Standard Deviation x-value after gv is pressed; to display the standard deviation of the y-values,press 4,820.59 Standard deviation of sales Linear Estimation 28,818.93 98 Section 6: Statistics Functions gR~d gR~d-~} 0gR 1 gR~d Weighted Mean Mathematics and Number-AlterationFunctions Section 7: Mathematics and Number-AlterationFunctions Integer Fractional 102 Section 7: Mathematics and Number-AlterationFunctions The Power Function in RPN Mode To Calculate 2Þ\3q –8.00 2\3yq Programming Programming Basics Section 8: Programming Basics 000 106 Section 8: Programming Basics 001 002 Running a Program Page 108 Section 8: Programming Basics Program Memory Identifying Instructions in Program Lines Instruction Keycode nnn ?=0 nnn,44 110 Section 8: Programming Basics 008,43,33,000 112 Section 8: Programming Basics The 000 Instruction and Program Line Expanding Program Memory Page 114 Section 8: Programming Basics Setting the Calculator to a Particular Program Line gi gi.000 Executing a Program One Line at a Time Page 116 Section 8: Programming Basics Interrupting Program Execution Pausing During Program Execution 118 Section 8: Programming Basics Section 8: Programming Basics ?+1 :0 b ?+2 ?+3 :0 b 120 Section 8: Programming Basics gu ?+1 :0 b gu ?+2 gu ?+1 :0 b gu ?+2 003,44 012,44 40 1,312.20 1,400.77 2,040.00 2,177.70 122 Section 8: Programming Basics 6,370.52 Stopping Program Execution 012,44 t t t 124 Section 8: Programming Basics Branching and Looping 126 Section 9: Branching and Looping Looping f! gu Section 9: Branching and Looping 007,43,33,002 150,000.00 –782.47 128 Section 9: Branching and Looping –593.75 –188.72 –593.00 –189.47 Conditional Branching 130 Section 9: Branching and Looping RPN program notes: f] fs 132 Section 9: Branching and Looping 004,43,33,007 006,43,33,008 ALG program notes: f[ fs :1 b 006,43,33,009 008,43,33,010 010 20,000.00 134 Section 9: Branching and Looping 15,000.00 3,000.00 20,000 25,000 25,000.00 006,43,33,008 Line 006: gi008 6,250.00 136 Section 9: Branching and Looping 012,43,33,000 Line 012: gi000 005, 43 34 Line 005: go 138 Section 9: Branching and Looping Program Editing 140 Section 10: Program Editing :2?6 fs gi.006 Adding Instructions at the End of a Program Section 10: Program Editing fs gi.008 fs gi.011 12,000.00 012 Adding Instructions within a Program Adding Instructions by Replacement Page 144 Section 10: Program Editing 016 Adding Instructions by Branching ~gogi fs gi.000 gi.010 001,43,33,012 011,43,33,000 146 Section 10: Program Editing 015,43,33,000 017,43,33,002 6,500.00 gi.016 go gi000 ?9 001,43,33,018 017,43,33,000 018 148 Section 10: Program Editing Multiple Programs 150 Section 11: Multiple Programs gi.017 018,43,33,000 021 023 Section 11: Multiple Programs 027 028 029 030 152 Section 11: Multiple Programs ?0 :0 f! gu gi.033 033 034,43,33,029 Running Another Program Page Solutions Real Estate and Lending Section 12: Real Estate and Lending ALG Mode: RPN: ALG: 160,000.00 158 Section 12: Real Estate and Lending :$750 :$-750 159,250.00 156,050.00 Price of a Mortgage Traded at a Discount or Premium 160 Section 12: Real Estate and Lending 9gC 9gC Discount rate (into i) 137.17P Yield of a Mortgage Traded at a Discount or Premium –300,000.00 162 Section 12: Real Estate and Lending 2,096.57 -42n –250,000.00 Calculate the remaining balance of the loan after five years 5gA Number of periods to be amortized 258,377.24 164 Section 12: Real Estate and Lending ?.1 004,44 017 Page: 164 of Page 166 Section 12: Real Estate and Lending 046 047 048 049 1.Key in the program 2.Key in the estimated down payment then press ?1 3.Key in the life of the mortgage then press ?2 4.Key in the annual mortgage interest rate then press ?3 5.Key in the estimated monthly taxes then press ?4 168 Section 12: Real Estate and Lending 7,000.00 3,700.00 270,000.00 53,095.65 Deferred Annuities 0gJ 0gK 8ga 15,218.35 170 Section 12: Real Estate and Lending 5ga 6ga 12,831.75 Investment Analysis Page Section 13: Investment Analysis 041,43,33 036,44 037,43,33 045,43,33 174 Section 13: Investment Analysis 6.Key in the year desired then press 7.Key in the number of months in the first year and press t.* The display will show the amount of depreciation for the desired year. If desired, press ~to see the remaining depreciable value then press 125,000.00 1,666.67 123,333.33 5,000.00 118,333.33 176 Section 13: Investment Analysis 6,730.00 Declining-BalanceDepreciation Page 178 Section 13: Investment Analysis 7.Key in the year desired then press Key in the number of months in first year 7.Key in the year desired then press ³ Key in the number of months in first year* and press 10.For a new case press gi000 and return to step 180 Section 13: Investment Analysis 11,458.33 Sum-of-the-Years-DigitsDepreciation Page 182 Section 13: Investment Analysis 7.Key in the number of months in first year* then press t.† The display Key in the number of months in first year* then press 9.For a new case press gi000 and return to step 12000$ Page: 183 of Full- and Partial-YearDepreciation with Crossover Page Page Page Page R1: Dep R3: Used R4: Used R5: Used R6: Used 190 Section 13: Investment Analysis First year depreciation desired 1,375.00 9,125.00 Excess Depreciation -gØ 10,500.00 1,312.50 8,531.25 Modified Internal Rate of Return Group # of Months Cash Flow ($) 0gK5ga 0gK9ga Black-ScholesFormula for Valuing European Options Reference: Page Page Page Page 113 114,44 115 116 117 200 Section 13: Investment Analysis :gAn :gC¼ :P§ 12gr§P Page Leasing Section 14: Leasing 3?0-n 1ÞP –1.00 $:0+ 204 Section 14: Leasing ?2t Þ$P 206 Section 14: Leasing Solving for Yield :P§+$ ?0n §:P³+ 015,45,43 208 Section 14: Leasing :gC 017,45,43 ? t Advance Payments With Residual 210 Section 14: Leasing 22,000.00 §30b³?3 6,600.00 ?1t 212 Section 14: Leasing –4,710.00 1,500.00 fL12§ fL§12³ Savings 214 Section 15: Savings Section 15: Savings Effective Rate Converted to Nominal Rate +ÞM¼ :n§ ³ÞM¼ §:n³ Continuous Rate Converted to Effective Rate g>à Bonds Page Section 16: Bonds 040,43,33 220 Section 16: Bonds Page 222 Section 16: Bonds Annual Coupon Bonds Page 224 Section 16: Bonds –4.58 –94.75 Page Appendices RPN and the Stack Appendix A: RPN and the Stack Getting Numbers Into the Stack: The Key 230 Appendix A: RPN and the Stack Termination of Digit Entry replaces Stack Lift Rearranging Numbers in the Stack The Key Pressing ~ exchanges the numbers in the X- and Y-registers roll down One-NumberFunctions and the Stack Two-NumberFunctions and the Stack Mathematics Functions 232 Appendix A: RPN and the Stack Percentage Functions Calendar and Financial Functions Register 234 Appendix A: RPN and the Stack The LAST X Register and the Key LAST Arithmetic Calculations with Constants 2 236 Appendix A: RPN and the Stack 84,000 Enters base amount into displayed X-register 168,000.00 Algebraic Mode (ALG) 238 Appendix B: Algebraic Mode (ALG) Keying in Negative Numbers () –75 –532.50 The Key in ALG Mode not new digit entry executed 240 Appendix B: Algebraic Mode (ALG) +d} Page 242 Appendix B: Algebraic Mode (ALG) Percent of Total The Power Function To Calculate Display More About L 244 Appendix C: More About L Searching for IRR :gt Error Conditions 246 Appendix D: Error Conditions Error 1: Storage Register Overflow Error 2: Statistics Error 3: IRR Error 4: Memory Appendix D: Error Conditions Error 5: Compound Interest OperationCondition 248 Appendix D: Error Conditions Error 6: Storage Registers Error 7: IRR Error 8: Calendar Error 9: Service Refer to Appendix F Pr Error Improper date format or illegal date Formulas Used I360 = 360n ⋅ PV ⋅ I365 = 365n ⋅ PV ⋅ 0 = PV + (1+ iS) ⋅ PMT ⋅ ⎢ PMT ∑ INT = ∑ INTj = INT1 + INT2 + ... + INTn ∑ PRN = ∑ PRNj = PRN1 + PRN2 + ... + PRNn PVn = PV0 + ∑ PRN NPV = CF CF2 CPN DSM Depreciation DPNJ SBV − SAL DPN SOYD DPNJ = (L − j + 1) ⋅ (SBV − SAL) NOM ⎞C EFF = ⎜1+ EFF = (eNOM − 1) yˆ = A + Bx − Bx sx = n∑ x2 − (∑ x )2 258 Appendix E: Formulas Used Battery, Warranty, and Service Information 260 Appendix F: Battery, Warranty, and Service Information Installing a New Battery Appendix F: Battery, Warranty, and Service Information Verifying Proper Operation (Self-Tests) For a calculator that does not respond to keystrokes: The display will show For a calculator that does respond to keystrokes: 1.With the calculator off, hold down the ;key and press § 262Appendix F: Battery, Warranty, and Service Information Page: 262 of Warranty 264 Appendix F: Battery, Warranty, and Service Information Service Regulatory Information USA 266 Appendix F: Battery, Warranty, and Service Information Canada Japan Temperature Specifications Noise Declaration Disposal of Waste Equipment by Users in Private Household in the European Union United Kingdom Calculations 268 Appendix G: United Kingdom Calculations Annual Percentage Rate (APR) Calculations Function Key Index 270 Function Key Index Financial CLEAR GClears contents of financial registers (page 42) (page 46) Sets payment mode to End for compound interest calculations involving payments Function Key Index (page 99) (page 96) (page 97) Modes Programming Key Index Programming Key Index (page 114) (page 109) (page 113) Pressed from Subject Index with Constants, arithmetic calculations with 47, 86, 88, 112 Continuous rate , 37–40 , 84 276 Subject Index Page 278 Subject Index