HP 12c Platinum Reference Manual
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HP 12c Platinum Reference Manual

Hp 12c platinum: reference guide
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See also: Instructions for Use Manual , Operating Instructions
HP 12C Platinum
Solutions Handbook
HP would like to thank the following for their contribution:
Tony Hutchins, Wellington, NZ
Luiz Vieira, UNIPAC, Brazil
Gene Wright, Lipscomb University, USA
NOTICE
Hewlett-Packard Company makes no express or implied warranty with regard to the keystroke
procedures and program material offered or their merchantability or their fitness for any
particular purpose. The keystroke procedures and program material are made available
solely on an "as is" basis, and the entire risk as to their quality and performance is with the
user. Should the keystroke procedures or program material prove defective, the user (and not
Hewlett-Packard Company nor any other party) shall bear the entire cost of all necessary
correction and all incidental and consequential damages. Hewlett-Packard Company shall not
be liable for any incidental or consequential damages in connection with or arising out of the
furnishing, use, or performance of the keystroke procedures or program material.
© Hewlett-Packard Development Company, L.P.
rev. 03.04

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  • Page 1 HP 12C Platinum Solutions Handbook HP would like to thank the following for their contribution: Tony Hutchins, Wellington, NZ Luiz Vieira, UNIPAC, Brazil Gene Wright, Lipscomb University, USA NOTICE Hewlett-Packard Company makes no express or implied warranty with regard to the keystroke procedures and program material offered or their merchantability or their fitness for any particular purpose.

  • Page 2: Introduction

    About This Handbook This HP 12C Platinum Solutions Handbook has been designed to supplement the HP 12C Platinum Owner's Handbook by providing a variety of applications in the financial area. Programs and/or step-by-step keystroke procedures with corresponding examples in each specific topic are explained.

  • Page 3: Using The Rpn Programs On The Hp-12C

    ALG alternative is then indicated parenthetically. Usage of \(³) To activate the ³ key it is sufficient just to press \, with the HP 12C Platinum in ALG mode. In step-by-step and program instructions where the only difference between the modes is that \ is used in RPN mode and ³...

  • Page 4: Table Of Contents

    Introduction ... 2 About This Handbook... 2 Presentation of Algebraic and RPN ... 2 Using the RPN Programs on the HP-12C ... 3 Contents... 4 Real Estate ... 7 Refinancing... 7 Wrap-Around Mortgage ... 8 Income Property Cash Flow Analysis... 12 Before-Tax Cash Flows ...
  • Page 5 Forecasting...74 Simple Moving Average ...74 Seasonal Variation Factors Based on Centered Moving Averages ...78 Gompertz Curve Trend Analysis...83 Forecasting with Exponential Smoothing ...87 Pricing Calculations ...92 Markup and Margin Calculations...92 Calculations of List and Net prices With Discounts...95 Statistics...98 Curve Fitting ...98 Exponential Curve Fit ...98 Logarithmic Curve Fit...102 Power Curve Fit ...104...
  • Page 6 Contents Section 15: Nominal Rate Converted to Effective Rate ... 152 Section 16: 30/360 Day Basis Bonds ... 153 Section 16: Annual Coupon Bonds ... 154 Appendix B: Formulas Used... 155 Real Estate ... 155 Wrap-Around Mortgage ... 155 After-Tax Cash Flows... 155 After-Tax Net Cash Proceeds of Resale...

  • Page 7: Real Estate

    What are the NPV and effective yield to the lender on the net amount of cash actually advanced? What is the NPV to the borrower on this amount if he can earn a 15.25% equity yield rate on the net proceeds of the loan? 12c platinum / 12C RPN Keystrokes g gÂ...

  • Page 8: Wrap-Around Mortgage

    8 Real Estate 12c platinum / 12C RPN Keystrokes 9.5gC 9.5gC 200000Þ$ 200000Þ$ :0+P +:0P 133190+?0 +133190³?0 11.5gC$ 11.5gC$$ -:0³ :0$¼ :0$¼ 12§ §12³ 15.25gC$ 15.25gC$$ -:0³ Wrap-Around Mortgage A wrap-around mortgage is essentially the same as a refinancing mortgage, except that the new mortgage is granted by a different lender, who assumes the payments on the existing mortgage, which remains in full force.
  • Page 9 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes g g fCLEARG fCLEARG 8-gA 8³gA 6.75gC 6.75gC 200132.06$ 200132.06$ 10gC 10gC 300000Þ$ 300000Þ$ :0+P +:0P 200132.06+$ +200132.06$ -99,867.94 ¼12§ ¼§12³ Sometimes the wrap around mortgage will have a longer payback period than the original mortgage, or a balloon payment may exist.
  • Page 10 240th month of $129,963.35. If you, as a lender, accept the proposal, what is your rate of return? $125010 $1681.71 $ -1051.61 200 mos. $ -200000 12c platinum / 12C RPN Keystrokes g fCLEARG 200000Þ\ 125010+gJ 1051.61Þ\ 1681.71+...
  • Page 11 12c platinum / 12C RPN Keystrokes gK99ga gFgK 39ga ~129963.35+ fL12§ If you, as a lender, know the yield on the entire transaction, and you wish to obtain the payment amount on the wrap-around mortgage to achieve this yield, use the following procedure.

  • Page 12: Income Property Cash Flow Analysis

    12 Real Estate 12c platinum / 12C RPN Keystrokes g g fCLEARG fCLEARG 200n12gC 200n12gC 1051.61ÞP 1051.61ÞP $74990+ $+74990³ Þ$ Þ$ 240n 240n 129963.35MP 129963.35MP 200000Þ$¼ 200000Þ$¼ 12§ §12³ Income Property Cash Flow Analysis Before-Tax Cash Flows The before-tax cash flows applicable to real estate analysis and problems are: •...

  • Page 13: Before-Tax Reversions (Resale Proceeds)

    The property has just been financed with a $700,000 mortgage, fully amortized in a level monthly payments at 11.5% over 20 years. a. What is the Effective Gross Income? b. What is the Net Operating Income? c. What is the Cash Throw-Off to Equity? 12c platinum / 12C RPN Keystrokes ALG Keystrokes g gÂ...

  • Page 14: After-Tax Cash Flows

    The After-Tax Cash Flow for the initial and successive years may be calculated by the following HP 12C Platinum program. This program calculates the Net Operating Income using the Potential Gross Income, operational cost and vacancy rate. The Net Operating...
  • Page 15 The user is able to change the method of finding the depreciation from declining balance to straight line. To make the change, key in fV at line 032 (ALG: 026) of the program in place of f#. 12c platinum / 12C RPN KEYSTROKES fCLEARÎ...
  • Page 16 16 Real Estate 12c platinum / 12C RPN KEYSTROKES 036, 037, 038, 039, 040,44 40 041, 042,45 48 043, 044, 045, 046, 047, 048,44 40 049, 050, 051, 052, ?§0 053,44 20 054, § 055, 056, 057, 058, § 059,...
  • Page 17 2.5% growth rate. The depreciable value is $75,000 with a projected useful life of $20 years. Assuming a 125% declining balance depreciation, what are the After-Tax Cash Flows for the first 10 years if the investors Marginal Tax Rate is 35%? 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes gÂ...
  • Page 18 18 Real Estate 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes 3291.75?3 3291.75?3 75000?4 75000?4 20?5 20?5 125?6 125?6 35?7 35?7 2.5?9 2.5?9 5?.0 5?.0 Example 2: An office building was purchased for $1,400,000. The value of depreciable improvements is $1,200,000 with a 35 year economic life.

  • Page 19: After-Tax Net Cash Proceeds Of Resale

    The After-Tax Net Cash Proceeds of Resale (ATNCPR) is the after-tax reversion to equity; generally, the estimated resale price of the property less commissions, outstanding debt and any tax claim. The After-Tax Net Cash Proceeds can be found using the HP 12C Platinum program which follows. 12c platinum...
  • Page 20 (ALG: 039) in place of fV. This means that all of the actual depreciation from purchase to sale is then treated as "excess" or unrecaptured depreciation. This is illustrated below in Example 2. 12c platinum / 12C RPN KEYSTROKES fCLEARÎ...
  • Page 21 12c platinum / 12C RPN KEYSTROKES 028, 029, 030, 031, 032, 033,44 40 034, 035, 036, § 037, 038, 039, 040, 041, 042,44 40 043, 044, 045, g(000 046,43,33,000 § n: Used i: Used FV: Used : Dep. value : CGTR Program Instructions: Key in the program and press fCLEARH.
  • Page 22 A $700,000 loan for 20 years at 9.5% annual interest was used to purchase the complex. When it was purchased the depreciable value was $750,000 with a useful life of 25 years. Using 125% declining balance depreciation, what are the After-Tax Net Cash Proceeds in year 10? 12c platinum / 12C RPN Keystrokes g gÂ...
  • Page 23 12c platinum / 12C RPN Keystrokes 25?4 25?4 125?5 125?5 48?6 48?6 19.2?7 19.2?7 900000\ 900000³ 1750000\ 1750000³ 8³ Example 2: Now, re-do the previous example assuming all depreciation is treated as excess or unrecaptured depreciation, with MTR=25% and CGTR=15%.

  • Page 24: Lending

    Loan With a Constant Amount Paid Towards Principal This type of loan is structured such that the principal is repaid in equal installments with the interest paid in addition. Therefore each periodic payment has a constant amount applied toward the principle and a varying amount of interest. Loan Reduction Schedule If the constant periodic payment to principal, annual interest rate, and loan amount are known, the total payment, interest portion of each payment, and remaining balance after...

  • Page 25: Add-On Interest Rate Converted To Apr

    6-year maturity. What is the loan reduction schedule for the first year? (Constant payment to principal is $5000 semi-annually). What is the fourth year's schedule (skip 4 payments)? 12c platinum / 12C RPN Keystrokes ALG Keystrokes 5000?0...

  • Page 26: Apr Converted To Add-On Interest Rate

    Key in the amount of the loan and press $ Press ~³ÞP . Press ¼§12³ to obtain the APR. Example 1: Calculate the APR and monthly payment of a 12% $1000 add-on loan which has a life of 18 months. 12c platinum / 12C RPN Keystrokes g g fCLEARG...

  • Page 27: Add-On Rate Loan With Credit Life

    §12³Þ Add-On Rate Loan with Credit Life This HP 12C Platinum program calculates the monthly payment amount, credit life amount (an optional insurance which cancels any remaining indebtedness at the death of the borrower), total finance charge, and annual percentage rate (APR) for an add-on interest rate (AIR) loan.
  • Page 28 Lending 12c platinum / 12C RPN KEYSTROKES § 011, 012, 013, 014, § 015, 016, § 017, 018, 019, 020, § 021, 022, 023, 024, 025, 026, § 027, 028, 029, 030, Þ 031, 032, 033, 034, 035, § 036, Þ...
  • Page 29 12c platinum / 12C RPN KEYSTROKES 055, 056, 057, 058, 059, 060, 061, 062, 063, 064, 065, 066, 067, Þ 068, 069, 070, 071, 072, 073, 074, 075, ¼ 076, 077,45,43 g(000 078,43,33,000 n: N i: i FV: 0 : Loan...

  • Page 30: Interest Rebate - Rule Of 78'S

    Example 1: You wish to quote a loan on a $3100 balance, payable over 36 months at an add-on rate of 6.75%. Credit life (CL) is 1%. What are the monthly payment amount, credit life amount, total finance charge, and APR? 12c platinum / 12C RPN Keystrokes fCLEARG...
  • Page 31 -25³?2 1+180§ +1§180³ :1g’+:1 §:1+ z~~§ z:2§ :2³ 39.33:2§ 39.33§:2 -~³ The following HP 12C Platinum program can be used to evaluate the previous example. 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001, 002, 003, 004, 005, 006, 007,...

  • Page 32: Graduated Payment Mortgages

    Lending 12c platinum / 12C RPN KEYSTROKES g(000 026,43,33,000 ~ N: Unused i: Unused FV: Unused : Fin. charge : Unused Program Instructions: Key in the program. Key in the number of months in the loan and press \(³). Key in the payment number when prepayment occurs and press \(³).
  • Page 33 Given the term of the mortgage (in years), the annual percentage rate, the loan amount, the percentage that the payments increase, and the number of years that the payments increase, the following HP 12C Platinum program determines the monthly payments and remaining balance for each year until the level payment is reached.
  • Page 34 Lending 12c platinum / 12C RPN KEYSTROKES 037, g(040 038,43,33,040 :2 g(025 039,43,33,025 ³ 040, 041, 042, 043, 044, 045, 046, 047, 048, 049, 050, 051, 052, 053, 054, 055, § 056, Þ 057, 058, 059, 060, 061, 062, 063, 064, Þ...
  • Page 35 12.5%. The monthly payments will be graduating at an annual rate of 5% for the first 5 years and then will be level for the remaining 25 years. What are the monthly payment amount for the first 6 years? 12c platinum / 12C 12c platinum RPN Keystrokes...

  • Page 36: Variable Rate Mortgages

    The period and limits to interest rate increases vary from state to state. Each periodic adjustment may be calculated by using the HP 12C Platinum with the following keystroke procedure. The original terms of the mortgage are assumed to be known.
  • Page 37 With a 30 year term, his current monthly payment is $495.15. When the interest rate is adjusted from 11.5% to 11.75%, what will the monthly payment be? If the monthly payment remained unchanged, find the revised remaining term on the mortgage. 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes gÂ...

  • Page 38: Skipped Payments

    Lending Skipped Payments Sometimes a loan (or lease) may be negotiated in which a specific set of monthly payments are going to be skipped each year. Seasonally is usually the reason for such an agreement. For example, because of heavy rainfall, a bulldozer cannot be operated in Oregon during December, January, and February, and the lessee wishes to make payments only when his machinery is being used.
  • Page 39 January, February, and March (months 4 thru 6). If the current interest rate is 14%, what is the monthly payment necessary to amortize the loan? 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes gÂ...

  • Page 40: Savings

    Example: You have just opened a savings account with a $200 deposit. If you deposit $50 a month, and the account earns 5 ¼ % compounded monthly, how much will you have in 3 years? 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes gÂ...

  • Page 41: Number Of Periods To Deplete A Savings Account Or To Reach A Specified Balance

    You wish to withdraw $300 a month until the account is depleted. How long will this take? If you wish to reduce the account to $5000, how many withdrawals can you make? 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes gÂ...

  • Page 42: Periodic Deposits And Withdrawals

    5 ½% compounded monthly. Your current balance is $1023.25. How much will you have accumulated in 5 months? The cash flow diagram looks like this: - 50 PV = - 1023.25 12c platinum / 12C RPN Keystrokes g g fCLEARG fCLEARG 50ÞP...
  • Page 43 You increase your monthly deposit to $65. How much will you have in 3 months? The cash flow diagram looks like this: - 65 PV = - 1219.22 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes Þ$ Þ$ 65ÞP...

  • Page 44: Savings Account Compounded Daily

    Savings Account Compounded Daily This HP 12C Platinum program determines the value of a savings account when interest is compounded daily, based on a 365 day year. The user is able to calculate the total amount remaining in the account after a series of transactions on specified dates.
  • Page 45 12c platinum / 12C RPN KEYSTROKES 032, 033, 034, 035, Þ 036, g(013 037,43,33,013 g(013 N: ∆days i: i/365 FV: Used : Initial date : Interest : Unused Program Instructions: Key in the program. Press fCLEARH and press gÕ. Key in the date (MM.DDYYYY) of the first transaction and press \(³).

  • Page 46: Compounding Periods Different From Payment Periods

    HP 12C Platinum. In savings plans however, money may become available for deposit or investment at a frequency different from the compounding frequencies offered. The HP 12C Platinum can easily be used in these calculations. However, because of the assumptions mentioned the periodic interest rate must be adjusted to correspond to an equivalent rate for the payment period.
  • Page 47 Example 1: Solving for future value. Starting today you make monthly deposits of $25 into an account paying 5% compounded daily (365-day basis). At the end of 7 years, how much will you receive from the account? 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes g×...
  • Page 48 Example 2: Solving for payment amount. For 8 years you wish to make weekly deposits in a savings account paying 5.5% compounded quarterly. What amount must you deposit each week to accumulate $6000. 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes g×...

  • Page 49: Investment Analysis

    The following HP 12C Platinum program assumes that the purchase is financed with a loan and that the loan is made for the term of the lease. The tax advantages of interest paid, depreciation, and the investment credit which accrues from ownership are compared to the tax advantage of treating the lease payment as an expense.
  • Page 50 Investment Analysis 12c platinum / 12C RPN KEYSTROKES 023, ¼ 024, 025, fÝ 026, 027,44 40 028, 029, 030,45 48 031, 032,45 48 033, 034,45 48 ¼ 035, 036, 037, § 038, 039, 040, 041, 042, 043, 044, 045, 046,...
  • Page 51 - Key in the annual interest rate and press ¼. - Key in the loan amount (purchase price) and press Þ$. - Press P to find the annual payment. Key in the marginal effective tax rate RPN: Key in the discount rate or cost of capital ALG: Key in the discount rate or cost of capital Key in the depreciable value and press ?5.
  • Page 52 Because lease payments are made in advance and standard loan payments are made in arrears the following cash flow schedule is appropriate for a lease with the last payment in advance. Year Maintenance 1500 12c platinum / 12C RPN Keystrokes ALG Keystrokes g g fCLEARH fCLEARH 10n12¼...

  • Page 53: Break-Even Analysis

    12c platinum / 12C RPN Keystrokes ALG Keystrokes 1500\ 1500³ 1700t 1700t 300\ 300³ 1700t 1700t 300\ 300³ 1700t 1700t 300\ 300³ 1700t 1700t 300\0t 300³0t 300\0t 300³0t 750\ 750³ 1:3-§ 1-:3§~³ 390.00 g(043t g(036t Break-Even Analysis Break-even analysis is basically a technique for analyzing the relationships among fixed costs, variable costs, and income.
  • Page 54 Investment Analysis The variables are: fixed costs (F), Sales price per unit (P), variable cost per unit (V), number of units sold (U), and gross profit (GP). One can readily evaluate GP, U or P given the four other variables. To calculate the break-even volume, simply let the gross profit equal zero and calculate the number of units sold (U).
  • Page 55 $12,000. The variable cost per copy, including printing and marketing the books are $6.75 per copy. The sales price per copy is $13.00. How many copies must be sold to break even? 12c platinum / 12C 12c platinum RPN Keystrokes...
  • Page 56 12c platinum RPN Keystrokes ALG Keystrokes 12000\ 12000+ 4500+ 4500z 2500z 2500+ 6.75+ 6.75³ For repeated calculation the following HP 12C Platinum program can be used. 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001, 002, 003, g(000 004,43,33,000 ³ 005, §...
  • Page 57 12c platinum / 12C RPN KEYSTROKES 019, 020, 021, 022, g(000 023,43,33,000 :4 n: Unused I: Unused FV: Unused : Unused Program Instructions: 1. Key in the program and store the known variables as follows: Key in the fixed costs, F and press ?1.
  • Page 58 $35,000 to produce. Each mirror has a variable cost of $8.25. The price of mirrors is tentatively set at $12.50 each. What volume is needed to break even? 12c platinum / 12C 12c platinum RPN Keystrokes...

  • Page 59: Operating Leverage

    Example 1: For the data given in example 1 of the Break-Even Analysis section, calculate the operating leverage at 2000 units and at 5000 units when the sales price is $13 a copy. 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes 6.75-...
  • Page 60 Investment Analysis For repeated calculations the following HP 12C Platinum program can be used: 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001, 002, 003, § 004, 005, 006, 007, 008, 009, g(000 010,43,33,000 Þ n: Unused i: Unused FV: Unused...

  • Page 61: Profit And Loss Analysis

    Profit and Loss Analysis The HP 12C Platinum may be programmed to perform simplified profit and loss analysis using the standard profit income formula and can be used as a dynamic simulator to quickly explore ranges of variables affecting the profitability of a marketing operation.
  • Page 62 Investment Analysis 12c platinum / 12C RPN KEYSTROKES 025, 026, § 027, g(000 028,43,33,000 à 029, Þ 030, 031, 032, 033, 034, 035, § 036, g(000 037,43,33,000 ³ 038, 039, 040, 041, g(000 042,43,33,000 :6 043, 044, 045, § 046,...
  • Page 63 Example: What is the net return on an item that is sold for $11.98, discounted through distribution an average of 35% and has a manufacturing cost of $2.50? The standard company operating expense is 32% of net shipping (sales) price and tax rate is 48%. 12c platinum / 12C 12c platinum RPN Keystrokes...
  • Page 64 Investment Analysis If manufacturing expenses increase to $3.25, what is the effect on net profit? 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes 3.25?3 3.25?3 g(012tt g(012tt 58.26 g(043t g(039t If the manufacturing cost is maintained at $3.25, how high could the overhead (operating...

  • Page 65: Securities And Options

    Securities and Options After-Tax Yield The following HP 12C Platinum program calculates the after-tax yield to maturity of a bond held for more than one year. The calculation assumes an actual/actual day basis. For after-tax computations, the interest or coupon payments are considered income, while the difference between the bond's face value and its purchase price is considered capital gains.
  • Page 66 Securities and Options 12c platinum / 12C RPN KEYSTROKES 030, g(000 031,43,33,000 fs n: Unused i: Yield FV: 0 : Used : Coupon rate : Capital rate : Used : Unused Program Instructions: Key in the program. Key in the purchase price and press ?1.

  • Page 67: Discounted Notes

    A note is a written agreement to pay a sum of money plus interest at a certain rate. Notes do not have periodic coupons, since all interest is paid at maturity. A discounted note is a note that is purchased below its face value. The following HP 12C Platinum program finds the price and/or yield...
  • Page 68 For a new case, go to step 3. Example 1: Calculate the price and yield on this bill: settlement date October 8, 2002; maturity date March 21, 2003; discount rate 7.80%. Compute on a 360 day basis. 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes gÕ...

  • Page 69: Black-Scholes Formula For Valuing European Options

    Example 2: Determine the yield of this security; settlement date June 25, 2002; maturity date September 10, 2002; price $99.45; redemption value $101.33. Assume 360 day basis. 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes 6.252002?1 6.252002?1 9.102002?2 9.102002?2...
  • Page 70 Securities and Options 12c platinum / 12C RPN KEYSTROKES g° 017, 018, 019, 020, 021, 022, 023, 024, 025, 026, 027, 028, 029, § 030, 031, 032, 033, 034, Þ 035, g> 036, 037, 038, 039, 040, 041, 042, 043,...
  • Page 71 12c platinum / 12C RPN KEYSTROKES § 061, 062, 063, 064, 065, 066, 067, 068, 069, 070, g(077 071,43,33,077 + 072, 073,44 30 Þ 074, ?§3 075,44 20 076, 077, 078, g(089 079,43,33,089 b 080, 081, 082, § 083, 084,...
  • Page 72 Securities and Options 12c platinum / 12C RPN KEYSTROKES n: Term to expiry i: Interest rate (%) FV: Strike price R Unused : N(d : Put value : Unused The n, i and PMT values must all be based on the same time unit (for example: n is Note: measured in years or months and i and PMT are rates per year or per month).
  • Page 73 ½% per month. Show how to re-scale n, i and PMT to use a yearly time unit, and how to re-scale them back again to the original monthly basis. 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes .5¼...

  • Page 74: Forecasting

    A simple moving average may be calculated with your HP 12C Platinum as follows. 1. Press fCLEARH. 2. Key in the first m data points (where m is the number of data points in the average) and press _ after each entry.
  • Page 75 300500_ gÖ gÖ 190060g^ 190060g^ 271120_ 271120_ gÖ gÖ For repeated calculations the following HP 12C Platinum program can be used for up to a 12 element moving average: 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001, 002, 003,...
  • Page 76 Forecasting 12c platinum / 12C RPN KEYSTROKES 027, 028, 029,45 48 030,44 48 031, 032,45 48 033,44 48 034, 035, 036, 037, 038, g(001 039,43,33,001 ?m n: Unused i: Unused FV: Unused This program can be used for a moving average of 2 to 12 elements. It may be shortened considerably for moving averages with less than 12 elements.
  • Page 77 7. Key in the next data point and press t to calculate the next moving average. 8. Repeat step 7 for each new data point. Example 2: Calculate the 3-element moving average for the data given in example 1. Your modified program listing will look like this: 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000,...

  • Page 78: Seasonal Variation Factors Based On Centered Moving Averages

    3rd quarter would then be the ratio of the actual sales in the 3rd quarter to the centered moving average for that quarter. While quarterly seasonal variations are commonly used, the HP 12C Platinum can also be programmed to calculate monthly seasonal variations using a centered 12 month moving average.
  • Page 79 12c platinum / 12C RPN KEYSTROKES 018, 019, 020, 021, 022, 023, 024, g(001 025,43,33,001 Z n: Unused i: Unused FV: Unused Program Instructions: 1. Key in the program. 2. Press fCLEARH. 3. Key in the quarterly sales figures starting with the first quarter: a.
  • Page 80 Example: Econo-Wise Home Appliance Company had quarterly sales for the years 2000 thru 2002 as follows: Quarterly 2000 2001 2002 Find the centered 4-quarter moving average and seasonal variation factor for each quarter. 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes fCLEARH fCLEARH 397?1...
  • Page 81 111.4_ 111.4_ 111.17_ 111.17_ gÖ gÖ An HP 12C Platinum program to calculate a centered 12 month moving average and seasonal variation factor is as follows: 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001, 002, 003,...
  • Page 82 Forecasting 12c platinum / 12C RPN KEYSTROKES 021, 022, 023, 024, 025, 026, 027, 028,45 48 029, 030, 031,45 48 032,44 48 033, 034,45 48 035,44 48 036, 037,45 48 038,44 48 039, 040, 041, 042, 043, 044, 045, 046,...

  • Page 83: Gompertz Curve Trend Analysis

    The points are divided serially into 3 groups for data entry. The following HP 12C Platinum program processes the data, fits it to a Gompertz curve and calculates estimated values for future data points. The 3 constants which characterize the curve are available to the user if desired.
  • Page 84 Forecasting 12c platinum / 12C RPN KEYSTROKES g° 004, 005,44 40 006, g° 007, 008,44 40 009, 010,44 40 011, g(000 012,43,33,000 g(000 013, 014, 015, 016, 017, 018, 019, 020, 021, 022, 023, 024, 025, § 026, 027, 028, §...
  • Page 85 12c platinum / 12C RPN KEYSTROKES 047, 048, 049, 050, 051, § 052, 053, 054, 055, 056, 057, 058, § 059, g> 060, 061, 062, 063, 064, 065, 066, 067, 068, 069, § 070, g(062 071,43,33,062 q n: Unused i: Unused...
  • Page 86 What annual sales rate would the curve have predicted for the 5th year of the product's life? (Arrange the data as follows:) 12c platinum / 12C 12c platinum RPN Keystrokes...

  • Page 87: Forecasting With Exponential Smoothing

    12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes g(013t g(013t 100t 100t Forecasting with Exponential Smoothing A common method for analyzing trends in sales, inventory and securities is the moving average. Exponential smoothing is a version of the weighted moving average which is readily adaptable to programmable calculator forecasting.
  • Page 88 Forecasting with exponential smoothing involves selecting the best smoothing factor based on historical data and then using the factor for updating subsequent data and forecasting. This procedure uses the following HP 12C Platinum program: 12c platinum / 12C RPN KEYSTROKES fCLEARÎ...
  • Page 89 12c platinum / 12C RPN KEYSTROKES 038, 039, 040, 041, 042, g(000 043,43,33,000 n: Unused i: Unused FV: Unused : Unused Program Instructions: Selecting the "best" smoothing constant (α ): Key in the program and press fCLEARH. RPN Mode: Key in the number 1 and press \.
  • Page 90 Example: Select the best smoothing constant based on sales (in thousands of dollars) of 22, 23, 23, 25, 23, 27, 25. Given the current sales in month 8 of 26, forecast the following month. Select the smoothing constant (α ): 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes...
  • Page 91 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes The procedure is repeated for several Smoothing Constant (α) Cumulative Error (Σe For the selected α = .25 Forecasting: 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes fCLEARH fCLEARH .25?0-...

  • Page 92: Pricing Calculations

    Margin is defined as the difference between selling price and cost, divided by selling price. In other words, markup is based on cost and margin is based on selling price. The following keystroke sequences are given to readily make these calculations on the HP 12C Platinum. CALCULATE GIVEN Selling Price Cost &...
  • Page 93 21\1\50 21y+50 b³y 50\\ 1~b+z y~b³y The following HP 12C Platinum program may be helpful for repetitive calculations of selling price and costs as well as conversions between markup and margin. 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001,...
  • Page 94 Example: Find the cost of an item selling for $38.00 with a margin of 30%. What is the markup on the item? If the markup is raised to 50%, what will the selling price be? 12c platinum / 12C 12c platinum...

  • Page 95: Calculations Of List And Net Prices With Discounts

    7. Press àÞ . Example: The list price of an item is $3.28 and the net price is $1.45. Two of the discount rates are 48% and 5%. What is the third discount rate? 12c platinum / 12C RPN Keystrokes ALG Keystrokes 48b-?§1...
  • Page 96 Pricing Calculations The following program for the HP 12C Platinum will be helpful in performing the calculations: 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001, 002, 003, 004, ?§1 005,44 20 g(000 006,43,33,000 ?§1 007, § 008, 009, 010,...
  • Page 97 008 t . Example: Calculate the unknown discount rate for the previous example. If the list price is now raised to $3.75 what is the new net price? 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes 1.45\...

  • Page 98: Statistics

    Curve Fitting Exponential Curve Fit Using the ° function of the HP 12C Platinum, a least squares exponential curve fit may be easily calculated according to the equation y=Ae technique is often used to determine the growth rate of a variable such as a stock's value over time, when it is suspected that the performance is non-linear.
  • Page 99 Example 1: A stock's price in history is listed below. What effective growth rate does this represent? If the stock continues this growth rate, what is the price projected to be at the end of 2004 (year 7)? 12c platinum / 12C 12c platinum RPN Keystrokes...
  • Page 100 Statistics For repeated use of this routine, the following HP 12C Platinum program will be useful. 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001, g° 002, 003, 004, g(000 005,43,33,000 g(000 006, 007, 008, 009, 010, g> 011, 012, 013, g>...
  • Page 101 028 t . 8. For a different set of data, press f CLEAR H and go to step 2. Example 2: Repeat example 1 using the program. 12c platinum /12C 12c platinum RPN Keystrokes...

  • Page 102: Logarithmic Curve Fit

    Statistics Logarithmic Curve Fit If your data does not fit a line or an exponential curve, try the following logarithmic curve fit. This is calculated according to the equation y = A + B (ln x ), and all x values must be positive.
  • Page 103 = A + B (ln x ), where y represents cumulative sales in units and x the number of months since the beginning. How many units will be sold by the end of the eighth month? Month Cumulative 1431 Sales (units) 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes fCLEARH fCLEARH 1431\ 1431³...

  • Page 104: Power Curve Fit

    Statistics Power Curve Fit Another method of analysis is the power curve or geometric curve. The equation of the power curve is y = Ax , and the values for A and B are computed by calculations similar to linear regression. Some examples of power curves are shown below. The following keystrokes fit a power curve according to the equation ln y = ln A + B(ln x): 1.

  • Page 105: Standard Error Of The Mean

    Find the power curve formulas that best expresses h as a function of t (h = At 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes fCLEARH fCLEARH 30g° 30g° 2g°_ 2g°_ 50g° 50g° 2.5g°_ 2.5g°_ 90g° 90g° 3.5g°_ 3.5g°_...

  • Page 106: Mean, Standard Deviation, Standard Error For Grouped Data

    $200 per month, two rent for $205 per month, one rents for $216 per month, and one rents for $220 per month. What are the mean monthly rental and the standard deviation? What is the standard error of the mean? 12c platinum / 12C 12c platinum RPN Keystrokes...
  • Page 107 §~³gF~_ 3.00 206\\ 206³92?+0 92?+0§_ §~³gF~_ 4.00 :0?1:6 :0?1:6 ?3gÖ ?3gÖ :0grz z:0gr³ Use the following HP 12C Platinum program for the previous example: 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001,44 40 § 002, 003, g(000 004,43,33,000 ³...
  • Page 108 Statistics 12c platinum / 12C RPN KEYSTROKES 011, 012, 013, 014, 015, g(000 016,43,33,000 t n: Unused FV: Unused : Σf : Unused Program Instructions: 1. Key in the program. 2. Press f CLEAR H . 3. RPN: Key in the first value and press \\ .

  • Page 109: Chi-Square Statistics

    12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes 195\\ 195³ 200\\ 200³ 206\\ 206³ g(005t g(009t Chi-Square Statistics The chi-square statistic is a measure of the goodness of fit between two sets of frequencies. It is used to test whether a set of observed frequencies differs from a set of expected frequencies sufficiently to reject the hypothesis under which the expected frequencies were obtained.
  • Page 110 χ freedom, and see that 0.05,5 to a 0.05 significance level (probability = .95), the die is fair. Try the following HP 12C Platinum program with the same example. Display χ to a 0.05 significance level with 5 degrees of χ...
  • Page 111 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001, 44 0 002, 30 003, 36 § 004, 20 005, 45 0 006, 10 007, 40 g(000 008,43,33,000 ~ n: Unused i: Unused FV: Unused Program Instructions: 1. Key in the program.

  • Page 112: Normal Distribution

    The normal (or Gaussian) distribution is an important tool in statistics and business analysis. The following HP 12C Platinum program gives an approximation to the upper tail area Q under a standardized normal distribution curve, given x. The upper tail area signifies the probability of occurrence of all values ≥...
  • Page 113 12c platinum / 12C RPN KEYSTROKES 008, 009, § 010, 011, 012, 013, 014, 015, 016, 017, 018, 019, 020, 021, 022, 023, 024, Þ 025, g> 026, 027, 028, g(000 029,43,33,000 g> n: Unused i: Unused FV: Unused Program Instructions: 1.

  • Page 114: Covariance

    5. Press gv 1 gRd§~§~³ to obtain the value of S 6. Press 1 -: 1 y§~³ to obtain S' Example 1: Find the sample covariance (S following paired variables: 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes...
  • Page 115 Try the previous example using the following HP 12C Platinum program: 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001, g(000 002,43,33,000 g(000 003, § 004, 005, 006, 007, § 008, 009, 010, 011, 012, 013, 014, § 015, g(000...

  • Page 116: Permutations

    69 ≥ m ≥ n ≥ 0. Use the following HP 12C Platinum program to calculate the number of possible permutations. 12c platinum / 12C RPN KEYSTROKES fCLEARÎ...

  • Page 117: Combinations

    Where m, n are integers and 69 ≥ m ≥ n ≥ 0. Use the following HP 12C Platinum to calculate the number of possible combinations. REGISTERS PV: Unused...
  • Page 118 Statistics 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001, 002, 003, 004, 005, 006, 007, 008, 009, § 010, 011, g(000 012,43,33,000 ge n: Unused i: Unused FV: Unused Program Instructions: 1. Key in the program. 2. Key in m and press \ ( ³ ).

  • Page 119: Random Number Generator

    Random Number Generator This HP 12C Platinum program calculates uniformly distributed pseudo-random numbers in the range The following method is used: • = fractional part of (997 u • where i = 0, 1, 2, ... • = 0.5284163 (seed) The period of this generator has a length of 500,000 numbers and the generator passes the frequency test (chi square) for uniformity, the serial test and the run test.
  • Page 120 1. Key in the program. 2. To generate a random number, press t . 3. Repeat step 2 as many times as desired. Example: Generate a sequence of 5 random numbers. 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes...

  • Page 121: Personal Finance

    Example: What would your monthly payments be on a $65,000 house in a neighborhood with a $25 per thousand tax rate and a 10 ¾ % interest rate on a 35 year loan with 10% down? 12c platinum / 12C RPN Keystrokes ALG Keystrokes gÂ...
  • Page 122 12c platinum RPN Keystrokes ALG Keystrokes 10b-$ -10b$ 25:1§ P:1§ 12000zÞ 25Þz12000+ -135.42 ³ The following HP 12C Platinum program may be used instead of the above. 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, g 001, 002, 003, 004,...
  • Page 123 9. For a new case, store only the new variables by performing steps 3 thru 7 as needed. Press t for the new approximate monthly payment. Example: Solve the previous example using the HP 12C Platinum program. 12c platinum / 12C...

  • Page 124: Tax-Free Individual Retirement (Ira) Or Keogh Plan

    The calculations run from the beginning of the first year to the end of the last year. • The interest (annual yield), i, should be entered to as many significant figures as possible for maximum accuracy. 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001, 002, §...
  • Page 125 12c platinum / 12C RPN KEYSTROKES 013, 014, 015, 016, 017, 018, 019, :¼ 020, 021, 022, 023, ¼ 024, 025, 026, g(012 027,43,33,012 :¼ n: Years i: Used FV: Used : Unused : Inflation % : Unused Program Instructions: Key in the program.
  • Page 126 What is the purchasing power of that figure in terms of today's dollars? 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes...

  • Page 127: Stock Portfolio Evaluation And Analysis

    The overall beta coefficient of the portfolio is also calculated. Note: The beta coefficient analysis is optional. Key in 1.00 if beta is not to be analyzed. 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000,...
  • Page 128 Personal Finance 12c platinum / 12C RPN KEYSTROKES g(001 020,43,33,001 ?+3 021, 022, 023, § 024, 025, 026,44 40 027, 028, 029, g(001 030,43,33,001 ?7 031, 032, 033, 034, à 035, 036, 037, 038, 039, 040, 041, 042, 043, 044,...
  • Page 129 16. For a new case return to step 2. Example: Evaluate the following portfolio: Number of Initial Shares Held Purchase Price 25.63 30.25 89.88 65.25 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes fCLEARH fCLEARH 100\ 100³ 25.63t 25.63t .8³...
  • Page 130 Personal Finance 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes 200\ 200³ 30.25t 30.25t 1.2\ 1.2³ 2.10\ 2.10³ 33.5t 33.5t 50³ 89.88t 89.88t 1.3\ 1.3³ 4.55\ 4.55³ 96.13t 96.13t 500\ 500³ 65.25t 65.25t .6³ 3.50\ 3.50³ 64.38t 64.38t...

  • Page 131: Canadian Mortgages

    United States and preprogrammed into the HP 12C Platinum. This difference can be easily handled by the addition of a few keystrokes. For any problem requiring an input for ¼ , the Canadian mortgage factor is calculated first and then this value is entered in for ¼...

  • Page 132: Number Of Periodic Payments To Fully Amortize A Mortgage

    Example 2: An investor can afford to pay $440 per month on a $56,000 Canadian mortgage. If the annual interest rate is 9 ¼ %, how long will it take to completely amortize this mortgage? 12c platinum / 12C 12c platinum RPN Keystrokes...
  • Page 133 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes fCLEARG fCLEARG g g 6n200\$ 2n8.75z2¼ 8.75+ÞM¼ 1$M12n¼ 612.77ÞP 612.77ÞP 10gA 10gA 75500$M 75500$M Canadian Mortgages Display Comments Canadian mortgage factor. 0.72 Outstanding balance remaining -61,877.18 at the end of 10 years.

  • Page 134: Miscellaneous

    Example 1: An electronic manufacturer begins a pilot run on a new instrument. From past experience he expects the process to have a learning factor, r, or 0.90. If the first unit costs $875 to produce, what is the expected cost of the 100th unit? 12c platinum / 12C RPN Keystrokes ALG Keystrokes 875\ 875³...
  • Page 135 These calculations may be rapidly done with the following HP 12C Platinum program: 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, g° 001, 002, g° 003, 004, 005, 006, 007, 008, 009, g° 010, 011, 012, g> 013, 014, g(000 015,43,33,000 ³...
  • Page 136 Miscellaneous 12c platinum / 12C RPN KEYSTROKES 039, 040, 041, 042, 043, 044, 045, 046, 047, § 048, g(000 049,43,33,000 q n: Unused i: Unused FV: Unused : K+1 12c platinum DISPLAY ALG KEYSTROKES 21 g° 30 + 10 ³...
  • Page 137 Example 2: The electronic manufacturer cited in example 1 found that the 100th instrument actually cost $395 to manufacture. Find the actual learning factor, r , the cost of the 500th unit and the average cost of units 500 thru 1000. (Recall that C 12c platinum / 12C 12c platinum RPN Keystrokes...

  • Page 138: Queuing And Waiting Theory

    Miscellaneous Queuing and Waiting Theory Waiting lines, or queues, cause problems in many marketing situations. Customer goodwill, business efficiency, labor and space considerations are only some of the problems which may be minimized by proper application of queuing theory. Although queuing theory can be complex and complicated subject, handheld calculators can be used to arrive at helpful decisions.
  • Page 139 2 minutes (0.5 customers per minute). What is the average waiting time in the queue? In the system? What is the average number of customers in the queue? In the system? 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes 1.2\...
  • Page 140 .9 per minute (µ). What is the average number of customers in the waiting line at any time? The average waiting time? What is the average total time for a customer to wait and be checked out? The average number of customers in the system? 12c platinum / 12C 12c platinum RPN Keystrokes ALG Keystrokes .5?1...
  • Page 141 With an HP 12C Platinum program one can readily calculate the necessary probabilities for this type of problem (dispensing with the use of tables) and perform additional calculations as well. 12c platinum / 12C RPN KEYSTROKES fCLEARÎ 000, 001, 002,44 33...
  • Page 142 Miscellaneous 12c platinum / 12C RPN KEYSTROKES § 037, 038, 039,45 48 040, 041, 042, 043,45 48 044, 045, 046, 047, 048, 049, 050, 051, 052, 053, 054, 055, 056, § 057, 058, § 059, g> 060, 061, § 062,...
  • Page 143 n: Unused i: Unused FV: Unused : λ : Unused Program Instructions: 1. Key in the program and press f CLEAR H . 2. Key in the number of servers, n and press ? 0 ? 7. RPN Mode: 3. Key in the arrival rate of customers, λ and press ? 8. 4.
  • Page 144 Miscellaneous 12c platinum / 12C RPN Keystrokes ALG Keystrokes fCLEARH fCLEARH 3?0?7 3?0?7 1.2?8 1.2?8z .5?9 .5?9 z?.0 ³?.0 12c platinum Display 0.00 3.00 1.20 0.50 2.40 2.16 0.06 0.65 2.59 4.99 4.16 0.36 Comments λ µ ρ average waiting time in queue.

  • Page 145: Appendix A : Programs From Part Iii Of The Owner's Handbook

    HP12C Platinum Owner's Handbook and Problem-Solving Guide. It does not cover the step-by-step examples given in Part III. These programs are solely for the HP 12C Platinum, and work properly only when the calculator is set to ALG mode. They should be tested by running the corresponding program examples given in the HP12C Platinum Owner's Handbook and Problem-Solving Guide.

  • Page 146: Algebraic Mode Programs

    Appendix A Algebraic Mode Programs Section 12: The Rent or Buy Decision ALG KEYSTROKES fCLEARÎ 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, 026, §...

  • Page 147: Section 13: Straight-Line Depreciation

    Section 13: Straight-Line Depreciation ALG KEYSTROKES fCLEARÎ 000, 001, 002, 003, ³ 004, 005, 006, 007, 008, 009, ³ 010, 011, 012, 013, § 014, 015, ³ 016, 017, 018, 019, 020, 021, 022, DISPLAY ALG KEYSTROKES 10 n 1 :0 2 gm 36 g(038 1 :2...

  • Page 148: Section 13: Declining-Balance Depreciation

    Appendix A Section 13: Declining-Balance Depreciation ALG KEYSTROKES fCLEARÎ 000, 001, 002, 003, ³ 004, 005, 006, 007, 008, 009, ³ 010, 011, 012, 013, § 014, 015, ³ 016, 017, 018, 019, 020, DISPLAY ALG KEYSTROKES 10 gm 1 g(034 2 :2 36 gu 1 :0...

  • Page 149: Section 13: Sum-Of-The-Years-Digits Depreciation

    Section 13: Sum-of-the-Years-Digits Depreciation ALG KEYSTROKES fCLEARÎ 000, 001, 002, 003, ³ 004, 005, 006, 007, 008, 009, ³ 010, 011, 012, fÝ 013, § 014, 015, ³ 016, 017, 018, 019, 020, 021, 022, DISPLAY ALG KEYSTROKES 10 n 1 :0 2 gm 36 g(038...

  • Page 150: Section 13: Full- And Partial- Year Depreciation With Crossover

    Appendix A Section 13: Full- and Partial- Year Depreciation with Crossover ALG KEYSTROKES fCLEARÎ 000, 001, 002, 003, ³ 004, 005, 006, 007, 008, ³ 009, 010, 011, 012, 013, 014,44 30 015, 016, 017, § 018, 019, ³ 020, 021, 022, 023,...

  • Page 151: Section 14: Lease With Advance Payments - Solving For Payment

    Full- and partial-Year Depreciation with Crossover (continued) ALG KEYSTROKES 081, 082,44 30 083,44 40 084,44 40 085, 086, 087, 088, g(078 089,43,33,078 g(062 090, Section 14: Lease with Advance Payments - Solving For Payment ALG KEYSTROKES fCLEARΠ000, g 001, fCLEARG 002, 003,...

  • Page 152: Section 14: Advance Payments With Residual - Solving For Payment

    Appendix A Section 14: Advance Payments With Residual - Solving for Payment ALG KEYSTROKES fCLEARÎ 000, g 001, fCLEARG 002, 003, 004, 005, ¼ 006, 007, 008, 009, 010, 011, ³ 012, 013, 014, Section 15: Nominal Rate Converted to Effective Rate ALG KEYSTROKES fCLEARÎ...

  • Page 153: Section 16: 30/360 Day Basis Bonds

    Section 16: 30/360 Day Basis Bonds ALG KEYSTROKES fCLEARÎ 000, fCLEARG 001, g× 002, 003, 004, 005, 006, 007, 008, 009, 010, 011, 012, gÒ 013, 014, 015, 016, 017, 018, 019, 020, 021, 022, 023, § 024, 025, DISPLAY ALG KEYSTROKES ³...

  • Page 154: Section 16: Annual Coupon Bonds

    Appendix A Section 16: Annual Coupon Bonds ALG KEYSTROKES fCLEARÎ 000, fCLEARG 001, g 002, 003, 004, 005, 006, 007, ¼ 008, 009, 010, 011, 012, 013, Æ 014, 015, Þ 016, ³ 017, 018, 019, DISPLAY ALG KEYSTROKES gÒ 34 :6 8 :4 0 gÒ...

  • Page 155: Appendix B: Formulas Used

    Real Estate Wrap-Around Mortgage = number of years remaining in original mortgage. = yearly payment of original mortgage. = remaining balance of original mortgage. = number of years in wrap-around mortgage. = yearly payment of wrap-around mortgage. = total amount of wrap-around mortgage. r = interest rate of wrap-around mortgage as a decimal.

  • Page 156: Lending

    Appendix B Lending Loans With a Constant Amount Paid Towards Principal = remaining balance after time period k. CPMT = Constant payment to principal. = PV − (k x CPMT) kth payment to interest = i (BAL kth total payment = CPMT + (PMT Add-On Interest Rate to APR r = add-on rate as a decimal.

  • Page 157: Graduated Payment Mortgage

    − Rebate = (n − k) × PMT − Rebate Graduated Payment Mortgage n = total number of payments in the loan I = interest rate per payment period, as a decimal A = number of payments per year B = number of years that payments increase C = percentage increase in periodic payments (as a decimal) = amount of the first payment PV = amount of the loan.

  • Page 158: Savings

    Appendix B Savings Compounding Periods Different From Payment Periods C = number of compounding periods per year. P = number of payment periods per year. i = periodic interest rate, expressed as a percentage. r = i / 100, periodic interest rate expressed as a decimal. = ((1 + r / C) Investment Analysis Lease vs.

  • Page 159: Securities And Options

    Securities and Options Discounted Notes Price (given discount rate) B = number of days in year (annual basis). DR = discount rate (as a decimal). DSM = number of days from settlement date to maturity date. P = dollar price per $100 per value. RV = redemption value per $100 par value.

  • Page 160: Forecasting

    Appendix B Forecasting Simple Moving Average moving average. number elements etc. Seasonal Variation Factors Based on a Centered Moving Average centered moving m = number of elements in the centered moving average. SV = Seasonal variation factor. = value of the ith data point. centered moving SV =...

  • Page 161: Forecasting With Exponential Smoothing

    ∑ ∑ ∑ a, b and c are determined by solving the three equations above simultaneously. Forecasting With Exponential Smoothing α = smoothing constant (0 < α < 1) = actual current period usage Smoothed average, Change, Trend, α Χ Current period expected usage, Forecast of next period expected usage, = ˆ...

  • Page 162: Calculations Of List And Net Prices With Discounts

    Appendix B −         −     − Calculations of List and Net Prices with Discounts L = List price. N = Net price. D = Discount(%). = ′ − × ′ ′...

  • Page 163: Logarithmic Curve Fit

    ∑    ˆ Logarithmic Curve Fit ∑ − ∑ ∑ ∑ − ˆ Power Curve Fit y = Ax (A>0) ∑ ∑ ∑    ˆ Standard Error of the Mean Mean, Standard Deviation, Standard Error for Grouped Data ∑...

  • Page 164: Personal Finance

    Appendix B Personal Finance Tax-Free Retirement Account (IRA) or Keogh Plan n = the number of years to retirement. i = the compounded annual interest. PMT = the total annual investment. FV= future value, after applicable taxes. r = the assumed tax rate on interest expressed as a decimal. w = the withdrawal tax rate expressed as a decimal.

  • Page 165: Miscellaneous

    Miscellaneous Learning Curve for Manufacturing Cost = Cost of the nth unit, C n = number of units, r = learning factor. k = ln r / ln 2, average   −   This formula is only approximate and may give appreciable error at small i. Queuing and Waiting Theory n = number of servers.

  • Page 166: Subject Index

    Page numbers in bold type indicate primary references: page numbers in regular type indicate secondary references. About This Handbook Add-On Interest Rate Converted to APR Add-On Rate Loan with Credit Life After-Tax Cash Flows After-Tax Net Cash Proceeds of Resale After-Tax Yield Algebraic Versions of Programs from Part III of the Owner's Handbook APR Converted to Add-On Interest Rate...
  • Page 167 Effective Interest Rate (Yield) Exponential Curve Fit Forecasting Forecasting with Exponential Smoothing Formulas Used Gompertz Curve Trend Analysis Graduated Payment Mortgage Homeowners Monthly Payment Estimator Income Property Cash Flow Analysis Initial Deposit with Periodic Deposits Interest Rebate - Rule of 78's Introduction Investment Analysis Learning Curve for Manufacturing Cost...
  • Page 168 Standard Error of the Mean Statistics Stock Portfolio Evaluation and Analysis T - W Tax-Free Individual Retirement (IRA) or Keogh Plan Using the RPN Programs on the HP-12C Variable Rate Mortgages Wrap-Around Mortgage 121 , 164 104 , 163 92 , 161...

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