Contents Page 10 At a Glance 21 1: Getting Started 31 2: Business Percentages 35 3: Number Storage and Arithmetic 43 4: Picturing Financial Problems 51 5: Time Value of Money Calculations 75 6; Cash Flow Calculations 85 7: Statistical Calculations 95 8: Additional Examples 116 A; Assistance, Batteries, and Service 127 B: More About Calculations 133 Messages 136 Index HEWLETT PACKARD F.
HP-lOB Who% HEWLE mLnM PACKAR
HfiWLBTT PACKAnO Toe 1. Interest conversion (page 71). 2. Time value of money (page 51). 3. Cash flows (page 75). 4. Store and recall (page 38). 5. Percent (page 31). 6. Clear all memory (page 23). 7. Separate two numbers (page 25), 8. Change sign (page 22). 9. Constant (page 35). 10. Shift: activate yellow labeled functions (page 24). BUSINESS 11. On. clear display.cancel operation (page 21). 12. n through Sxy: statistical summation registers (page 89). 13. Statistical functions (page 88). 14.
HP-1 OB Business Calculator Owner’s Manual HEWLETT PACKARD Edition 6 Pan Number 00010-^)0037
Notice For warranly and regulatory information for this calculator, see pages 123 and 126. This manual and any examples contained herein arc provided "as is" and arc subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose. Hewlett-Packard Co.
Welcome to the HP-1 OB Your HP-lOB rcflccls ihc superior quality and attention to detail in engineering and manufacturing that have distinguished Hewlett-Packard products for 50 years. Hewlett-Packard stands behind this calculator —we offer expertise to support its use (see inside the back cover) and world wide scr\icc. Hewlett-Packard Quality Our calculators arc made to excel and to be easy to use.
Features The fc;iUircs of ihc HP-lOB and ihc manual reflect the needs and wishes of many customers; ■ A large 12-charactcr display. ■ An At-a-Glancc section in the manual for quick reference. ■ Applications to solve business and financial tasks: ■ Time Value of Money. Loans, savings, leases, and amortiza tion schedules. m Interest Conversion. Nominal and effective rates. ■ Cash Flows. Net present value and internal rate of return. ■ Business Percentages. Percent change, markup, and margin calculations.
Contents 10 At a Glance... 10 11 12 13 14 15 16 17 19 Basics Percentages Memory Keys Time Value of Money (TVM) TVM Whal if...
2 3 4 28 28 29 29 Interchanging the Period and Comma Rounding Numbers Messages Picturing Memory 31 31 31 32 32 33 33 34 34 Business Percentages 35 35 35 37 38 39 40 41 41 43 43 44 45 45 45 46 47 47 47 49 Contenu Percent Key Finding a Percent Adding or Subtracting a Percent Percent Change Margin and Markup Culculalinns Margin Calculations Markup on Cost Calculations Using Margin and Markup Together Number Storage and Arithmetic Using Stored Numbers in Calculations Using Constants Using the M Regis
5 6 7 51 51 53 53 53 58 62 66 71 71 73 Time Value of Money Calculations 75 75 77 77 78 79 80 83 84 Cash Flow Calculations 85 85 86 86 86 87 87 87 88 89 91 94 Statistical Calculations Using the TVM Application Clearing TVM Begin and End Modes Loan Calculations Savings Calculations Lease Calculations Amortization Interest Rate Conversions Investments With Different Compounding Periods Compounding and Payment Periods Differ How to Use the Cash Flow Application NPV and IRR/YR: Discounting Cash Flows O
8 95 95 95 95 96 97 97 98 99 101 102 104 105 106 107 107 109 111 112 112 114 116 116 117 118 118 119 120 121 123 123 123 124 124 124 125 8 Contents Additional Examples Business Applications Setting a Sales Price Forecasting Bused on History Cost of Not Taking a Cash Discount Loans and Mortgages Simple Annual Interest Continuous Compounding Yield of a Discounted (or Premium) Mortgage Annual Percentage Rate for a Loan With Fees Loan With a Partial (Odd) First Period Automobile Loan Canadian Mortgages Wha
5 Shipping Instructions 126 Warranty on Service 126 Service Agreements 126 Regulatory lnform
At a Glance... This section is designed Гог you if you're already familiar with calculator operation or financial concepts. You can use it for quick reference. The rest of the manual is filled with explanations and examples of the concepts presented in this section. Basics—At a Glance. !'------------- ' onoocju Qoaooo mmmoom ODOoa oaaao • aaoo [■aaoaj >— ---------О Keys: Display: Description: m 0.00 Turns calculator on. ■ 0.00 Displays shift annuncialor(.^). ■ 0.00 Discontinues shift.
Percentages—At a Glance... —'• OUOUDcl' CDOOCCi oaoco!. Doaoc, ooGOc:« loonoci Percent. (CST) Cost. Price. i^ARl Margin. Markup. Add 15% to $17.50. Keys: Display: Description: 17.50 0 17.50 Enters number. 15® 0 20.13 Adds 15 %. Find (he margin if the cost is $15.00 and .selling price Ls $22.00. 15 iesD 15.00 Enters cost. 22 iP^ 22.00 Enters price. fMM] 31.82 Calculates margin. If the cost is $20.00 and the markup is 33%, what is the selling price? 20 (cUl 20.00 Enters cost.
Memory Keys—At a Glance... pooooo paaaoo xz=)aaao □ oooo • OCDOO ooooa Doaoa 0 Stores a constant operation. Em) Stores a value in the M register (memory location). m Recalls a value from the M register. m Adds a value to the number .stored in the M register. Stores a value in a numbered register. Recalls a value from a numbered register. Multiply 17, 22, and 25 by 7, storing “x 7* as a constant operation. Keys: Display: Description: 170711 7.00 Stores “x 7” as a co operation. 0 119.
Time Value of Money (TVM)—At a Glance.. Ji’ Enter any four of the five values and solve for the fifth. immmmc DOOOOO C3000C {OOOOO oooed oaac MOOC A negative sign in the display represents money paid out; money received is positive. (N) Number of payments. [iTyrI Interest per year. m Present value. iasfl Payment. (Ey) Future value. Begin or End mode. liPTYR] Number of payments per year mode.
TVM What if...—At a Glance... U is nol necessary to reenter TVM values Гог each example. ommma Using the values you just entered (page 13), how much can ooooool aoooo you borrow if you want a payment of $100.00? ooooo; □ oooc Qoaac: OOOOC!; Keys: 100 Ea ши (pg Display: Description: 100.00 Enters new payment amount. (Money paid out is negative.) 11.395.08 Calculates amount you can borrow. - How much can you borrow at a 9.5% interest rate? 9.5 IÌ7YRÌ 9.50 Enters new interest rate. (pg 11,892.
Amortization—At a Glance... t ooooao oooooo After calculating a payment using Time Value of Money (TVM), enter the periods to amortize, then press BlAMORTI. moooo oaooo □ oaoo aoooD Using the previous TVM example (page 13), amortize a single payment and then a range of payments. □ OOMO Amortize the 20th payment of the loan. Keys: Display: Description: 20 lINPUTi 20.00 Enters payment to amortize. PEr20- msEo 20 Int Q -115.61 Displays payment to amortize. Displays interest.
Interest Rate Conversion—At a Glance... ommmoo oooooo fCDOnOO aooao nooao OOOCTO UOOOf ) To convert between nominal and cfTcctive interest rates, enter the known rale and the number of periods per year, then solve for the unknown rate. Nominal interest percent. ■FES Effective interest percent. ■ÎP7ŸR1 Periods per year. Find the annual cfTcctive interest rate of 10% nominal interest com pounded monthly. Keys: Display: Description: 10 10.00 Enters nominal rate. 12KEZŸH1 12.
IRR/YR and NPV—At a Glance... oooaoci oommmzi t300CC‘ ooDc:c poncoc nnc( K:i C)i3Duc::| V. ------------------- / ■rpTVRl Number of periods per year (default is 12). [cRl Cash flows, up to 15 (“y“ identifies the cash flowii///?i/?cT), ■(Nj] Number of consecutive times cash flow **y’* occurs. ■IonmoD Internal rale of return per year. Net present value. If you have an initial cash outflow of $-40,(XX), followcii by monthly caslt inflows of $4,700. $7,OCX). $7,000, and $23,000.
23000 (cEB CF3 Enters third cash flow. 23,000.00 onifili] a 12 0 15.96 Calculates IRR/YR. 1.33 Calculates IRR per month. What is the NPy if the discount rate is 10%7 10 E 18 At a Glance... 10.00 Enters l/YR, 622.85 Calculates NPV.
Statistics—At a Glance. I 000008 OOOOOO ommmc^ ^•OOC ocir aaoocj joc:' ■fcm Clear statistical registers. number Enter one-variable statistical data. number BfZ^ Delete one-variable statistical data. numberl number2 (|3 Enter two-variable statistical data. numberJ liNPUTi number! BO Delete two-variable statistical data. WED Emm Mean of.v and}». Bd^ Mean of.v weighted by>^. BdEiD wmm Sample standard deviation o(x andy. BE5ZZ1 EMM Population standard deviation of.v and}».
Using the following data, find the mean of j; aiidy, the sample standard deviation of at andy, and they-intcrcept and the slope of the linear regres sion forecast line. Then, use summation statistics to find n and Sty. x-data 2 4 6 y-data 50 90 160 Keys: Display: Description: ■fern 0.00 Clears stalistics registers. 2iiNPUTl50 1.00 Enters first .V,)» pair. 4 fiNPDTl90 2.00 Enters second pair. SfiNRJTl 160 3.00 Enters third pair. IdiD 4.00 Displays mean ofx. 100.
1 Getting Started Power On and Off To turn on your HP-lOB, press O (ihc key above ihe “ON oocoao label). To turn the calculator off, press the yellow shift key oooaoo ki^ooon (I )> then [§ (also written BIOPFI). □ DOOO {oaooc »oao loao Since the calculator has continuous memory, turning it off ^ docs not affect the information you’ve stored. To conserve energy, the calculator turns itself off approximately 10 minutes after you stop using it.
If you make a typing mistake while entering a number, press [♦] to erase the incorrect digits. Keys: Display: Description: 24.71 0 62.47 0 87.18 Adds 24.71 and 62.47. When a calculation has been completed (by pressing 0), pressing a number key starts a new calculation. 19 0 12.68 0 240.92 Calculates 19 x 12.68. If you press an operator key after completing a calculation, the calculation is continued. 0 115.5 0 356.42 Completes calculation of 240.92 + 115.5.
Understanding the Display and Keyboard Cursor The cursor (_) is visible when you arc entering a number. Clearing the Calculator ill L oooooc OOODOO =JOOC« oooac aooooi oonnr'. ooeg When the cursor is on, 0 erases the last digit you entered. Otherwise, 0 clears the display and cancels the calculation. While you arc entering a number, pressing (C) clears it to zero. Otherwise, (c) clears (he display of its current contents and cancels the current calculation. Clearing Messages.
To dear all memory and reset calculator inodes, press and hold down O, then press and hold down both and When you release all three, all memory is cleared. The ALL CLr message is displayed. Annunciators Annunciators are symbols in the display that indicate the status of the calculator. Annunciator Status Shift Is active: when a key is pressed, the function labeled in yellow above the key, is executed (below). • • liNPUTi has been oressed. or two values have been entered or returned (page 25).
INPUT Key OOODOD OOOOOO BaOOG The lINPUTI key is used lo separate two numbers when using two-number functions or two-variable statistics. ooooc The : annunciator is displayed if lINPUTI has been pressed. If оооос ooooa a number is in the display, press [c] to erase the : annuncia ooooo tor and clear the display. If the cursor or an error message is visible in the display, press O twice lo erase the : annunciator.
Keys: Display; 89.25 Ш{Щ\ 9.45 3.57 0 2.36 Ш\Ш} 0.42 a 3.99 Description; Calculates square root. 1/2,36 is calculated first. Adds 3.57 and 1/2.36. Two-Number Functions. When a function requires two DCOOOO lOOCOO ■■nacD aDOCio ooooa оезооа ooaoc numbers, the numbers are entered like this: number I №UT number2 followed by the operation. Pressing lINPUTi evalu ates the current expression and displays the : annunciator.
Specifying Displayed Decimal Places To specify the number of displayed decimal places; 1. Press 2. Enter the number of digits (0 through 9) that you wish to appear after the decimal point. Keys: та Display: Description: 0.00 Clears display. 0.000 Displays three decimal places. 45.6 0.1256 0 5.727 ■в) 9 5.727360000 Displays nine decimal places. ■fPiSPl 2 5.73 Restores two decimal places and rounds number in display.
Displaying the Full Precision of Numbers To SCI your calculator to display numbers as precisely as pos ooQooa sible, press BlDlSPl 0 (trailing zeros arc not displayed.) To □OOGOO temporarily \aew all 12 digits of the number in the display C3GOOO oaooo (regardless of the current display format setting), press oaaoo cooao BloiSPl and hold 0* The number is displayed as long as you ooMMc: continue holding 0. The decimal point is not shown. Start with two decimal places (| [■Ma 2).
Keys: Display: Description: 9.87654321 9.87654321 Enters a number with more than Iwo non-zero decimal places. 9.88 Displays two decimal places. 987654321000 Displays all digits without the decimal while you press 0. 9.88 Rounds to two decimal places (specified by pressing BiDISR 2). 988000000000 Shows rounded, stored number. raiga a fiHSTl] |(RND) 0 Messages The HP-lOB displays messages about the status of the calculator or informs you that you have attempted an incorrect operation.
N l/YR or NOM% PV PMT FV P/YR EFF% M CST PRC MAR or MU Ro Ri R2 R3 «4 Re General Storage and Cash Flows R? > Summation Statistics «8 R9 R.0 R.1 R.2 R.3 R.4 Numbered Memory Registers You can picture each memory register as a separate box (hat has a name and can hold one number at a time. If you store a number in a register, you write over the number that was previously stored there. Notice that I/YR and NOM% share the same register, and that MAR and MU share the same register.
2 Business Percentages You can U.SC(he HP-lOB to calculate simple percent, percent change, cost, price, margin, and markup. Percent Key oooaoo lOOOQO CZJOOQO The key has two functions: finding a percent and adding or subtracting a percent. oooao ooocao ooooo OODOC Finding a Percent The @ key divides a number by 100 unless it is preceded by an addition or subtraction sign. Example. Find 25% of 200. Keys: Display: Description: 2000 200.00 Enters 200. 25® 0.25 Converts 25% to a decimal. 0 50.
Adding or Subtracting a Percent You can add or subtract a percent in one calculation. Example. Decrease 200 by 25%. Keys: Display: Description: 200 0 200.00 Enters 200. 25 ® 50.00 Multiplies 200 by 0.25. 0 150.00 Subtracts 50 from 200. Example. You borrow $1,2S0 from a relative, and you agree to repay the loan in a year with 7% simple Interest. How much money will you owe? Keys; Display: Description: 1250 07® 87.50 Calculates loan interest. 0 1.337.50 Adds $87.50 and $1,250.
Example. Calculate the percent change between (12 x S) and (65 + 18). Keys: Display: Description: 12 fx] 5 lINPUTI 60.00 Calculates and enters D|. 65 0 18 Bi%CHGl 38.33 Calculates percent change. Margin and Markup Calculations The MP-lOB can calculate cost, selling price, margin, or markup. Application Margin iesn. (PRÇ], CŒID Markup Description Keys (MS. (PRÇ]. wm Margin is markup expressed as a percent of price. Markup calculations are expressed as a percent of cost.
Markup on Cost Calculations Example. The standard markup on costume jewelry at Kleiner’s Knsmetique is 60%. They just received a shipment of chokers costing $19.00 each. What is the retail price per choker? Keys: Display: Description: 19 IC^ 19.00 Stores cost. 60 60.00 Stores markup. GIIS 30.40 Calculates retail price. Using Margin and Markup Together Example. A food cooperative buys eases of canned .soup with an invoice cost of $9.60 per ease.
3 Number Storage and Arithmetic Using Stored Numbers in Calculations You can Store numbers, for reuse, in several different ways: ■ Use E) (Constant) to store a number and its operator for repetitive operations. ■ Use 3 Key Memory [RMl. and (M+J) to store, recall, and sum numbers with a single keystroke. « Use mstQl and IRCLI to store and recall the 15 numbered registers. Using Constants L oooooc oooooc CTDOODO OOQOCD oaor^ Use [K] to store a number and arithmetic operator for repeti tive calculations.
Operation Keys 0 number (Q 0 Stores "+ number" as constant. 0 number 0 0 Stores number" as constant. 0 number 0 0 Stores “x number " as constant. 0 number 0 0 Stores ‘‘-f number " as constant. KFl X value (K) 0 Stores *y * ” as constant. 0 number 0 0 0 Stores “ + number %" as constant. 0 number 0 0 0 Stores " - number %" as constant. 0 number 0 0 0 Stores "x number %" as constant. 0 number 0 0 0 Stores number %” as constant. Example. Calculate 5 + 2,6 + 2, and 7 + 2.
Example. Calculate 2^ and 4^. Description: Keys: Display: 2i(Z] 3 (K) 3.00 0 40 8.00 Calculates 2\ 64.00 Calculates 4^ Stores as constant. Using the M Register The I-»ML IRMI. and keys perform memory operations oooooo on a single storage register, called the M register. In most oooooa l■ •0 eases, it is unnecessary to clear the M register, since I-»Ml 00000 replaces the previous contents. However, you can clear the ooooa oaaac) M register by pressing 0 I-»Ml.
4.65 Ea (M±] -4.65 Adds -4.65 lo M register. m 43.55 Recalls contents of the M register. Using Numbered Registers L The BiSTOI and IRCLI keys access storage registers Rq oooooo through R9 and R 0 through R.4. (Refer to “Picturing oaoooo C300DD Memory*' on page 29.) The BISTOI key is used to copy the oasMO displayed number to a designated register. The IRCLI key is used to copy a number from a register to the display. To store or recall a number in two steps: 1- Press BlSTOl or [RCLl.
In most cases, it is unnecessary to clear a storage register since storing a number replaces the previous contents. However, you can clear a sin^e register by storing 0 in it. To clear all the registers at once, press ■l CLEAR ALD. Doing Arithmetic Inside Registers You can do arithmetic inside storage registers Rq through R9. The result is stored in the register.
Doing Arithmetic oooooo Math functions operate on the number in the display. □GOOD CZDOOOO OOOO QOOO ommm jOOCDO 'J Example. Calculate Ihcn calculate + 47.2 + 1.1^. Keys: Display: Description: 4 loa 0.25 Calculates the reciprocal of 4. 20 i(^ 4.47 Calculates 0 47.2 0 51.67 Calculates47.20. 1.1 iE) 1.21 Calculates 1.1^. 0 52.88 Completes the calcula tion. Example. Calculate natural logarithm (c^). Then calculate 790 + 4! Keys: Display: Description: 2.5 Id!) 12.
Power Operator The power operator, B0> raises the preceding number (yoooooo valuc) to the power of the following number (x-valuc). OOOOOOj K=)OOOD ooooo OQoai oaoooj ooooo —■') Example. Calculate 125^ then find the cube root of 125. Keys: Display: Description: 125i(Z)3tJ 1251(0 3100 (3 5.00 1,953,125.00 Calculates 125’. Calculates cube root of 125, which is the same as 125'/’.
Keys: Display: Description: 30 0 10 85 0 85.00 No calculation yet. 73.00 Calculates 85 - 12. 0.41 Calculates 30 *r 73. 3.70 Multiplies the result by 9.
4 Picturing Financial Problems How to Approach a Financial Problem The financial vocabulary of the HP-lOB is simplified to apply to all finan cial fields. For example, your profession may use the term balance, bal loon payment, residual, maturity \^alue, or remaining amount to designate a value that the HP-lOB knows as (future value). (E3 The simplified terminology of the HP-lOB is based on cash flow diagrams. Cash flow diagrams are pictures of financial problems that show cash flows over time.
Up-arrows represent positive cash flows (money received). ' The horizontal line represents time. It is divided into regular periods. 1I2I3 4I5I6 A * ' 5,000.00 7 I 8 I 9 I 10i 11 12 113 114 115 116 \-\-r\ Down-arrows represent negative cash flows (money paid out). - 5,000.00 - 6.000.00 - 7.000.00 Any cash flow example can be represented by a cash flow diagram. As you draw a cash flow diagram, identify what is known and unknown about the transaction.
Periods and Cash Flows In addition to the sign convention (cash flowing out is negative, cash flowing in is positive) on cash flow diagrams, there arc several more considerations; ■ The time line is divided into equal time intervals. The most common period is a month, but days, quarters, and annual periods are also common. The period is normally defined in a contract and must be known before you can begin calculating.
Compound Interest A compound-interest contract is like a scries of simplc-intcrcst contracts that arc connected. The length of each simplc-intcrcst contract is equal to one compounding period. At the end of each period the interest earned on each simple-interest contract is added to the principal. For example, if you deposit $1,000.
Interest Rates When you approach a financial problem, it is important to rccogni/e that the interest rate or rate of return can be described in at least three different ways: ■ As a periodic rate. This is the rate that is applied to your money from period to period. ■ As an annual nominal rate. This is the periodic rate multiplied by the number of periods in a year. ■ As an annual effective rate. This is an annual rate that considers com pounding. In the previous example of a $1,000.
m шш Number of periods or payments. Annual percentage interest rate (usually the annual nomi nal rate). ш Present value (the cash flow at the beginning of the time line). Ш] Periodic payment. (ЁУ) Future value (the cash flow at the end of the cash flow diagram, in addition to any regular periodic payment). You can calculate any value after entering the other four.
FV « 25,327.38 l/YR = 8.00% PMT - 0.00 ■ -I --i I ^ I ^ h • -I— I I ^ I ^ N « 60 PV = -17,000.00 Time value of money calculations arc described in the next chapter. Recognizing a Cash Flow Problem A financial problem that docs not have regular, uniform payments (some times called uneven cash flows) is a cash flow problem rather than a TVM problem. A cash flow diagram for an investment in a mutual fund follows.
16,567.20 5,000.00 41516 1I213 11■ 11 7 1 8 1 9 1 10 ill 1 1 1 1 •5,000.00 T > r - 6.000.00 ^ -7,000.00 Cash flow problems arc described in chapter 6.
5 Time Value of Money Calculations Using the TVM Application ____i.i The time value of money (TVM) application is used for compound interest calculations that involve regular, uniform cash joooooo* ‘ ,, , ^I, . eZDOODO nows —called payments. Once the values arc entered you oaooo can vary one value at a time, without entering all (he values ooooc oaooc again. ocaoowj To use TVM, several prerequisites must be met: ■ The amount of each payment must be the same.
Key Stores or Calculates The number of payments or compounding periods. mm The annual nominal interest rate. I E 3 The present value of future cash flows. PV is usually an initial Investment or loan amount and always occurs at the beginning of the first period. fp^ The amount of periodic payments. All payments are equal, and none are skipped; payments can occur at the beginning or end of each period. The future value.
Clearing TVM Press BICLEAR ALLI lo dear the TVM registers. This sets N, f/YR, PV, PM Ty and FV to zero and briefly displays the current value in P/YR, Begin and End Modes IL OOODOQj OOOOOC' CZDOOOCii OOOOCl ooooc^ oooac {OBOOc: Before you start a TVM calculation, identify whether the first periodic payment occurs at the beginning or end of the first period.
PV = 7,250-1,500 PMT = ? End Mode Scl (o F.nd mode. Prc.s.s | lIS7iiZBl if BEGIN annuncialor is displayed. Keys: Display: Description: 12i(EZYR) 12.00 Sets periods per year. 3 0 12® 36.00 Stores number of periods in loan. 10.5 [¡TYRI 10.50 Stores annual nominal interest rate. 7250 0 1500 (Py] 5,750.00 Stores amount borrowed. 0 (pg 0.00 Stores the amount left to pay after 3 years. -186.89 Calculates the monthly payment. The negative sign indicates money paid out. Part 2.
Part 3. If interest is 10.5%, what is the maximum you can spend on the car to lower your car payment to $175.00? 10.5 flTYRl 10.50 Stores original interest rate. 175 m -175.00 Stores desired payment. 5.384.21 Calculates amount of money to finance. 6,884.21 Adds the down payment to the amount financed for total price of the car. Slil 01500 0 Example: A Home Mortgage. You decide tha( the maximum monthly mortgage payment you can afford is $630.00.
30 WxP/YRI X 360.00 Stores the length of the mortgage (30 12). 0.00 Pays mortgage off in 30 years. 11.5 n/YRl 11.50 Stores interest rate. 630(S (PmT) -630.00 Stores desired payment (money paid out is negative). 63,617.64 Calculates the loan you can afford with a $630 payment. 75,617.64 Adds $12,000 down payment for the total purchase price. m a 12000 a Example: A Mortgage With a Balloon Payment. You’ve obtained a 25 year, $72,500 mortgage at 13.8% annual interest.
Set (o End mode. Press if BEGIN annunciator is displayed. Keys: Display: Description: 12 12.00 Sets periods per year. 25 KxPZVr) 300.00 Stores length of mortgage (25 X 12 = 300 months). 0 (FV) 0.00 Stores loan balance after 25 years. 72500 (PyJ 72,500.00 Stores original loan balance. 13.8 QZŸR] 13.80 Stores annual interest rate. -861.65 Calculates monthly payment. Step 2. Since (he payment is at the end of the month, the last payment and the balloon payment occur at the same time.
I 000*00 [OOOOOO nOQC* taoooo boooo. jOOOOC ^ooocjj The value in PMT should always be rounded lo two decimal places when calculating FU'or PVio avoid small» accumula tive discrepancies between non-rounded numbers and actual (dollars and cents) payments. If the display is not set to two decimal places» press BlDISPi 2. Keys: Display: Description: ■ÍRÑDl ÍPMD -861.65 Rounds payment lo two decimal places, then stores. 48® 48.00 Stores 4 year term (12 x 4) that you expect to own house. m -70,725.
FV » 3.000.00 Since this account has no regular payments {PMT = 0), the payment mode (End or Begin) is irrelevant. Keys: Display: Description: ■I CLEAR ALLI 12 P Yr Displays a temporary message and clears all registers. o.oo” 1 liPTYRl 1.00 Sets P/YR to 1 since interest is compounded annually. 2000 -2,000.00 Stores amount paid out for first deposit. 3000 iFVl 3,000.00 Stores the amount you wish to accumulate. 7.2 7.20 Stores annual interest rate. i] 5.
Since (he calculated value of N is between S and 6, it will take six years of annual compounding to achieve a balance of at least $3,000. Calculate the actual balance at the end of six years. 6® 6.00 Sets ® to 6 years. m 3,035,28 Calculates amount you can withdraw after 6 years. Example: An Individual Retirement Account. You opened an individual retirement account on April IS, 1985, ^^ith a deposit of $2,000. Thereafter, you deposit $80.00 to the account at the end of each half month.
80 -80.00 Stores regular semi monthly deposits. 8.3 8.30 Stores interest rate. 15 lIxP/YRl 360.00 Stores number of deposits. 63.963.84 Calculates balance. ши Example: An Annuity Account. You opt Гог an early retirement after a successful business career. You have accumulated a savings of $400,000 that earns an average of 10% annual interest, compounded monthly.
50BxP/YRI 0 (FV] Ш) 600.00 0.00 3.328.68 Stores number of withdrawals. Stores balance of account after 50 years. Calculates amount that you can withdraw at the beginning of each month. Lease Calculations A lease is a loan of valuable properly (Икс real estate, automobiles, or equipment) for a specific amount of lime, in exchange for regular pay* mcnls. Some leases arc written as purchase agreements, with an option to buy at the end of the lca.se (sometimes for as little as Sl.OO).
FV = 7,500.00 Ж РМТ - ? жЖ 35 I/YR - 14% N - 36 P/YR - 12 36 Money received by lessor is positive. Money paid out by lessor is negative. PV «■ -13,500.00 Begin Mode Set to Begin mode. if annunciator is not displayed. Keys: Display: Description: 12а[р7щ 12.00 Sets payments per year. 14 [ITYRI 14.00 Stores desired annual yield. 13500 Ea (pg -13,500.00 Stores lease price. 7500 7,500.00 Stores residual (buy out value). 36 (n] 36.00 Stores length of lease, in month.s. [рШ1 289.
Ii‘ the annual interest rate is 18%, what is the capitalized value of the lease? Begin Mode PV = ? This solution requires four steps. 1. Calculate the present value of the 47 monthly payments: (4x12) -1 = 47. 2. Add the value of the additional advance payment. 3. Find the present value of the buy option. 4. Sum the values calculated in steps 2 and 3. Step 1- Find the present value of the monthly payments. Set to Begin mode. Press BIBEG/ENDI if annunciator is not displayed.
oEy) 0.00 Stores FV for step 1. 18 il/YR 18.00 Stores interest rate. m 81.735.58 Calculates present value of 47 monthly payments. Step 2. Add the additional advance payment to PV. Store the answer. m iRCLi iPMTi m S Fm] 84,135.58 84,135.58 Adds additional advance payment. Stores result in M register. Step 3. Find the present value of the buy option. El 48.00 Stores month when buy option occurs. 0 fPMTl 0.00 Stores zero payment for this step of solution. 15000 m iFVI -15,000.
Amortization ooooaoi oooooo ^30000 ooooo OOOQO oooac OOOOC3 Amorlization is the process of dividing a payment into the amount that applies to interest and the amount that applies to principal. Payments near the beginning of a loan contribute more interest, and less principal, than payments near the end of a loan. TIME The Miamorti key on the HP-lOB allows you to calculate. ■ The amount applied to interest in a range of payments. m The amount applied to principal in a range of payments.
The BlAMQRTI function assumes you have just calculated a payment or you have stored the appropriate amortization values in I/YR^ FV, PMT^ wdP/YR. msi Annual nominal interest rate. Starting balance. QQÛI Payment amount (rounded to the display format), ■iP/YRl Number of payments per year. The numbers displayed for interest, principal, and balance arc rounded to the current display setting. To Amortize. To amortize a single payment, enter the period number and press lINPUTi, then press BlAMORTl.
Exampio: Amortizing a Range of Paymanta. Calcuiate the first tvb-o years of (he annual amortization schedule for a 30 year, $80,000 mortgage, at 9.75% annual interest with monthly payments. Set to End mode. Press №B£0/ENDI if aEOIN annunciator is displayed. Display: Deacrlption: 12.00 Sets payments per year. 360.00 Stores total number of payments. 9.75 9.75 Stores interest per year. 80000 fPVl 80.000.00 Stores present value. o(E3 0.00 Stores future value. [РЙТ1 -687.
Amortize the !U:cond year; РЕПЗ-24 Displa)*s next range of periods. 0 Int -7,731.67 Displays interest paid in second year. 0 Prin -516.17 Displays principal paid in second year. 0 bAL 79,015.41 Displays loan balance after 24 payments. The amount paid toward interest and principal (7,731,67 + 516.17 » 8,247JM) equals the total of 12 monthly payments (12 x 68732 * 8,24734). The remaining balance equals the initial mortgage less the amount applied toward principal (80,000 - 468.42 - 516.17 » 79,015.
Amortize the 1st, 2Sth, and 54tli payments. 0 1.00 Enters first payment. PEr 1 - 1 Displays amortized payment period. Int Displays interest. 0.00 0 Prin -310.42 Displays first principal payment. 0 bAL 13,939.58 Displays loan balance after one payment. 25 lINPUTI 25.00 Enters payment to amortize. ■IamortI PEr 25 - 25 Displays amortized payment period. 0 Int -90.21 Displays interest paid on 25th payment. 0 Prin Displays principal paid on 25th payment. -220.
Interest Rate Conversions ommmoo ooooon сэоооо □ ооосз! □ oooo The Inlcrcsl Conversion application uses three keys: BlNOM%l. BIEFF%L and Mp7yrI, They convert between nominal and annual cfTective interest rates. Nominal and effective interest rates arc described on page 47. OODOO □ ooao If you know an annual nominal interest rale and you wish to solve for the corresponding annual effective rate: 1. Enter the nominal rate and press BlNOM%l. 2. Enter the number of compounding periods and press BIP/YRI.
Firsl Bank 6.70% annual interest, compounded quarterly. Second Bank 6.65% annual interest, compounded monthly. Third Bank 6.63% annual interest, compounded 360 times per year. First Bank. Keys: Display: Description: 6.7 6.70 Stores nominal rate. 4.00 Stores quarterly com pounding periods. 6.87 Calculates annual effective rale. 6.65 6.65 Stores nominal rate. 12i(PZ?S) 12.00 Stores monthly com pounding periods. 6.86 Calculates annual cfTcctivc rate. 6.63 6.63 Stores nominal rate.
Compounding and Payment Periods j •■■OOj ooooo oooo ooooo □ oooo ooooo ooooo The TVM application assumes that the compounding periods and the payment periods are the some. Some loan install ments or savings deposits and withdrawals do not coincide with the bank's compounding periods. If the payment period differs from the compounding period, adjust the interest rate to match the payment period before solving the problem.
Step 2. Calculate the future value. Set to Begin mode. Press B(BegZenQ if annunciator is not displayed. 0.00 Stores present value. 25mipRm -25.00 Storc.s payment. 7llxP/YRI 84.00 Stores number of pay ments per year. ea 2,519.61 Calculates balance after' years.
6 Cash Flow Calculations How to Use the Cash Flow Application oaoaoo daaasD BOOOC oaaoo aooao ODOOD loooac The cash flow application is used to solve problems where cash flows occur over regular intervals but arc of varying amounts. You can also use cash How calculations to solve problems with rcgtilar, equal, periodic cash flows, but these situations are handled more easily using TVM. In general, these arc the steps for cash flow calculations on the HP-IOB. 1.
A1 Flows received are positive. Flows paid out are negative. Keys: Display: Description: ■Icl6Ar aLLI 0.00 12.00 Clears all registers. 12BiP7VR1 5000 W] CFO -5,000.00 CF1 2000 Ea Stores periods per year. Enters initial cash flow. Displays cash flow group numlrer while you hold down iCFlI. Enters next cash flow. -2,000.00 CF2 4000 iC^ Enters next cash ftow. -4,000.00 11765.29 ISdl CF3 Enters final cash How. 11,765.29 Qm»aD 012Q 76 38.98 Calculates annual nominal yield. 3.
NPV and IRR/YR: Discounting Cash Flows Chapter 4 demonstrates the use of cash flow diagrams to clarify financial problems. This section describes discounted cash flows. The NPViund ¡RR/YR functions arc frequently referred to as discoutUed cash flow functions. When a cash flow is discounted, you calculate its present value. When multiple cash flows arc discounted, you calculate the present values and add them together. The net present value {NPV) function finds the present value of a series of cash flows.
CF 3 « 10,000, N 3 » 1 Whenever you enter a series of cash ffows, it is important to account for every period on the cash flow diagram, even periods with cash flows of zero. Entering Cash Flows The HP-lOB can store an initial cash flow plus 14 additional cash flow groups. Each cash flow group can have up to 99 cash flows. The cash flows arc stored in registers Rq tlirough Ro and R o through R Enter cash flows using the following steps; 1. Press BiCLEAR all] to clear the registers.
Example. Enter the cash flows from the preceding diagram and calcu late the JRR/YR. Then calculate the effective interest rate. Assume there arc 12 periods per year. Keys: Display: Description: ■l CLEAR ALLl 0.00 Clears all registers. 121íp7yr1 12.00 Sets Ip/YRI to 12. 11000 m CFO Enters initial cash flow. Displays cash flow group number for as long as you hold down ICFjl. -11,000.00 CF1 [gdi 0.00 6|[ÑI] n1 6.00 1000 fCFH CF2 , 1 000.
To replace a cash flow, enter the new cash flow and press BiSTOl followed by the cash flow (register) number. To replace the number of limes a particular cash flow occurs, IRCLI the cash flow whose number of occurrences will change. Then, enter (he number of times it occurs and press BfRIl. To replace both the cash flow and number of times it occurs, enter the new cash now, press BiSTOl followed by the cash flow (register) number.
10.000 I/YR = 15% Keys: Display; Description: ■ICLEAR ALU 0,00 Clears registers. 12BiP7YRl 12.00 Sets payments per year. 0(CF]) CFO 0.00 Enters initial cash flow of zero. The cash flow number is displayed as long as you hold down the (CFil key. o(cHj) CF1 Enters first cash flow. 0.00 n1 5000 fCFil 3.00 Enters number of occurrences. CF2 Enters second cash flow. 5,000.00 0(CFl) CF3 Enters third cash flow. 0.00 4 mm 5000 fCF]l n3 4.00 Enters number of occurrences.
0 fCFjl CF5 Enters fifth cash flow. 0.00 4|[^ n5 4.00 Enters number of occurrences. 7500ÎCFJ1 CF6 7,500.00 Enters sixth cash flow. 0[çEB CF7 Enters seventh cash flow. 0.00 n7 9|[^ 9.00 10000 fcFil CF8 10,000.00 Enters number of occurrences. Enters next cash flow. The cash flows thaï describe your prospective investment arc now in the calculator. You can press IRCLl 0, followed by IRCLl ÎCFII and IRCLI BED, repeatedly to view the cash flows and number of times each occurs.
Calculating Internal Rate of Return 1. Press BICLEAR ALU, store number of periods per year in P/YR. 2. Enter the cash flows using (CF^ and (Nfl. 3. Press II 1шгдп When you calculate ¡RR/YR^ you get llic annual nominal rate that gives an NPV of /его. The following example uses the cash flows that were entered in the previous example. More than one IRR/YR can exist. If you get the no SoLution message see Appendbc В (page 127). Example.
10.000 7.500 ' jк 5,000 5.000 ^ >к > 4-1-Ь ■b u 1 1 M I-I H-I 1 1 1 -b11 13 15 17 19 21 1MI 23 25 IRR/YR = ? Y -28,000 Keys: 28000 ^ ■ (ШШ Display: Description: 0 -28.000.00 Changes initial cash How. 12.49 Calculates annual nomi nal yield. More examples (hat use NPV and IRR/YR calculations arc given in chapters, “Additional Examples.” Automatic Storage of IRR/YR and NPV When you calculate NPVy the result is stored in PV Гог your convenience.
7 Statistical Calculations _______ l! The (13 and ШШВ зге used to enlcr and delete data for *□ 00000 iwo-variablc statistics. Summation data is accumu
Entering Statistical Data There is no limit to the number of values you can accumulate in the statistical registers. * One-Varfable Statistics To enter jc data for one-variable statistics complete the following steps: 1. Clear the contents of through R9 by pressing BlcL zl. 2. Enter the first value and press (13. T'hc HP-lOB displays n, the number of items accumulated. 3. Continue accumulating values by entering the numbers and pressing d+).
Correcting Statistical Data Incorrect entries can be deleted using B[13- If either value of an a:,v oair is incorrect, you must delete and reenter both values. Correcting One^Variable Data To delete and reenter statistical data; 1. Key in the X-value to be deleted. 2. Press i(B to delete the value. The n-value is decreased by one. 3. Enter the correct value using [ZTI, Correcting Two-Variable Data To delete and r e e n t e r . p a i r s of statistical data: 1.
Summary of Statistical Calculations Some functions return two values. The : annunciator indicates that two values have been returned. Press BisWAPl to sec the hidden value. Keys Description Arithmetic mean (aver age) of the y-values. SIswAPi to Display Mean (average) of the y-values if you entered y-data. Mean of the x-values weighted by the y-vaiues. Sampie standard devia tion of the x-values.* Sample standard devia tion of the y-values if you entered y-data.
Description Keys (RCLl 4 (n) Number of data points entered. fRCLl5(E)i) Sum of the x-values. (R^6(i:y) Sum of the y-values. RCL17(D<2) Sum of the squares of the x-values. (RcOsoy) Sum of the squares of the y-values. fRcqgiExy) Sum of the products of the x- and y-values.
4.5 (1+) 1.00 Enters first time. 4d+) 2.00 Enters second time. 2g±) 3.00 Enters third time. 3.25 d±] 4.00 Enters fourth time. 3.5 d3 5.00 Enters fifth time. 3.75 d±] 6.00 Enters sbah time. ■(M) 3.50 Calculates the mean. ■EiSa 0.85 Calculates the sample .standard deviation. iRCp7 77.13 Displays Ev^. m iRCD4 6.00 Displays ;i. Ql(^ 3.59 Calculates the root mean square. 1________1 QOOOOO oooooo CZDOOOO aovao • aacDo ooooa ooooo ^ ..............
177 iINPUTi 83 fg»1 3.00 Enters liciglit and wciglit of player 3. 185 lINPUTI 77 (13 4.00 Enters height and weight of player 4.. ■diS 184.25 Calculates mean of heights (r). 82.75 Displays mean of weights 02E3a O')M\cr_x,cry\ iRCOS 5.80 Calculates population standard delation for heights (jtr). 4.71 Displays population standard dc\aation for weights (y). 331.00 Displays the total of the /s.
Linear Estimation. The straight line calculated by linear regression can be used to estimate ay-value for a given jc-valuc, or vice versa: 1. Enter the A;y-data using the instructions on page 86. 2. Enter the known x-valuc ory-valuc. m To estimate X for the giveny, enter thcy-valuc, then press ■da. ■ To cstimalcy for the given x, enter thex-valuc, then press l(£^. Example: Forecasting. Ali's A/^ileus advertises on a local radio sta tion.
3.000,00 . / , (forecasted) • /• 2 000.00 / Sales in Dollars / m e 425.88 /• 1,000,00 V / “1-------- 1----- 1-----r 1-------- 1----- 1----- \----- 1“ 0 12 3 45678 Minutes of Advertising Keys: Display: Description: ШШИ 0.00 Clears statistical registers. 2 IINPUTI 1400 fZ+1 1.00 Enters minutes and sales for consecutive weeks. 1 IlNPUTl 920 d+) 2.00 3 IINPUTI 1100 iZ+1 3.00 5 IINPUTI 2265 (Ё+1 4.00 5 IINPUTI 2890 fZ+1 5.00 4 IINPUTI 2200 i!+l 6.00 0Ш [Ш 376.
im 3.357.38 Estimalcs sales if 7 minutes of advertising were purchased. 3.783.25 Estimates sales if 8 minutes were purchased. How many minutes of advertising should Ali’s buy to attain sales of $3,000? 6.16 3000 |[^ Estimates minutes of advertising required for $3,000 in sales. Weighted Mean The following procedure calculates the weighted mean of data points.v¡, ^2,.. -tXn occurring with weights >»1,^2»* ••>yn1. Use IINPUTI and [|+] to enter pairs. Thcy-valucs arc the weights of the.r-values. 2.
8 Additional Examples Business Applications Setting a Sales Price One method for setting the per unit sales price is to determine the cost of production per unit, and then multiply by the desired rale of return. For this method to be accurate, you must identify all costs associated with the product. The following equation calculates unit price based on total cost and rate of return: PRICE = TOTAL COST -r NUMBER OF UNITS x (1 + (%RTN -r 100)) Example. To produce 2,000 units, your co.st is $40,000.
Example. Given the following sales data, what are the sales estimates for years six and seven? Year 1 Sales $ 10,000 2 11,210 3 13,060 4 16,075 5 20,590 Keys; Display: Description: ■iem 0.00 Clears statistics registers. 1 QnpDt] 10000 ШЗ 1.00 Enters first year and sales for that year. 2QnpDT) 11210 d±] 2.00 Enters .second year’s data. 3 QnpDT) 13060 Ё+] 3.00 Continues data entry. 4 fiNPPfl 16075 ШВ 4.00 5 lINPUTI 20590 Ш+] 5.00 ешш 22,000.50 Estimates .sales for year .six.
COST% - DISC% X 360 X 100 ((100 - D1SC%) X (TOTAL DAYS - DISC DAYS)) DISC% is ihc discount percent if the payment is made early. TOTAL DAYS is the total number of days until the bill must be paid. D/5C DAYS is the number of days for which the discount is available. Example. You receive a bill with the credit terms 2/10, NET/30. What Is the cost of not taking the cash discount? Keys: Display: Description: 2 0 360 (x) 100 (3 72,000.00 Calculates numerator in equation.
Keys: Display: Description: 450 r^Mlixl 10 0.10 Stores interest. 0 60 0 365 0 7.40 Calculates interest owed. 0@M]0 457.40 Calculates total owed. Continuous Compounding The equation Гог calculating an cfTcclive rale for continuous compounding is: EFF% = (c
18.14 Calculates annual nomi nal rate for a monthly paynicnt period. Set to End Mode. Press BiBEG/ENPl if BEGIN annunciator is displayed. isifip; 180.00 Stores number of months. 250 m -250.00 Stores regular payment. 4572.8 Ea (Pg -4,572.80 Stores current balance as a negative value (like an initial investment). m 297.640.27 Calculates account bal ance after 15 years of payments with 18% interest compounded continuously.
Keys: Display: Description: 12SiPTYRl 12.00 Sets payment.^ per year. 9.00 Stores interest rate. 20BlxP/YRI 240.00 Stores number of months. 100000 fPVl -100,000.00 Stores original amount of mortgage. 0(PV) 0.00 Enters amount left to pay after 20 years. (PMT] 899.73 Calculates regular payment. Step 2. Enter the new value for N indicating when the balloon occurs, then find FVt the amount of the balloon. Display: Description: 899.73 Rounds payment to two decimal places for accuracy.
Annual Percentage Rate for a Loan With Fees The annual percentage ralc./lP^, incorporates fees usually charged when a mortgage is issued, which cfTcctivcIy raises the interest rale. The actual amount received by the borrower (the Pl'^ is reduced, while the periodic payments remain the same. Thot/^/? can be calculated given the term of the mortgage {N periods), the annual interest rale {I/YR)^ the mortgage amount (newPi^, and the amount of the fee.
Example: Interest-Only Loan With Fee« A $1,000,000, lO-ycar, 12% (annual interest) intcrest^oniy loan has an origination fee of three points. What is the yield to the lender? Assume that monthly payments of interest arc made. Set to End mode. Press | if BEGIN annunciator is displayed. Keys: Display: Description: 121(EZyH) 12.00 Sets payments per year. 12 G Ш 12.00 Stores interest rate. 101 120.00 Stores length of mortgage. 1000000 fPVl 1,000.000.00 Stores original amount of mortgage.
1. Calculate the amount of simple interest that accrues during the frac tional first period and add it to the loan amount. This is the new FK You must be able to calculate the length of the odd first period as a fraction of the whole period. (For example, a 15-day odd first period would be 0.5 periods as.suming a whole period to be a 30-day month.) 2. Calculate the payment using the newPy, with N equal to the number of full periods.
Automobile Loan Example. You arc buying a new $14,000.00 sedan. Your down payment is $1,500 and you arc going to finance the remaining $12,500. The car dealer is ofTcring two choices for financing: ■ A 3-ycar loan with an annual interest rate of 3.5%. ■ A 3-year loan with an annual interest rate of 9.5% and a $1,000.00 rebate. With which choice do you pay less for the car? Set to End mode. Press BlBEt^EN^ if BEGIN annunciator is displayed. Calculate the first option; Keys: Display: Description: 12 12.
Canadian Mortgages In Canadian mortgages, the compounding and payment periods are not the same. Interest is compounded semi-annually wliile payments arc made monthly. To use the TVM application in the HP*10B, you need to calculate a Canadian mortgage factor (which is an adjusted interest rate) to store in I/YR. For additional information on interest rate conversions, see the section “Interest Rate Conversions” in chapter 5. Example.
What if ... TVM Calculations One of the mosl valuable aspects of (he HP-10B*sTVM application is the ease with which it handles the question ‘'what i f . . i n financial calcula tions. For example, one of the most popular “what if.. questions is, “What if the interest rate changes to...
(Ш шв шшт 514.82 Calculates number of biweekly payments. 19.80 Displays years required to pay off loan. Part 3. What if you had monthly payments as in part 1, but chose a 15-year term? What would your new payment be? What would be the total mtcrest paid on the contract? Keys: Display: Description: 12 |j 12.00 Sets payments per year. 151 П;1Ш 180.00 Stores new term. -8.446.53 Calculates payment for shorter term. ® ШШЕИ+1 -1.520,374.70 Calculates total paid. ШШ(РУ)Е) -785,374.
This problem is solved in two steps. First calculate the amount you’ll need when she starts college. Start with an interest rate conversion because of the monthly compounding. ^ $15,000 > I/YR =9% m i i i H i n H i m i n n Year 1 Year 2 i m i m m i m u m n Years Year 4 Keys: Display: Description: 9 lEEia 9.00 Stores annual nominal rate. 121(EZXSI 12.00 Stores number of com pounding periods used with this nominal rate. 9.38 Culcululcs annual effective rate.
OÍFVl 0.00 Stores balance at end of four years. -52.713.28 Calculates amount required when your daughter starts college. Then use that Py as the fV on the following cash flow diagram, and cal culate the PMT, FV from A previous calculation. l/YR - 9% 1---------1 2 3 4 142 143 144 PMT - ? Set to End mode. Press | am EHeBUS if BEGIN annunciator is displayed. 52,713.28 Stores amount you need. 0(PV) 0.00 Stores amount you are starting with. 12MiP77ff] 12.00 Sets payments per year.
The purchasing power of that future value depends upon the inflation rate and the duration of the account. Example. You are considering opening a lax-deferred account with a dividend rate of 8.175%.
8 flTYR] 0 f^Tl f^] 339,994.39 Stores after-tax future value in - 22.995.36 Calculates present-value purchasing power of afler-tax FK, assuming an 8% inflation rale. Value of a Taxable Retirement Account This problem uses the TVM application to calculate the future value of a taxable retirement account that receives regular, annual payments begin ning today (Begin mode). The annual tax on the interest is paid out of the account. (Assume the deposits have been taxed already.) Example.
345.505.61 m SnZYBJO GG91 (pg -23,368.11 Calculates amount in account at retirement. Calculates present-value purchasing power of FV^ assuming an 8% inflation rate. Cash Flow Examples Wrap-Around Mortgages A wrap-around mortgage is a combination of refinancing a mortgage and borrowing against real estate equity. Usually the two unknown quantities in the wrapped mortgage are the new payment and the rate of return to the lender.
Keys: 1Ш Display: Description: CFO -35.000.00 Enters $35,000 for loan amount. CF1 Enters net payment for first 82 months. JESS 754 Ш 107.59 82 (БШ S2D 180Е]82| liiUWdil n1 82.00 Enters number of times payment occurs. CF2 861.59 Enters net payment for next 98 months. n2 98.00 Enters number of times payment occurs. 10.16 Calculates annual return.
Scl to End mode. Press BiBEG/ENDl Keys; Display: ■ICLEAR ALLI if BEGIN annunciator is displayed. Description: Clears all registers. 12SfP7YR) 12.00 12000 CFO -12,000.00 Enters initial cash flow. 0(^ CF1 Enters amount in 0.00 group 1. n1 2.00 Enters number of times payment occurs. 3000 (CFj] CF2 -3,000.00 Enters amount in group 2. 3|[nD n2 3.00 Enters number of times payment occurs. OiCFilOirNll n3 9.00 Enters number of times payment occurs.
A Assistance, Batteries, and Service Wc at Hewlett-Packard are committed to providing you with ongoing support. You can obtain answers to questions about using your calculator from our Calculator Support department. Plca.se read “Answers to Common Questions” before contacting us. Our experience has shown that many of our customers have .similar questions about our products. If you don't find an answer to your question, you can contact us using the address or phone number listed on the inside back cover.
A: Exponent of ten (for example» 2.51 x 10'*^). Refer to “Scientific and Engineering Notation*' on page 27. Q: Why do I get a wrong answer or the no SoLution message when using TVM? A: Be sure to enter a value for four of the five TVM values before you .solve for the fifth, even if one of the values is zero. (Don’t forget to store a zero for (FVI if you completely pay ofT a loan.) Clearing all the registers (BiCLEAR ALLh before entering your known values accomplishes the same thing.
Noise Declaration. In (he operator position under normal operation (per ISO 7779); LpA < 70dB. Power and Batteries The calculator is powered by three button cell batteries. Expected battery life depends on how (he calculator is used and (he chemical content of the battery. Use only fresh button-cell batteries. Do not use rechargeable batteries. Low Power Annunciator When the low buttery annunciator (
Installing Batteries 1, Have three fresh bullon-ccll baUcries u( hand. Only touch batteries by their edges. Wipe each battery with a lint-free cloth to remove dirt and oil. 2. Make sure the calculator is off. You will lose memory if the bat teries are removed when the calculator is on. Do not press (C) again until the entire procedure for chan^ng batteries Ls completed. 3- Hold the calculator as shown.
6. Slide the tab of the battery-compartment door back into the slot in the calculator case. Determining if the Calculator Requires Service Use these guidelines to determine if the calculator requires service. If these procedures confirm that the calculator is not functioning properly, read the section “If the Calculator Requires Service” on page 124. ■ The calculator won’t turn on (nothing is in the display): 1. Reset the calculator. Hold down the O key and press (E3 at the same time.
The calculator doesn’t respond to keystrokes (nothing happens when you press the keys): Reset the calculator (sec step 1 above). 2. Erase memory (sec step 2 above). 3« ir the calculator fails to respond after steps 1 and 2, remove the batteries (page 119) and lightly press a coin against both calcu lator battery contacts. Put the batteries back in and turn on the calculator. It should display ALL CLr. If steps 1 through 3 fail to restore calculator function^ the calculator requires service.
3. Starling at the upper left corner ([^) and moving from left to right, press each key in the top row. Then, moving left to right, press each key in the second row, third row, etc., until you've pressed each key. ■ If you press the keys in the proper order, and they arc functioning properly, the calculator displays two-digit numbers. (The calculator is counting the keys using hexadecimal base.
Limited One-Year Warranty What Is Covered The calculator (except for the batteries, or damage caused by the bat teries) is warranted by Hewlett-Packard against defects in materials and workmanship for one year from the date of original purchase. If you sell your unit or give it as a gift, the warranty is automatically transferred to the new owner and remains in cifcct for the original one-year period.
Products arc sold on the basis of specifications applicable at the time of manufacture. Hewlett-Packard shall have no obligation to modify or update products, once sold. Consumer Transactions in the United Kingdom This warranty shall not apply to consumer transactions and shall not affect (he statutory rights of a consumer. In relation to such transactions, the rights and obligations of Seller and Buyer shall be determined by statute.
In other countries: Conlact your HewIcU-Packard sales ofTicc or dealer or write to the Corvallis Service Center (listed on the inside of the back cover) for the location of other ser\ace centers. If local service is unavailable, you can ship the calculator to the Corvallis Service Center for repair. All shipping, reimportation arrangements, and customs costs arc your responsibility. Service Charge There is a standard repair charge for out-of-warranty service.
Warranty on Service Service is warranted against defects in materials and workmanship for 90 days from the date of service. Service Agreements In the U.S., a support agreement is available for repair and service. Refer to the form in the front of the manual. For additional information, contact the Corvallis Service Center (sec the inside of the back cover). Regulatory Information U.S.A. The HP-lOB generates and uses radio frequency energy and may interfere with radio and television reception.
B More About Calculations IRR/YR Calculations The calculator determines IRR/YR for a set of cash flows using mathematical formulas that “search” for the answer. The process finds a solution by estimating an answer and then using that estimate to do another calculation —this is called an iterative process. In most cases, the calculator finds the desired answer, since there is usu ally only one solution to the calculation. However, calculating IRR/YR for certain sets of cash flows is more complex.
Case 5. The calculator displays; no Solution. There is no answer. This situation might be the result of an error, such as a mistake in keying in the ca.sh flows. A common mistake that results in this mes* sage is putting the wrong sign on a cash flow. A valid cash-flow .series for an IRR/YR calculation must have at least one positive and one negative cash flow. Halting and Restarting iRR/YR The search for IRR/YR may take a relatively long time.
Effect of Using E~ to Correct Data The HP-lOB stores the statistical numbers in an ''accumulated” fashion. It doesn't store every number that you enter, but rather it performs inter mediate calculations when you press the EJ The BE l^cy performs the opposite intermediate calculations to cfTcctively remove a number or pair of numbers from the stored results.
Time Value of Money (TVM) Paymcnl Mode Factor: S = 0 for End mode; 1 for Begin mode. P/YR -N 1 0 = PV + 1+ i%X5 100 “ xPMTy 100 i% 100 + FVx 1+ i% -N 100 Amortization EfNT = accumulated interest EPRN = accumulated principal I = periodic interest rate BAL is initially PV rounded to the current display setting. PMT is initially PMT rounded to the current display setting.
For each payment amortized: INT' « BALxi (¡NT' is rounded to the current display selling; ¡NT' = 0 for period 0 in Begin mode.) ¡NT = INr (with sign oiPMT) PRN = PMT + INr + PPN E!NT^ = S/yV7^rf + ¡NT IPRN^ - + PP^ Interest Rate Conversions EFF% 1+ r/Y R NOM% lOOxP/YR -1 xlOO Cash-Flow Calculations i% = periodic interest rate j = the group number of the cash flow.
— Sx — Sy — Елу n E)' iSxji Sx^ - Sx /1 = -1 n Sy2 /I 5>^ = V S.v^ - n -1 S; ;i OX = .2 ■ i^)L n n /I Ел> /I r= Sy' _ (M S.2 . iM /I n S.^. - ^ /I m- . \2 S.
Messages Press [C] or 0 to clear a message from the display. ALL CLr (All Clear), Memory has been erased (page 23). bAL (Balance). Balance in an amortization schedule (page 67). CF (Cash Flow/). Cash flow number (page 78). COPr. HP 1987 (Copyright HP 1987). Copyright is displayed during self-test. Error - Func (Error “ Function). ■ Attempt to divide by zero. ■ Attempt to calculate n! with n< 0 or n a noninteger. ■ Attempt to calculate the logarithm of zero or a negative number.
Error - P_Yr (Error - Payments per Year). Attempt lo solve for F/YRy or store a number in P/YR (hat is outside (he legal range (1 to 999) or is not an integer. Error - PEr (Error - Period). Attempt to enter a value in that is outside the legal range (1 to 99) or is not an integer. Error - Soln (Error - Solution). A .solution for IRR/YR or f/YR may or may not exist. If you arc attempting to solve l/YRy you may be able to perform the calcu lation using IRR/YR.
OFLO (Overflow). The magnitude of a result is too large for the calculator to handle. Message is displayed for a moment, then the overflow result is returned (±9.99999999999E499). The overflow message is also displayed if an intermediate TVM or cashflow calculation results in an overflow condition. In this ease, the message remains in the display. PEr - (Periods starling - ending). Displays beginning and ending payments for an amortization schedule (page 67).
Index Special Characters 0,21 I, 21, 24,118 0, 21 (3,21 0.21 ;,24 (S,22 □.28 ED. 28 , 31,45 BSiS ,32 1.24 (^, 26,40 QZ3. 26,40, 41 E],40 (B, 41 3, 41 0,41 E±),85 S.85 |o-.t,',85 85 85 Sxy,85 IxP/YRI. 52 0, 22 136 Index Accumulative discrepancies, 58 Add percent, 31 Adjusted interest rate, 73 Advance payments, 63 ALL CLr, 24,133 (AMORT).
Aulo incrcmcnl, 67 Automatic coustant, 35 Automobile loan, 104 Average, 88 B Backspace, 22 bAL,67 Balance, 43,67 Balloon payment, 43,56 Basics at a glance, 10 Batteries, 118 changing, 118 Bf.
Display all digils, 28 Display format, 21 Dot, 28 Down payment, 53, 55 Future value, 43,48 E3,43,48, 52 Grouping cash flows, 77 Guess for/ЛЛ/УЛ, 127 (E),40 E, 27 (11.
K, L 0, 35 Lease, 62 advance payntenis, 63 Linear regression, 85.91 EH],-«) Loan, with fees, 101 Loans, S3 interest only, 102 number of payments. 52 odd first payment, 102 cash flows, 44 numbers, 22 sign. 13 Net future value, 114 Net present value, 17, 49, 80 Netted value, 82 ED. 78 |N0M%I.51.71 Nominal annual rale, 47 rate, 71 Nominal rale, 16 NPK 77 M (m3. 35.37 M register, 29. 37, 35 Malfunction, 116 (MM). 33 Margin, 11, 33 Markup, 11, 33 Maturity value.
Present value, 48 Price, 11 Prin, 67 Principal, 45,67 Principal reduction, 66 Setting a sales price, 95 Shift key, 10,24 Short term investment, 75 Sign (py), 48,52 iPTYRi.
Taxable retirement account, 111 Tax-deferred account, 110 Tax-free account, 110 3 Key Memory, 35 Timeout, 21 Trailing zeros, 28 Turn off, 21 Turn on. 21 TVM, 14 equations, 130 problems, 47 TVM at a glance, 13 Two-number functions, 26 Two-variable statistics, 86 u,v Uneven cash flows, 80 Value of a fund, 114 Viewing cash flows, 79 w Warranty, 123 Weighted mean, 94 What i f . . . . 14,106 What i f . . .
