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HP 35s Scientific Miscellaneous Programs and Equations, Time Value of Money, TVM equation is

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17

Miscellaneous Programs and Equations

Time Value of Money

Given any four of the five values in the "Time–Value–of–Money equation" (TVM), you can solve for the fifth value. This equation is useful in a wide variety of financial applications such as consumer and home loans and savings accounts.

The TVM equation is:
⎡		−N ⎤	+ F(1+ (I 100))−N + B = 0
P⎢1− (1+ I 100)		⎥	+ F(1+ (I 100))−N + B = 0
⎣	I 100	⎦

Balance, B

		Payments, P
1	2	3	N_1

N

Future Value, F

The signs of the cash values (balance, B; payment, P; and future balance, F) correspond to the direction of the cash flow. Money that you receive has a positive sign while money that you pay has a negative sign. Note that any problem can be viewed from two perspectives. The lender and the borrower view the same problem with reversed signs.

Miscellaneous Programs and Equations 17-1

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HP 35s Scientific manual Miscellaneous Programs and Equations, Time Value of Money, TVM equation is

Contents

Users guide HP 35s scientific calculatorPrinting History Contents RPN The Automatic Memory Stack Viewing a Variable ContentsStoring Data into Variables Hyperbolic Functions Real-Number FunctionsQuotient and Remainder of Division Trigonometry Entering πEntering and Evaluating Equations FractionsVector Arithmetic 10-1 Solving EquationsIntegrating Equations Operations with Complex NumbersCreating Vectors from Variables or Registers 10-8 Base Conversions and Arithmetic and Logic 11-1Statistical Operations 12-1 10-7Simple Programming 13-1 Part 2. ProgrammingProgramming Techniques 14-1 Statistics Programs 16-1 Support, Batteries, and ServicePart 3. Appendixes and Reference Solving and Integrating Programs 15-1ALG Summary User Memory and the StackMore about Solving How the Integral Is Evaluated Round-Off ErrorMore about Integration Messages Operation IndexContents Part Page Turning the Calculator On and Off Adjusting Display ContrastGetting Started Important PreliminariesShifted Keys Highlights of the Keyboard and Display2Getting Started Left-shifted function Right-shifted Letter for alphabetic Alpha KeysCursor Keys Function Key4Getting Started  Clear or CancelBackspacing and Clearing Keys for ClearingClear menu       Key Description6Getting Started Using Menusˆ ˆ    HP 35s Menus Chapter NameOther functions Programming Instructions8 Exiting Menusor  KeysDisplay RPN and ALG Modes Keys Display10Getting Started RPN mode ALG modeUndo key 12Getting Started Display and AnnunciatorsFirst Line Second Line AnnunciatorsEQN HP 35s Annunciators Meaning Chapter14Getting Started Making Numbers Negative Keying in NumbersExponents of Ten z 16Getting Started  Understanding Entry CursorRange of Numbers and Overflow Single Argument or Unary Operations Performing Arithmetic Calculations18Getting Started  Two Argument or Binary OperationsKey RPN,RPN Program ALG, Equation, ALG Program Õ  Key RPN, RPN Program ALG, Equation, ALG Program Controlling the Display Format22Getting Started Periods and Commas in Numbers   24Getting Started Complex number display format  ,  , 8 8 SHOWing Full 12-Digit Precision8   8×Entering Fractions Fractions26Getting Started  Messages  ÉChecking Available Memory Calculator Memory28Getting Started Clearing All of Memory 30Getting Started What the Stack Is RPN The Automatic Memory StackRPN The Automatic Memory Stack 2RPN The Automatic Memory Stack Clearing the X-Register X and Y-Registers are in the DisplayReviewing the Stack Press  Exchanging the X- and Y-Registers in the Stack4RPN The Automatic Memory Stack Arithmetic How the Stack Does It 6RPN The Automatic Memory Stack How Enter WorksFilling the stack with a constant How to Clear the Stack8RPN The Automatic Memory Stack Last X RegisterCorrecting Mistakes with Last  Reusing Numbers with Last Ù    Chain Calculations in RPN ModeWork from the Parentheses Out     ExercisesOrder of Calculation      More Exercises    18RPN The Automatic Memory Stack Keys DisplayDescription AStoring Data into Variables Press letter-key  Storing and Recalling Numbers2Storing Data into Variables Press letter-key G  A  4Storing Data into Variables Using the MEM CatalogViewing a Variable VAR catalogD E CStorage arithmetic uses , , , or  Arithmetic with Stored VariablesStorage Arithmetic 6Storing Data into VariablesRecall Arithmetic E Exchanging x with Any Variable D D Variables I and JA 10Storing Data into Variables Real-Number Functions Exponential and Logarithmic Functions  Power FunctionsQuotient and Remainder of Division  Entering π Trigonometry4Real-Number Functions Setting the Angular ModeTrigonometric Functions Option Description Annunciator  Percentage Functions Hyperbolic Functions    Const Menu Items Description Value Physics Constants8Real-Number Functions Items Description Value Rectangular/Polar Conversions Conversion Functions10Real-Number Functions 30o 6 812Real-Number Functions Angle Conversions Time Conversions Unit Conversions Probability Probability FunctionsFactorial Gamma 16Real-Number Functions Absolute value Parts of NumbersInteger part Fractional partPressDisplay To calculate18Real-Number Functions Entering Fractions Fractions  Display Rules Fractions in the Display2Fractions Entered Value Internal Value Displayed Fraction Accuracy IndicatorsChanging the Fraction Display Setting the Maximum Denominator4Fractions  6Fractions Choosing a Fraction FormatTo Get This Fraction Format Change These Flags   jExamples of Fraction Displays Rounding FractionsFractions in Equations 10Fractions Fractions in Programs= .25 π d2 l Entering and Evaluating EquationsHow You Can Use Equations Entering and Evaluating Equations2Entering and Evaluating Equations    D Value   Key Operation Summary of Equation OperationsVariables in Equations Entering Equations into the Equation List4Entering and Evaluating Equations Functions in Equations Numbers in Equations Displaying and Selecting EquationsParentheses in Equations  Ö  8Entering and Evaluating Equations Editing and Clearing EquationsTypes of Equations 10Entering and Evaluating Equations Evaluating EquationsType of Equation Result for  Result for  Using Enter for Evaluation      Using XEQ for Evaluation12Entering and Evaluating Equations  Responding to Equation Prompts Operator Precedence Syntax of Equations14Entering and Evaluating Equations Equations Meaning Order Operation Example16Entering and Evaluating Equations Equation FunctionsΣxy Perimeter = a + b + h sin1θ + sin1φ RPN Operation Equation functionArea = 18Entering and Evaluating EquationsVerifying Equations Syntax Errors Õ 20Entering and Evaluating Equations Markup ⋅ Cost = Price Solving EquationsSolving an Equation Solving Equations= v0 t + 1/2 g t 2Solving Equations  G     P   P 6Solving Equations Solving built-in Equation Verifying the Result Understanding and Controlling Solve Choosing Initial Guesses for Solve Interrupting a Solve Calculation8Solving Equations Solving Equations Equation 10Solving Equations= 40 H ⋅ 20 H ⋅ 4 ⋅ H Type in the equationH   4H  value 12Solving Equations For More InformationIntegrating Equations Integrating Equations2Integrating Equations Integrating Equations FN  J0 x = π 0 cosx sin t dt= t 4Integrating Equations X  SinxX 6Integrating Equations Accuracy of IntegrationSpecifying Accuracy Interpreting Accuracy8        8Integrating Equations 8Form  Operations with Complex NumbersComplex Operations Complex Stack2Operations with Complex Numbers Functions for One Complex Number, z To Calculate Press 4Operations with Complex Numbers 8  68  6 6 6 Display DescriptionUsing Complex Numbers in Polar Notation 6Operations with Complex Numbers ?  ?  ? 6 ? ? Complex Numbers in Equations       Program lines ALG modeComplex Number in Program   Vector operations Vector ArithmeticVector Arithmetic     Õ 3 3  Absolute value of the vector10-4Vector Arithmetic Dot product   3 33   Angle between vectors Õ  3   Vectors in Equations10-6Vector Arithmetic Program lines Description Vectors in ProgramsThen hC Õ hA Creating Vectors from Variables or Registers10-8Vector Arithmetic Base Conversions and Arithmetic and Logic Base Conversions and Arithmetic and LogicBase Menu Menu label Description   11-2Base Conversions and Arithmetic and Logic Õ  Logic Menu Arithmetic in Bases 2, 8,11-4Base Conversions and Arithmetic and Logic          Representation of NumbersNegative Numbers  Range of Numbers    Using base in program and equationsWindows for Long Binary Numbers Entering Statistical Data Statistical OperationsStatistical Operations 12-2Statistical Operations Correcting Errors in Data EntryEntering One-Variable Data Entering Two-Variable DataInitial x, y Corrected x, y  Menu Key Description Statistical CalculationsMean Statistics Menus       Sample Standard Deviation Linear Regression Population Standard DeviationLinear Regression Menu  ˆ Õ ˆ12-8Statistical Operations        Limitations on Precision of Data12-10Statistical Operations Summation Statistics Summation Values and the Statistics Registers12-12Statistical Operations Access to the Statistics RegistersStatistical Operations 12-14Statistical Operations Programming Page Simple Programming Simple Programming13-2Simple Programming Area = πx2  X  Selecting a ModeKeysDisplay In ALG mode Designing a Program letter-key Using RPN, ALG and Equations in ProgramsProgram Boundaries LBL and RTN 13-4Simple ProgrammingStrengths of RPN Operations Data Input and Output13-6Simple Programming Entering a ProgramClear functions and backspace key A Function Names in Programs13-8Simple Programming  R  RPN modeE R13-10Simple Programming Running a ProgramExecuting a Program XEQ Keys Display Description RPN mode Testing a Program 13-12Simple Programming Entering and Displaying DataRPN mode ALG mode Using Input for Entering Data13-14Simple Programming Using View for Displaying Data   ÇR ÇH Using Equations to Display Messages13-16Simple Programming  V  S     Keys RPN mode R H V  R R H   V OL  A RE A  C  value Displaying Information without Stopping  13-18Simple ProgrammingInterrupting a Running Program Error StopsStopping or Interrupting a Program Programming a Stop or Pause STOP, PSE13-20Simple Programming Editing a ProgramViewing Program Memory Program MemoryCatalog of Programs MEM Memory Usage13-22Simple Programming Checksum Clearing One or More Programs  Nonprogrammable FunctionsProgramming with Base Decimal mode set Selecting a Base Mode in a ProgramNumbers Entered in Program Lines 13-26Simple Programming Polynomial Expressions and Horners MethodAx4 + Bx3 + Cx2 + Dx + E A    A X    13-28Simple Programming Programming Techniques Programming TechniquesRoutines in Programs Calling Subroutines XEQ, RTN14-2Programming Techniques Nested SubroutinesA2 + b2 + c2 + d2 14-4Programming Techniques Branching GTOA2 + B2 Programmed GTO Instruction Using GTO from the Keyboard14-6Programming Techniques Conditional InstructionsTest Menus Tests of Comparison x?y, x?014-8Programming Techniques Program Lines Description RPN modeMeanings of Flags FlagsClear Flag Fraction-Control Flags14-10Programming Techniques Programming Techniques 14-12Programming Techniques Flags Menu… takes the natural log of the X-input 14-14Programming Techniques  S  value   value Number F      Loops14-16Programming Techniques Conditional Loops GTO 14-18Programming Techniques Loops with Counters DSE, ISGProgramming Techniques Variables I and J Indirectly Addressing Variables and Labels14-20Programming Techniques Indirect Address, I and J 14-22Programming Techniques If I/J contains Then I/J will addressEquations with I/J Program Control with I/JUnnamed indirect variables 14-24Programming Techniques Solving a Program Solving and Integrating ProgramsSolving and Integrating Programs V= N x R x T 15-2Solving and Integrating ProgramsP  value   value Keys Display Description ALG modeProgram Lines Description ALG mode G   HP   L  15-6Solving and Integrating Programs Using Solve in a Program label  variable Integrating a Program Program Lines In RPN mode15-8Solving and Integrating Programs Sin  S   X15-10Solving and Integrating Programs Using Integration in a Program label   variable Restrictions on Solving and Integrating 15-12Solving and Integrating Programs Curve Fitting Statistics ProgramsStatistics Programs 16-2Statistics Programs = B + MInProgram Listing 16-4Statistics Programs    16-6Statistics Programs Determines if D001 or B001 should be run 16-8Statistics Programs   S         Logarithmic Exponential PowerNormal and Inverse-Normal Distributions 16-12Statistics Programs Qx = 0.5 − σ 12π xx e−x −x ⎟σ 2 ⎟2dxThis routine initializes the normal distribution program 16-14Statistics Programs Program LinesProgram Lines Program S 16-16Statistics Programs To the inverseD  16-18Statistics Programs Grouped Standard Deviation∑ x f   16-20Statistics Programs Statistics register Index variable used to indirectly address the correctRegister Summation Σ f Summation Σ x i f  U     16-24Statistics Programs TVM equation is Miscellaneous Programs and EquationsTime Value of Money Miscellaneous Programs and EquationsNÕ P4 II P  value KeysDisplay In RPN mode    17-4Miscellaneous Programs and Equations  17-6Miscellaneous Programs and Equations I   Prime Number Generator17-8Miscellaneous Programs and Equations Tests to see whether all possible factors have been tried 17-10Miscellaneous Programs and Equations  Cross Product in Vectors 17-12Miscellaneous Programs and Equations z 17-14Miscellaneous Programs and Equations Appendixes and Reference Page Answers to Common Questions Support, Batteries, and ServiceSupport, Batteries, and Service A-1 Calculator SupportEnvironmental Limits 2Support, Batteries, and ServiceChanging the Batteries Support, Batteries, and Service A-34Support, Batteries, and Service Testing Calculator OperationSelf-Test Support, Batteries, and Service A-56Support, Batteries, and Service Support, Batteries, and Service A-7 WarrantyCustomer Support 8Support, Batteries, and ServiceEmea Support, Batteries, and Service A-910Support, Batteries, and Service Invent Support, Batteries, and Service A-1112Support, Batteries, and Service Yyyy+ Support, Batteries, and Service A-1314Support, Batteries, and Service Managing Calculator Memory User Memory and the StackUser Memory and the Stack B-1 2User Memory and the Stack Resetting the CalculatorUser Memory and the Stack B-3 Clearing Memory4User Memory and the Stack DefaultStatus of Stack Lift CategoryNeutral Operations Disabling OperationsUser Memory and the Stack B-5 ˆ ˆ Status of the Last X Register6User Memory and the Stack Accessing Stack Register Contents 8User Memory and the Stack ALG Summary C-1 ALG SummaryAbout ALG ,Simple Arithmetic Doing Two argument Arithmetic in ALGPercentage Calculations Power FunctionsxÕ Parentheses CalculationsPermutations and Combinations Quotient and Remainder Of Division 4 Õ Hyperbolic functions Trigonometric FunctionsALG Summary C-7 Reviewing the StackOperations with Complex Numbers Integrating an Equation8ALG Summary ALG Summary C-9 66Õ4 6 8Ë4 66 Entering Statistical Two-Variable Data Z6 z Σ12ALG Summary ALG Summary C-13   ˆ Õ ˆ14ALG Summary How Solve Finds a Root More about SolvingMore about Solving D-1 Function Whose Roots Can Be Found 2More about SolvingMore about Solving D-3 Interpreting Results4More about Solving X  X X  X XX X XÕ  6More about Solving More about Solving D-7 X  X4 X Õ  X   When Solve Cannot Find a Root8More about Solving    XMore about Solving D-9 10More about Solving X    X More about Solving D-11 X4 X ÕÕ12More about Solving X   X   Round-Off ErrorMore about Solving D-13 14More about Solving How the Integral Is Evaluated More about IntegrationMore about Integration 2More about Integration Conditions That Could Cause Incorrect Results∞ xe−xdx 4More about Integration  More about Integration 6More about Integration   Conditions That Prolong Calculation Time8More about Integration More about Integration 10More about Integration Messages F-1 MessagesOr program. This might take a while 2MessagesMessages F-3    Solve include EQN and PGM modecannot find 4MessagesMessages F-5 FN each uses a level, they can also generate this error6Messages Name Keys and Description Operation IndexOperation Index G-1 Ø ×2Operation Index Operation Index G-3 4Operation Index = Denominator Operation Index G-56Operation Index  Fractional part Operation Index G-7Natural exponential label 8Operation Index  Integer part ISG variable variable Operation Index G-9 Input variable variableNatural logarithm 10Operation Index LBL label labelDegrees to radians. Returns 2π/360 Operation Index G-11RCL variable  Pause12Operation Index Operation Index G-13 XEQ label label 14Operation IndexHyperbolic Tangent View variable variableOperation Index G-15 ÕÕ≠ Õ≤11-4 16Operation Index=y? 14-7 Menu ≠0?Operation Index G-17 Power18Operation Index Index-1 IndexIndex-2 EQN List TOP 6-7, F-2 Index-3Index-4 Index-5 Index-6 Index-7 Index-8 Index-9 Index-10 Angle between two vectors Index-11Index-12