Relative error less than 0.042% over the range 0 x, 114 | HP 12C

Relative error less than 0.042% over the range 0 < x < 5.5

Reference:

Stephen E. Derenzo, "Approximations for Hand Calculators Using Small Integer Coefficients," Mathematics of Computation, Vol. 31, No. 137, page 214-225; Jan 1977.

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HP 12C manual Relative error less than 0.042% over the range 0 x, Reference, 114

Contents

Page Introduction Refinancing Real Estate Wrap-Around Mortgage PMT Final cash flow Cash flow occurs 39 timesRate of return to lender Number of periods and monthly Before-Tax Cash Flows Income Property Cash Flow AnalysisDerivation of these cash flows follows a set sequence Before-Tax Reversions Resale Proceeds Vacancy LossDerivation of these reversions are as follows After-Tax Cash Flows Keystrokes Display 30-43 33-44 35-43 40-44 42-45 48-44 53-44 Registers 3291.75 ATCF1 After-Tax Net Cash Proceeds of Resale 18-44 33-44 39-44 48-43 Key in the number of years after purchase and press Atncpr Loan With a Constant Amount Paid Towards Principal LendingLoan Reduction Schedule Add-On Interest Rate Converted to APR APR Converted to Add-On Interest Rate Add-On Rate Loan with Credit Life Page 53-43 77-45 78-43 PMT PMT Credit life Interest Rebate Rule of 78s 26-43 Graduated Payment Mortgages Keystrokes Display 34-44 38-43 39-43 68-44 69-44 72-43 73-43 77-43 Keystrokes Display Variable Rate Mortgages Keystrokes Display Skipped Payments Group of payments is skipped Initial Deposit with Periodic Deposits Savings Periodic Deposits and Withdrawals FV = ? Cash flow diagram looks like this PV = Savings Account Compounded Daily Keystrokes Display 27-44 37-43 Compounding Periods Different From Payment Periods Clear 519.61 Future value Lease vs. Purchase Investment Analysis 16-44 18-44 27-44 30-45 32-45 34-45 Instructions Year Maintenance Lease Payment Tax Credit Buy Back 200 1700 1000 1500 300 750 Break-Even Analysis Profit To calculate the gross profit at a given volume Find the gross profit if 2500 units are sold 04-43 09-43 15-43 23-43 Gross Profit Operating Leverage 10-43 Profit and Loss Analysis 11-43 28-43 37-43 42-43 47-43 Page 100.00 48% tax rate Manufacturing cost $ After-Tax Yield Securities Purchase price Discounted Notes 30-43 Settl. date Maturity dtae Simple Moving Average Forecasting Keystrokes Display 26-45 29-45 30-44 32-45 33-44 Unused PV Unused PMT Unused FV Unused R .4 Unused 12-43 Seasonal Variation Factors Based on Centered Moving Averages 25-43 Sales in $K Quarterly 1st 2nd 3rd 4th 98.86 99.95 99.41 1st quarter average seasonal Variation, % 02-2 28-45 31-45 32-44 34-45 35-44 37-45 38-44 Gompertz Curve Trend Analysis 02-44 05-44 08-44 10-44 12-43 Page 71-43 Year III Forecasting with Exponential Smoothing 07-44 Page Forecasting Selecting the best smoothing constant α 22.00 23.00 23.25 25.25 23.69 27.13 25.95 Procedure is repeated for several αs Markup and Margin Calculations Pricing Calculations 02-43 14-43 Calculations of List and Net prices With Discounts 100 10.51 3rd discount rate % 05-44 06-43 16-43 Page Curve Fitting StatisticsExponential Curve Fit 100 101 102 Logarithmic Curve Fit 104 Power Curve Fit Formula that best expresses h as a function of t is Standard Error of the Mean Mean, Standard Deviation, Standard Error for Grouped Data 108 Use the following HP-12C program for the previous example 109 Chi-Square Statistics 111 112 Normal Distribution Reference Relative error less than 0.042% over the range 0 x114 115 116 Example Find Qx for x = 1.18 and x = Covariance117 118 Try the previous example using the following HP-12C program Permutation 120 121 Combination 122 Random Number Generator 123 Example Generate a sequence of 5 random numbers Homeowners Monthly Payment Estimator Personal Finance124 125 Following HP-12C program may be used instead of the above What if the down payment is increased to 20%? Example Solve the previous example using the HP-12C program126 127 Tax-Free Individual Retirement IRA of Keogh Plan 128 129 Stock Portfolio Evaluation and Analysis 131 132 133 134 Example Evaluate the following portfolio 135 Periodic Payment Amount Canadian Mortgages136 137 Number of Periodic Payments to Fully Amortize a MortgageEffective Interest Rate Yield Balance Remaining at End of Specified Period 138 Learning Curve for Manufacturing Costs Miscellaneous139 140 141 142 143 Queuing and Waiting Theory Intensity factor 145 146 147 148 149 150 AppendixReal Estate Wrap-Around Mortgage Add-On to APR with Credit Life LendingLoans with a constant amount paid towards Principal Add-On Interest Rate to APR 152 SavingsRule of 78s Rebate Skipped Payments Break-Even Analysis and Operating Leverage Investment AnalysisCompounding Periods Different From Payment Periods Lease vs. Purchase Discounted Notes Price given discount rate SecuritiesForecasting Profit and Loss Analysis Gompertz Curve Trend Analysis Simple Moving Average155 156 Forecasting With Exponential Smoothing 157 Pricing CalculationsForecast of next period expected usage Markup and Margin Calculations 158 Calculations of List and Net Prices with Discounts Statistics159 160 For tax-free investment Personal FinanceTax-Free Retirement Account IRA or Keogh Plan For ordinary taxable investment Learning Curve for Manufacturing Cost Canadian MortgagesMiscellaneous Portfolio beta coefficient Graduated Payment Mortgage Queuing and Waiting Theory163 + C 164