Copyright: (c) 1994 Wave Software, All Rights Reserved


Table of Contents
Calculator Help Index:

Menu Help

Working with the Financial Registers

The Stack

Index of Calculator Formulae


The n Financial Key
The [image] Financial Key:

The [image] key stores or computes the number of compounding periods.

See also:

Formula for compound interest

Working with the Financial Registers


The i Financial Key
The [image] Financial Key:

The [image] key stores or computes the compound interest rate based on the numbers in the other financial registers.  The interest rate is expressed as a percentage and not as a decimal.

See also:

Formula for compound interest

Simple interest calculations

Compound interest calculations

Working with the Financial Registers


The PV Key
The [image] Financial Key:

The [image] key stores or computes the present value based on the numbers in the other financial registers.

See also:

Formula for compound interest

Working with the Financial Registers


The PMT Key
The [image] Financial Key:

The [image] key stores or calculates the value of the periodic payment.

See also:

Formula for compound interest

Working with the Financial Registers


The [image] Financial Key:

The [image] key stores or calculates the value of the future value.

See also:

Formula for compound interest

Working with the Financial Registers


Working with the Financial Registers
Working with the Financial Registers:

The [image] [image] [image] [image] and [image] keys are collectively known as the financial registers.  These special memory registers allow the variables of different financial functions to be stored or calculated.  Whether the number is stored or calculated depends on the previous operation.  If a number was just stored by any means into one of the financial registers, then pressing a financial register key will attempt to calculate the value of that variable based on the contents of the other financial registers.  Otherwise, the number in the display is stored in the financial register corresponding to the key pressed.

The contents of a financial register may be retrieved by pressing [image] followed by the one of the financial register keys.

See Also:

The [image] Key

The [image] Key

The [image] Key

The [image] Key

The [image] Key


The CHS Key
The [image] Key:

The [image] key either changes the sign of number in the display or the sign of the exponent if scientific notation is being used.

See also:

The [image] Key

Scientific Notation


Digit Keys
 through [image] digit keys:

The 0 through 9 digit keys are used for three functions:

1) To key in digits of a number to use in calculations.

2) If the [image] shift key is pressed before the digit, the length of the decimal number in the display is changed to the number of decimal places corresponding to the digit pressed.

3) After pressing [image] or [image], the digit specifies which storage register to reference.


Changing the number of decimal places
Changing the number of decimal digits displayed:

The 12C++ internally calculates all functions with 19 digits of accuracy, but the display of these numbers is limited to a rounded representation using 0 to 9 decimal digits.  To change the number of digits after the decimal place, press the f prefix key followed by a number, 0 through 9, that corresponds to the number of digits.

Example:

Assume that the calculator contains the number 1,234.56789

Keystrokes	Display

 	1,235.

 	1,234.6

 	1,234.568

 	1,234.567890000

The display accuracy is limited to 15 total digits.  If there are more than 6 digits to the left of the decimal, the digits to the right of the decimal displayed may be less than the number set using the [image] prefix key.

See Also:

The [image] Key

The [image] Key


The arithmetic operation keys:

The [image] [image] [image] and [image] keys perform arithmetic operations between the numbers in the X-register and Y-register.


The [image] Key:

The [image]  key raises the number in the y stack register to the x power.


The [image] Key:

The  [image] key divides 1 by the number in the x stack register.


The %T Key
The [image] Key:

The [image] key calculates what percentage the number in the x register is of the number in the y register.

Example:

The population of the United States is 250,000,000 people, and the population of California is 30,000,000 people.  What percent of the total US population lives in California?

Solution:

Keystrokes		Display
250		250.00
30		12.00	California is 12% of the US population

See also:

Percent Formulae


The D% Key
The [image] Key:

The [image] key calculates the percentage change between two numbers.  The initial number (or base number) is in the y register and the new number is in the x register.

Example:

Nevada's population in 1980 was 800,000 and 1,111,000 in 1989.  What was the percentage change in Nevada's population during the 1980's?

Keystrokes		Display
800		800.00
1111		38.88	Nevada's population grew by 38.88%

See Also:

Percent Formulae

Keyboard Accelerator for


The Keyboard Accelerator for [image] is either upper or lower case "D".


The % Key
The [image] Key:

The [image] key calculates a number that is x percent of y where x is the number in the x register and y is the number in the y register.

Example:

What is the sales tax on a $900.00 camera if the sales tax is 8.75 percent?

Keystrokes		Display
900		900.00
8.75		78.75	You will pay $78.75 in sales tax.
		978.75	The total price for the camera.

See also:

Percent Formulae

Stack Calculations


The EEX Key
The [image] Key:

The [image] key allows numbers to be entered in scientific notation.  The 3 digits at the right of the calculator's display represent the exponent and the digits to the left are the mantissa.

Example:

To key in the number $123,785,000,000 (the 1991 federal budget deficit), first convert the number to scientific notation (x.xxx   10x).  In this case, that would be 1.23785 x 1011.  To enter that into the calculator:

1) First enter the mantissa (1.23785 in the example)

2) Press the [image] key if you wish to enter a negative number

3) Press the [image] key to enter the exponent (11 in the example)

4) Press the [image] key if you wish to change the sign of the exponent.

See Also:

Scientific Notation


The R/S key
The [image] Key

The [image] key either starts a program or pauses an already running program.


The SST key
The [image] Key

The [image] Key allows the program in the calculator's memory to be stepped through one step at a time.


The f key
The [image] Key:

The [image] key is a prefix key to change the functions assigned to the other keys on the calculator key pad.  The functions that are accessed by pressing the [image] key are on the top of each button:


The g key
The [image] Key:

The [image] Key is a prefix key to change the functions assigned to the other keys on the calculator key pad.  The functions that are accessed by pressing the [image] Key are on the bottom of each button:


The STO key
The [image] Key

The [image] key will store the number in the display in one of 20 number storage registers.  These registers are addressed by pressing [image] followed by either a number 0 - 9 to address the first 10 registers, or by the [image] key then a digit 0 - 9 to address the next 10 registers.

See Also:

The [image] Key


The RCL Key
The [image] Key

The [image] key will recall the number in one of 20 number storage registers, push the stack, then place the number in the X register.  These storage registers are addressed by pressing [image] followed by either a number 0 - 9 to address the first 10 registers, or by the [image] key then a digit 0 - 9 to address the next 10 registers.

See Also:

The [image] Key


The [image] Function

The RND function rounds the internal representation of the displayed number to be the same as the displayed version.

Example:

Assume that the calculator contains the number 1,234.56789

Keystrokes	Display

 	1,235.

 	1,234.6

 	1,234.568

 	1,234.567890000

 	1,234.568

 	1,234.568

 	1,234.568000000

See Also:

Changing the number of decimal digits displayed


Switches the payment mode to assume all annuity payment occur at the beginning of a period.

See Also:

Payment Mode


Switches the payment mode to assume all annuity payment occur at the end of a period.

See Also:

Payment Mode


The [image] key calculates the price one should pay for a bond in order to achieve a desired yield to maturity.  To calculate:

1)	Enter the percent yield to maturity desired in the [image] register.

2)	Enter the annual percent coupon on the face of the bond (as a percent) in the [image] register.

3)	Enter the settlement date and press [image].

4)	Enter the maturity date.

5)	Press [image] [image].

The price (as a percent of redemption or par value) is shown in the display.  The interest accrued since the last payment date is held in the Y register.

See Also:

YTM

Entering Dates


Bond Functions

These functions allow you to calculate for either yield-to-maturity (YTM) or bond price with or without accrued interest.

See Also:

YTM

Price


Square Root

This function calculates the square root of the number in the display.


Yield to Maturity function

The [image] key calculates the Yield-to-Maturity of a bond.  To calculate:

1)	Enter the price (as a percent of redemption value, or par) in the [image] register.

2)	Enter the face coupon rate of the bond (as a percent) in the [image] register.

3)	Enter the settlement date and press [image].

4)	Enter the maturity.

5)	Press

See Also:

Price

Entering Dates


e ^ x

This function calculates the constant e to the exponent in the display.

Example

What is the future value of $1,000 invested at a continuously compounded 10% annual rate for 3 years?

The Future Value formula with continuous compounding is:

FV = Co e^(r t)

FV = Future Value

Co = Initial Investment

e = 2.71828

r = nominal interest rate per period

t = number of periods

Keystrokes	Display	Comment
.1	0.10	The Nominal Annual Interest Rate
3	0.30	Number of Periods
	1.35	Multiplier for Future Value
1000	1,000.00	The Present Value
	1,349.86	The Future Value

Example

A bank is quoting 9% compounded continuously on savings.  What is the equivalent rate for annual compounding?

The formula for effective annual interest rate is:

Effective Annual Interest = e ^ rate - 1

Keystrokes	Display	Comment
.09	1.09	e ^ 9%
1	0.09	The Present Value
100	9.42	Effective Annual Interest


This function calculates the natural logarithm of the number in the display.


Depreciation Calculations

The 12C++ is able to use three common methods to calculate depreciation and the remaining depreciable balance.  These three methods are straight line, sum-of-the-years-digits, and declining balance.  No matter which method of calculation is used, the input if the variables is similar:

1)	Enter the original asset cost in the PV register.

2)	Enter the salvage value in the FV register.  If the salvage value is 0, enter that.

3)	Enter the useful life of the asset in the n register.

4)	If the declining-balance method is used, enter the declining balance factor in the i register as a percent.  For example, if the factor used is 1.5 times the straight line method, enter 150 into the I register.

5)	Enter the number of years that you wish to calculate on the depreciation schedule into the display.

Press
  to calculate the straight line depreciation.
  to calculate the sum-of-the-years-digits depreciation.
  to calculate the declining-balance depreciation.

No matter which depreciation method is chosen, the calculated depreciation is displayed.  To display the remaining depreciable balance, press the [image] key.

See Also:

SL	Straight Line

SOYD	Sum-Of-the-Years-Digits

DB	Declining Balance

Formulae

Straight Line Method

Sum of the Years' Digits

Declining Balance


SL Straight Line Depreciation

This function calculates the straight line depreciation.

See Also:

Depreciation Calculations


SOYD Sum of the Years Digits Depreciation

This function calculates Sum-Of-theYears-Digits depreciation.

See Also:

Depreciation Calculations


DB Declining Balance Depreciation

This function calculates Declining Balance deprecation.

See Also:

Depreciation Calculations


FRAC

Returns the fractional part of the number in the display.


INTG

Returns the integer part of the number in the display.


P/R

Enters the program mode.


PSE

The PSE key inserts a one-second pause into a program.  This pause is usually inserted to allow intermediate results to be seen on the display.


Status Indicators
The Status Indicators

The status indicators are in a line at the bottom of the display.  These status indicators indicate various internal states of the calculator, such as whether the [image] or [image] keys have been pressed, the date format, and whether the calculator is in program mode.

The meaning of all the indicators is summarized in the table below.

Status Indicator	Meaning
f	The functions on the TOP of each button are used
g	The functions on the BOTTOM of each button are used
BEGIN	Cash flows are assumed to occur at the beginning of each period (annuity due) for the financial functions rather than at the end.
D.MY	The date format is DAY.MONTHYEAR rather than MONTH.DAYYEAR
C	Compound interest is used for odd periods rather than simple interest
PRGM	The calculator is in program mode, and keystrokes are stored as steps in a program

See Also:

The [image] Key

The [image] Key

Payment Mode

D.MY

Switching Between Simple and Compound Interest for Odd Period

PRGM


Scientific Notation

A short hand for representing large numbers.  In Scientific Notation, a large number is represented by a mantissa and exponent.  The mantissa is a number less than 10 and the exponent is a power to raise 10 to in order to reproduce the magnitude of the number.

The sign of the mantissa determines the sign of the number (negative or positive) and the sign of the exponent determines the magnitude of the number (larger if positive, smaller if negative).

In the calculator's display, a number in scientific notation is represented in this way:

This number is:

1) negative since the Mantissa is negative

2) a decimal place followed by 5 zeros since the exponent is negative

3) then the mantissa 1234

So the number is: -0.000001234

See Also:

The [image] Key


The AMORT Function
The [image] Function

The [image] key calculates the amount of each periodic payment (or group of payments) applied towards reduction of principle, and the amount applied toward periodic interest.  The sum of interest and principle payment will equal the periodic payment.  The values for [image] must be keyed in (or calculated) before calculating the amortized amounts.

Example:

You bought a house with a $130,000 15 year mortgage.  The annual interest is 8.25% and the monthly payments are $1,261.18.  Assuming that the first payment was made in March, how much interest was paid in the remainder of the year?

Solution:

Keystrokes	Display	Comment
CLEAR		Clear the financial registers
8.25	0.69	Periodic Interest
130000	130,000.00	Start Balance
1261.18	-1,261.18	Calculate total periodic payment
10	-8,821.72	Total Interest paid
	-3,790.11	Total Principle
	126,209.89	Remaining Loan Balance
If you key in any new payment number, that number will now be used as if the payment followed the payments just calculated.  For example, to calculate the following years interest (after the first 10 months calculated above) this is how you would proceed:

Keystrokes	Display	Comment
12	-10,229.61	Total Interest paid the next year
	-4,904.58	Total Principle paid the next year
	121,305.32	Remaining Loan Balance
	22	Total payments amortized

Note:

The number kept in [image] , the total payments amortized, is only accurate if the value of [image] starts at 0.  In other words, if you use [image] to calculate one of the other financial variables, reset [image] to 0 or the count of total amortized payments will not be accurate.

See Also:


The D.MY key
The [image] Key

Pushing the [image] button allows dates to be entered using the DD.MMYYYY form where DD is the day, MM is the month and YYYY is the year.


The M.DY key
The [image] Key

Pushing the [image] button allows dates using the MM.DDYYYY form where DD is the day, MM is the month, and YYYY is the year.

See Also

The [image] Key

Entering Dates


Entering Dates

Dates are entered in either MM.DDYYYY format or in DD.MMYYYY format.

Month/Day/Year Pressing the [image] key set the calculator to use the MM.DDYYYY format commonly used in the United States.  To key in a date in this format:

1.	First key in the month number.  This can be one or two digits.

2.	Press a decimal point to separate the month from the day.

3.	Enter TWO digits corresponding to the day of the month.

4.	Enter FOUR digits for the year.

Examples:

August 27, 1993 would be 8.271993.

January 1, '70 would be 1.011970 (or 01.011970)

Day/Month/Year Pressing the [image] key set the calculator to use the DD.MMYYYY format commonly used outside of the United States.  After the D.MY key is pressed, the calculator display will light the D.MY indicator.  If there is no D.MY in the display, the input format is M.DY.

See Also:

M.DY

D.MY


The DATE Function
The [image] Function

The [image] key calculates the date that is a given number of days before or after a date keyed in.

Example:

President Smith has been told that all US presidents achieve the bulk of their agenda in the first 100 days in office.  If Smith is sworn in on January 20, 1996, by what date must he complete his agenda?

Solution:

Keystroke	Display
		Set to American date style
1.201996	1.20	Enter the date of the inaugural
100	4/29/1996 Monday	Smith need to complete his agenda by March 29, 1996
See Also:

The [image] Key

The [image] Key

Entering Dates


The Delta Days Function
  (Δ DYS)

The [image] function calculates the number of days between two given dates.  The calculation is performed using both actual number of days and the 30/360 method.  After the key is pressed, the actual number of days is in the display (the X register), and the 30/360 day count is in the Y register.

Example:

Interest on government bonds is usually calculated using the actual number of days between dates.  Interest on corporate bonds is usually calculated on the basis of a 30 day month and a 360 day year.  Over the course of a 30 year bond, how many extra days of interest does the government pay?  Assume January 15, 1980 as the starting date, January 15, 2010 as the ending date, and the month-day-year format for expressing dates.

Solution:

Keystroke	Display
		Set to American date style
1.151980	1.15	Enter the start date.
1.152010	1.15	The ending date
	10,958.00	The number of ACTUAL days.
	10,800.00	The number of 30/360 basis days.
	158.00	The government pays interest on 158 more days than a corporation in the same period
See Also:

The [image] Key

Entering Dates


Weighted Mean

The weighted mean function is used to calculate the mean of a set of numbers where each element in the set may carry a weight other than 1.  The data are entered in by keying in the element, pressing [image], then the weight, then pressing

Example:

You bought the following shares of XYZ corp. at the prices indicated:

Shares	Price per share

100	$12

300	$15

200	$22

What is the average cost per share?

Solution:

In this case, the weight is the number of shares, and the data element is the price per share.

Keystroke	Display
CLEAR	0.00	Clear the statistics registers and prepare for the problem
12 [image] 100	1.00	First element and weight
15 [image] 300	2.00	Second element and weight
22 [image] 200	3.00	Third element and weight
	16.83	The average price per share is $16.83


The 12x Key

The [image] Key

The [image] key is used to enter the total number of amortization periods into the [image] financial registers by keying in the number of years.

Example:

Keystroke	Display
30	30	Enter 30 YEARS
	360.00	30 years x 12 is 360 total periods.


The INT Key
The [image] Function

The [image] key calculates the simple interest on the principle amount in the [image] register using both a 360 day and actual basis.  The number of days to use in the calculation is in the [image] register, and the interest is in the [image] register.  After pressing [image], the 360 basis interest calculation will be in the display, the loan principle will be in the Y register, and the actual basis calculation will be in the Z register.

Example:

Calculate the simple interest and total due on a $1,250 loan for 62 days.  The interest is 7.65% simple interest:

Keystroke	Display
62	62.00	Store 62 days
7.65	7.65	Store the annual interest rate
1250	-1,250.00	Store the loan principle
	16.47	Accrued interest calculated on a 360 day basis
	1,266.47	Total due; principle plus interest

Calculate the same problem but using actual basis:

Keystroke	Display
62	62.00	Store 62 days
7.65	7.65	Store the annual interest rate
1250	-1,250.00	Store the loan principle
	16.24	Accrued interest calculated on a 365 day basis
	1,266.24	Total due; principle plus interest

See also:

Formula for simple interest

Working with the Financial Registers


The 12 / Key
The [image] Key

The [image] key is used to enter a monthly periodic interest rate into the [image] financial register by keying in an annual periodic rate.

Example:

Keystroke	Display
10	10.	Enter the annual periodic rate
	0.83	Divide 10% by 12 and save the result in the [image] register.


Clear Statistics Registers
Clear [image] (Clear Statistics Registers)

The Clear statistics key combination clears (sets to 0) the registers used for Statistical calculations.

See also:

Statistics Registers


Statistics Registers
Statistics Registers:

The table shows which memory registers are used for the various statistical calculations.

Register	Calculation

Register 1 	n	count of data pairs

Register 2	Σ x 	Sum of all X-values

Register 3	Σ xx	Sum of all X-values squared

Register 4	Σ y 	Sum of all Y-values

Register 5	Σ yy	Sum of all Y-values squared

Register 6	Σ xy 	Sum of all X and Y products

Each time the [image] key is pressed, the numbers in the X and Y registers are used to add to the indicated statistic in the chart.  After the [image] key is pressed, the number in the X register is the same number as Register 1, which gives the total count of the number added to the statistics registers.

To see the value of any of the statistics registers, use the [image] key followed by the number of the register.

See Also:

Correcting a Statistics Entry


Correcting a Statistics Entry

If an incorrect number or data pair is entered in using the [image] key, the entry can be reversed using the [image] key at any time.


Clear

The Clear [image] key will clear all steps in the program stored in memory.  The calculator must be in the PGRM mode for this key to be functional.  The Clear [image] PGRM key is not able to be used as a step in a program.


GTO

The GTO function unconditionally branches to a new program line.


Clear FIN Registers
Clear

The Clear FIN key combination clears the contents of the financial registers.  The financial registers are  [image].


X<=Y

The X<=Y function is used for conditional branching in a program.


Clear REG (Clear ALL)
Clear

The Clear REG key combination will clear:

1) All memory registers

2) All financial registers

3) Stack registers

4) Last X register

5) Display

Any program in memory is not cleared.


X == Y
X==0

The X==0 key is used for conditional branching during a program.


Clear Prefix
Clear

The Clear [image] key combination will clear the [image] or [image] Prefix.  This allows another key to be pressed without [image] or [image].  Note:  If you press the [image] or [image] key twice the effect is also to clear the [image] or [image] prefix.

See Also:

The [image] Key

The [image] Key


The LST x Key

The [image] key recalls the number display before the last function key was pressed.  This allows mistakes to be corrected or the number that generated an answer to be checked.

See Also:

The Stack

Rearranging the stack


After accumulating two-variable statistical data, a new value for x can be estimated given a value for y.  The new x value is displayed, and the value of the correlation coefficient is in the y-stack register.

See Also:

The Statistics Registers

Formula for Linear Estimation


After accumulating two-variable statistical data, a new value for y can be estimated given a value for x.  The new y value is displayed, and the value of the correlation coefficient is in the y-stack register.

See Also:

The Statistics Registers

Formula for Linear Estimation


Pressing the [image] key calculates the factorial of the number in the display.

See Also:

Factorial Formula


Mean

Pressing the [image] key will calculate the mean or arithmetic average of the accumulated x and y values.  After pressing the [image] key, the mean of the x values is displayed.  Press the [image] key to display the mean of the y values.

See Also:

The Statistics Registers

Formula for Mean


The [image] key calculates the standard deviation of the accumulated x and y values .  After pressing the [image] key, the standard deviation of the x values is displayed.  The standard deviation of the y values is in the y register.

See Also:

The Statistics Registers

Standard Deviation Formula


This key will add the numbers in the X and Y stack registers to the statistics registers.

See Also:

The Statistics Registers


This key will delete the numbers in the X and Y stack registers from the accumulated statistics registers.

See Also:

The Statistics Registers


Clear Keys

The clear keys will "clear" the different parts of the calculators memory represented by the clear key.  For example, pressing [image] CLEAR [image] will clear the statistics registers to 0.

See Also:

Clear

Clear

Clear

Clear

Clear


Depreciation Keys

The depreciation keys allows depreciation to be calculated using the one of the three most common calculation methods.  To learn to use one of these, jump to one of the topics highlighted below.

See Also:

SL	Straight Line

SOYD	Sum-Of-the-Years-Digits

DB	Declining Balance


Display

The 12C++ uses the display to indicate several different status indicators as well as displaying the number in the calculator's X stack register.

The 12C++ calculator uses 19 decimal place accuracy for all calculations.  However, the number on the calculator display is a rounded representation of the number held internally.  Changing the number of decimal places displayed does not affect the accuracy of the calculator in any way.

See Also:

Changing the decimal places displayed

The Status Indicators

Scientific Notation


Entering and Analyzing Cash Flows:

For both NPV and IRR calculations, the cash flows to be analyzed must first be entered into the calculator.  Consider the following cash flow diagram:

In this case, the initial investment, CF0, is -$17,000.  The negative sign indicates that the $17,000 was paid out and not received.

Keystrokes	Display	Comment
CLEAR	0.00	Clear the storage and financial registers
17000	-17,000.00	Enter the initial cash flow
3000	-3,000.00	Enter CF1
6000	6,000.00	Enter CF2
7000	7,000.00	Enter CF3
8000	8,000.00	Enter CF4
5000	-5,000.00	Enter CF5
15000	15,000.00	Enter final cash flow
8	8.00	Enter the desired discount rate
	1,317.22	The NPV is positive, the investment would be attractive at an 8% discount rate.
	11.90	The IRR, or the discount rate where the NPV is 0.

Rather than use the method the HP 12C uses to input the cash flows, try using the Cash Flow Dialog Box.  This dialog box allows the user to more easily input the cash flows.  To use it, pull down the Edit|Cash Flows menu choice.

See Also

The [image] Function

The [image] Function

The [image] Function


NPV Net Present Value
The [image] Function

The [image] key calculates the Net Present Value of the cash flows entered into the calculator.  Net Present Value (NPV) is a widely used measure to evaluate different investments.  The NPV calculation discounts a series of cash flows using the interest rate in the [image] register.  The present value of the future cash flows is then subtracted from the initial investment.  The result of the NPV calculation is used in this manner:

If NPV is greater than 0, the investment will increase the investor's assets more than the interest rate in the [image] register.  The investment is attractive.

If the NPV is 0, the investment will increase the investor's assets no faster than the rate in the [image] register.  The investor would be indifferent towards the investment.

If NPV is less than 0, the investor's assets will not keep up with the interest rate in the [image] register.  The investment should be avoided.

See Also:

Entering Cash Flows

The [image] Formula

The [image] Function

The [image] Formula


The [image] Function

This button enters the initial cash flow of a series of cash flows.  The initial cash flow usually corresponds to the investment.

See Also:

Entering Cash Flows


The [image] Function

This button enters interim or final cash flows.  The interim cash flows may be multiplied by the number in the corresponding Nj register.

See Also:

Entering Cash Flows


IRR Internal Rate of Return
The [image] Function

IRR calculates the internal rate of return.  IRR is closely related to NPV.  It is the discount rate where NPV = 0.

See Also:

The [image] Function

Entering Cash Flows

The [image] Formula

The [image] Function

The [image] Formula


The [image] Function

The Nj function allows interim cash flows to be grouped together and multiplied by j.

Keystrokes	Display	Comment
CLEAR	0.00	Clear the storage and financial registers
17000	-17,000.00	Enter the initial cash flow
3000	-3,000.00	Enter CF1
6000	6,000.00	Enter CF2 - CF5
4	6,000.00	Enter the number of consecutive cash flows.
15000	15,000.00	Enter final cash flow
10	10.00	Enter the desired discount rate
	6,030.01	The NPV is positive, the investment would be attractive at an 10% discount rate.
	17.53	The IRR, or the discount rate where the NPV is 0.

Rather than use the method the HP 12C uses to input the cash flows, try using the Cash Flow Dialog Box.  This dialog box allows the user to more easily input the cash flows.  To use it, pull down the Edit|Cash Flows menu choice.

See Also:

The [image] Function

The [image] Function

Entering Cash Flows


Formula Index
Formulae Used:

Percentage

Interest

Compound Interest

Simple Interest

Discounted Cash Flow

Net Present Value

Internal Rate of Return

Calendar

Actual Day Basis

30/360 Day Basis

Bonds

Price

Yield to Maturity

Depreciation

Straight Line Method

Sum of the Years' Digits

Declining Balance

Statistics

Mean

Weighted Mean

Linear Estimation

Standard Deviation

Factorial


Percent Formulas
Percent Formulas:

x = X Register

y = Y Register


SimpleInterestFormula
Formula Used for Simple Interest:

n	=	Number of days
PV	=	Present Value
i	=	Simple Interest Rate (Decimal)
I360	=	Interest for 30/360 Basis
I365	=	Interest for Actual Basis


Compound Interest Formula
Formula Used for Compound Interest:

n	=	Number of compounding periods (Integer)
i	=	Periodic Interest Rate (Decimal)
PV	=	Present Value
Mode	=	Payment Mode.  0 = Begin, 1 = End
OP	=	Fractional portion of payment period (Decimal)
FV	=	Future Value
PMT	=	Periodic Payment

With Simple Interest for an Odd Period:   (default)

With Compound Interest for an Odd Period:

See Also:

Switching Between Simple and Compound Interest for Odd Period

Payment Mode

Switching Between Begin and End Payment Mode


To switch between Simple and Compound Interest for the odd period press [image] then [image].  When Compound Interest is used, there will be a "C" in the display area.  If there is no "C", Simple Interest is being used for the odd period.


To switch to Begin Payment mode, press [image] followed by [image].  The BEGIN indicator will show in the calculator display.

To switch to End Payment mode, press [image] followed by [image].  There will be no indicator in the calculator display.


Payment Mode
Payment Mode:

Periodic payment on an annuity can be received either at the beginning or the end of each payment period:

Begin	End

Examples of annuities that are usually calculated with payment at the beginning of each payment period are pension plans and savings plans.

Examples of annuities that are usually calculated with payments at the end of each payment period are mortgages, leases, and installment loans.

See Also:

Switching Between Begin and End Payment Mode


NPV Formula
Formula Used for Net Present Value:

Where

CT	=	Cash flow in period T
N	=	Number of cash flows

See Also:

Internal Rate of Return


IRR Formula
Formula used for Internal Rate of Return:

Where

CT	=	Cash flow in period T
N	=	Number of cash flows
C0	=	Initial Investment

The solution to irr must be found through a process of trial and error.  Various values for irr in the equation are tried until a number sufficiently close to 0 is found.

There are many groups of cash flows that either have no solutions or more than one solution.  Given a system of N cash flow, it is possible to have as many as N-1 arithmetically correct solutions.  IRR should be used with caution.

See Also:

Net Present Value


Actual Date Difference Formula
Formula Used for Actual Δ Days Calculation:

Where

JD	=	Julian Day Count(Month,Day,Year)
M	=	Month of the Date
Day	=	Day of the Date
Y	=	Year of the Date
INT	=	Integer Function

If Month = 1 or 2, Y = Year - 1 and M = M + 12

If Month > 2, Y = Year and M = Month

B = 2 - A - INT(A / 4)	If the date is in the Gregorian Calender.

B  =  0 	If the date is in the Julian Calender.

JD = INT(365.25(Y + 4716)) + INT(30.6001(M + 1)) + Day + B - 1524.5

Δ Days = JD(Date 2) - JD(Date 1)

See Also:

Julian Day Count


The Gregorian Calendar refers to those reforms to the Julian Calendar implemented by Pope Gregory in 1582.  These reforms changed the definition of a year to 365.2425 days from 365.25 days.


The Julian Calendar refers to the calendar introduced by Julius Caesar in 46 BC.  The Julian calendar defined a year as 365.25 days (3 365 day years followed by a 366 day leap year) with the same months now used.  The Gregorian Calendar has replaced the Julian Calendar in most countries.


The Julian Day Count is closely related to the Gregorian Calender which was implemented at different times thoughout the world.  For example, Rome adopted the Gregorian Calender reforms on October 15, 1582 AD.  The English Empire adopted the Gregorian Calender in 1754, and Turkey and Russia did not adopt the reforms until the twentieth century.

This calculator assumes the Gregorian Calender in all date problems.

The Julian Day Count is the number of days from January 1, 4713 BC. On this day, the Julian calender, the lunar calender, and the Roman Tax collector's calender all coincide - something that won't happen again until 3267 AD.  The Julian Day Count was developed in 1582 (coincident with the Gregorian calender) by Joseph Justus Scalinger and named in honor of his father Julius Ceasar Scalinger.  With a true Julian Day Count, the count would reset to 1 after a 7,980 year period when the above mentioned three calendering schemes again agree, but this one keeps counting.

The Julian Day Count is not related to the less accurate Julian calender used by the Romans.  The Julian calender assumes each year to be 365.25 days which is 11 minutes 14.5 seconds off the true length in 1990.  The Gregorian calender corrects the Julian calender by ommiting the leap year in any year divisable by 100 unless they were divisable by 400.  That eliminates 3 leap years per 400 years.  By this system, 400 years contain 400 * 365 + 100 - 3 = 146,097 days; the average length of a year is then 146,097 / 400 = 365.2425 days which is a much better approximation of the true tropical year length of 365.2422 days.

 The Julian day count uses the same enumeration and is therefor as accurate as the Gregorian calender.

The Gregorian calender is still off by .12 days per 400 years or about 25 seconds per year.  Additionally, the actual length of the year changes by approximately .5 seconds per year.  Therefore, modern time keepers add leap seconds from time to time.  Since this is not predictable, neither the Gregorian calender nor this function take leap seconds into account.


30/360 Date Difference Formula
Formula Used for 30/360 Δ Days Calculation:

Δ Days = Date Count(Date 2) - Date Count(Date 1)

Date Count = 360(Year) + 30(Month) + z

for Date 1

if Day 1 = 31 then z = 30

if Day 1 < 31 then z = Day 1

for Date 2

if Day 2 = 31 and Day 1 > 29 then z = 30

if Day 2 = 31 and Day 1 < 30 then z = 31

if Day 2 < 31 then z = Day 2


Bond Price Formula
Bond Price:

DSC	=	Days between settlement and the next coupon date
DCS	=	Days from last coupon date to settlement date
CP	=	Days in coupon period
n	=	Number of coupons remaining
i	=	Periodic interest (Yield divided by 2)
AI	=	Accrued interest ($)
c	=	Periodic coupon ($)


Yield to Maturity

Price	=	Price of the bond
c	=	periodic interest payment
M	=	Maturity value
n	=	total periods
y	=	periodic interest

Yield to maturity is solved through a process of trial and error.  Differing values for y are tried until a value is found where the present value of the coupon payments as well as the present value of the $1,000 face amount are equal to the price paid.


Strait-Line Depreciation


Sum-of-Years' Digits

Life	=	Life of asset
Cost	=	Original cost or book value
SYD	=	Sum-of-Years' Digits


Declining-Balance Depreciation

DBj	=	Declining Balance Depreciation in period j
Cost	=	Cost of asset
Fact	=	Declining-Balance Factor
L	=	Life of Asset


Factorial Formula
Factorial:

if n = 0, n! = 1

n > 1 where n is an integer:


Standard Deviation Formula
Standard Deviation:

See Also:

Statistics Registers


Mean Formula
Mean:

See Also:

Statistics Registers


Weighted Mean:

See Also:

Statistics Registers


Linear Estimation

See Also:

Statistics Registers


The Stack
The Stack:

This calculator uses a Memory Stack to enter and hold numbers used in calculations.  The number in the X-register is always displayed.  The Y-register is used primarily to hold the second number in a calculation.  The Z-register and the T-register are used to hold interim values in longer calculations.

The Stack

This method of number entry, called RPN, is a very natural way to translate written calculations into a form that the calculator can understand.  By using a stack, there is no need to use parentheses since the position on the stack determines the order in which the numbers are used in calculations.

Example:

Calculate 3-1=?

Since subtraction in not cummutitive, the order which the numbers are entered is important.

Example:

Calculate  (1+2) × (4+5) = ?

The keystrokes will correspond to a left-to-right (and top-to-bottom) reading of the formula with the parentheses taken into account.

Any time that you wish to see the contents of the four stack registers and the Last X register, pull down the SHOW menu and select Stack.

See Also:

Rearranging the stack

Viewing the Stack


Rearranging the Stack
Rearranging the Stack:

The [image] key

The [image] key

The [image] key


The CLx Key
The [image] Key

The [image] key clears the number in the X register.  The X register is the Stack register that is also displayed.


The Enter key
The [image] Key

The [image] key is used as a separator between two numbers to be used in a calculation.

Keystrokes

See Also:

The Stack


The DOWN key
The [image] Key

The [image] key pushes every stack register down, and the number formerly displayed (the X register) is copied to the top register.

See Also:

Functions that return more than one number

The Stack


The x<->y key
The [image] Key:

Pressing the [image] key will switch the numbers in the display (the X-register) and Y-register.  This is useful when numbers are entered in the wrong order or to see the second number from a calculation that returns more than one number.

Keystrokes

See also:

Functions that return more than one number

The Stack


Functions that return more than one number:

These functions return morethan one number on the stack:

The [image] Function

The [image] Function

The [image] Function

The [image] Function

The [image] Function

The [image] Function

The [image] Function

The [image] Function

The [image] Function

The [image] Function

The [image] Function


The OK key
The [image] Key:

The [image] Key will save the total state of the calculator and terminate the program.  There is no accelerator for the [image] Key.


Commutative

A mathematical operation in which the order of the operands does not affect the result.

Examples of commutative operations:

2 + 3 = 3 + 2

5 × 6 = 6 × 5

Examples of NON commutative operations:

(3 - 2) ≠ (2 - 3)

(4 ^ 5) ≠ (5 ^ 4)


Mantissa

An number less than +10.0 and greater than -10.0 used to represent a larger number in Scientific Notation.


Factorial or n!

The product of all the integers from 1 to n.

Example:

4! = (1  2  3  4) = 24


Correlation Coefficient

The Correlation Coefficient or r is a measure of how well an estimate can be made from accumulated data.  The closer the correlation coefficient is to 1 (or -1), the closer the data points are to a straight line on a graph, and the more reliable an estimate would be based on these data points.  Conversly, if the correlation coefficient is 0 or close to 0, there is no or little linear correlation between the data points and an estimate based on these pairs would not be reliable.


Basis:

The number of days in a coupon or intererest rate period.  For corporate bonds, the basis period is usually calculated on an assumed 360 day year and 30 day month; this is refered to as 30/360 basis.  For governement or Treasury securities, the basis period based on the actual number of days in the period and is refered to as actual basis.


e

The constant e (aproximately 2.71828) is used in finance to calculate problems involving continuous compounding.


Calculator State

This program is designed to save its entire state includeing:

Numbers in the Stack

Numbers in Storage Registers

Program Steps


Menu Help

File Menu

Edit Menu

Show Menu

Options Menu

Help Menu


File Menu

Open

Save As

Exit


Open (File Menu)

This opens an existing calculator state.


Save As (File Menu)

This will save the calculator state in a file


Exit (File Menu)

This save the calculator state and exits the program.


Edit Menu

Copy

Paste

Storage Registers...

Cash Flows...


Copy (Edit Menu)

This copies number in the calculator's display as text to the clipboard.


Paste (Edit Menu)

This will paste the text in the clipboard in to the calculator as a number.


Storage Registers...(Edit Menu)
Storage Registers (Edit Menu)

This allows the individual storage registers to be edited in a dialog box.


Cash Flows... (Edit Menu)

This menu choice allows the individual cash flows to be edited in a dialog box.  The Cash Flows dialog box has 20 larger edit controls that correspond to the calculator's storage registers (CF20 corresponds to the FV financial register).  To the right of each of the storage registers is a smaller edit control that corresponds to each of the 20 Nj registers.  By using only the storage registers (leaving the Nj registers blank), up to 20 unique cash flows may be entered for analysis.  Larger problems may be handled if there are groups of cash flows that are equal and consecutive.  To enter a group of equal and consecutive cash flows, enter a number in the corresponding Nj edit control for the number of consecutive cash flows.

Dialog Box Buttons

OK

Saves the numbers into the corresponding memory registers of the calculator.

Cancel

The numbers in the dialog box are discarded.

Clear All

Reset the numbers in the dialog box to 0.0.

Calculate

Calculate NPV and IRR of the numbers in the dialog box.

Copy

Copies the cash flows to the clipboard for use in another application.

Help

Displays this help screen.


Options Menu

Always on Top

Key Clicks

Use Conversion Calculator


Always on Top (Options Menu)

The option Always on Top will keep the calculator displayed regardless of whether the calculator is in control.  This option is only available with Windows 3.1 and later.


Key Click (Options Menu)
Key Clicks (Options Menu)

The Key Clicks options will "click" every time a button is pressed either through a mouse action or keyboard accelerator.  This option is only available with Windows 3.1 or Multi Media Windows 3.0.


Use as Windows Calculator (Options Menu)
Use Conversion Calculator (Options Menu)

This menu choice will allow different units of measurement to be freeely converted.


Help Menu

Index

What is that

Help on Help

About


Index (Help Menu)

This calls the Windows hypertext help system and displays an index to the calculator's help file.


What is That... (Help Menu)
What is that (Help Menu)

After selecting What is That... the cursor will change to an arrow with a question mark.  Simply point to the text or button on the face of the calculator to get help for that topic.


Help on Help (Help Menu)

Use Help on Help if you wish a tutorial on using the Windows Help system.


About (Help Menu)

Use About to see the version number of this program as well as other useful information.


Show Menu

Stack...

Financial Registers...

Statistics...

Amortization Schedule...


Stack... (Show Menu)

This menu choice brings up a dialog box that shows the contents of the stack registers.

See Also:

The Stack


Financial Register... (Show Menu)
Financial Registers... (Show Menu)

This menu choice brings up a dialog box that shows the contents of the financial registers

See Also:

Working with the Financial Registers


Statistics... (Show Menu)

Use this menu choice to see the contents of the statistics registers in a dialog box.

See Also:

Statistics Registers


Amortization Schedule... (Show Menu)

This menu choice brings up a dialog box that contains the entire amortization schedule that corresponds to the loan data in the [image] financial registers.  This amortization schedule can then be printed, graphed, or copied to the clipboard.

See Also:

Working with the Financial Registers


Size (System Menu)

This command will display a four-headed arrow that is used to size the active window.

When the calculator is resized, the individual buttons, text, and display are also resized proportionate to the new calculator size.


Move (System Menu)

This command will display a four-headed arrow that is used to move a window or dialog box.


Minimize (System Menu)

Use this command to shrink the active window to an icon.  The program will still be available be double clicking on the icon.


Maximize (System Menu)

Use this command to enlarge the active window to its maximum size.


#define SC_NEXTWINDOW  0xF040


#define SC_PREVWINDOW   0xF050


Close (System Menu)

Use this command to close the current window.  When the calculator is closed, all numbers in the calculator are saved automatically.


#define SC_VSCROLL   0xF070


#define SC_HSCROLL   0xF080


#define SC_MOUSEMENU 0xF090


#define SC_KEYMENU   0xF100


#define SC_ARRANGE   0xF110


Restore (System Menu)

Use this command to restore a window to the size it was previous to a Maximize or Minimize size command.


Switch To... (System Menu)

Use this command to call a dialog box that will allow the active window to be chosen.


#define SC_SCREENSAVE   0xF140


#define SC_HOTKEY       0xF150