
A Novel Set of SoftwareBased
Calculation Devices that Carry Out Over 75 Calculations Involving
Rate, Time, and Money, and Provide
Calculated Estimates of Present and Future
Business Performance 


David@TechForText.com 2010©



To contact the author used the above email
address 


On this page there are eight softwarebased
Calculators that are useful for any size business, and they are provided
free of charge. These devices carry out OVER 75 calculations,
involving RATE, TIME, and MONEY. The Calculators provide
ongoing calculated feedback, and estimates of future business performance,
from a unique perspective. This feedback may indicate weeks in advance
when a business is headed for financial problems or prosperity.
This early feedback may provides the time needed to develop and
implement strategies to prevent problems from developing, and to maximize
opportunities. The feedback from these devices can also
provide early indications of the relative degree of success or failure of
newly implemented business strategies. 


Feedback, and The Feedback Correction Process
for Business 


The use of this software, can help you become
more aware of feedback in relation to the business you are managing.
This raises some questions. What is feedback, and how
do you interpret feedback, and use it to improve the functioning of a
business. This is briefly explained in the following
paragraphs. 


The word feedback has a number of
definitions. Sometimes people use this term as a synonym for
opinions or criticisms provided by others. The term feedback
as defined in this text, is NOT based on opinion. It is based
on RESULTS, which may or may not be successful. The feedback process, can
function with unsuccessful, partly successful or successful results.
In fact, the primary purpose of the feedback process is to correct
results that are less than optimal. 


As defined for this text: feedback
is an evaluation of the RESULTS of goal related activities, carried out by
the entity that initiated the activities. For example,
management attempts to increase sales volume, with a new advertising
campaign, and a week later, they evaluate the results of their
efforts. The RESULTS are evaluated to
determine if the goal was obtained, to determine if the goal related
activities are going to continue, and to determine the need to modify the
activities in some way, such as to correct errors, prevent problems, and
make improvements. In some cases, the evaluation of RESULTS
may indicate an unrealistic goal, the need to modify a goal, or the need
to set a new goal, because the initial objective was achieved. 


The underlined words (above)
represent a very important principle of the feedback process, which is a
corrective response, based on the results. That is, the
feedback process is not passive. It often involves a series
of actions, evaluations, and corrections, that continue in a sequence. 


Note, this version of the software
contains descriptive text, including technical material . It
also contains Calculator 9, which was created for demonstration and
experimental purposes. If you want to use this software for
an actual business, you should go to the main website, and download a
simpler version without extraneous material. (It is provided without
charge.) 



For
additional information, or other versions of this software, left click on
these words.
www.TechForText.com/RateTimeAndBusiness 




INSTRUCTIONS 




The Calculators are very easy to use.
Just read the simple instructions on each Calculator, and enter the
required numbers in the white boxes. (To enter or delete
numbers, left click with the mouse on the relevant white box.)





Numbers must be
entered in sequence, starting from Calculator
1, 2, 3, 4, 5, 6, 7, 8. (This is because entered numbers and
calculated results from one device are transmitted to the Calculators that
follow it, for additional calculations.) If you do not want
to use all of the Calculators, this software will function providing you
enter numbers in sequence starting from Calculator 1.
Examples are: Calculators 1 and
2; Calculators 1, 2 and 3; Calculators
1, 2, 3, 4, 5 and 6; Calculators 1, 2, 3, 4,
5, 6 and 7. 




The currency
symbol used for the calculations can be
changed. If you do not see the currency symbol you need in
the pink box below, scroll all the way down, about 15 screens, and you
will see a device and instructions to change the currency symbol.
This is located below Calculator 8. 



Is this the currency symbol you need?










































Calculator 1, for the Average Rate
of Revenue 




In the white box below, enter the total gross revenue that the business earned for any number of:days,
weeks, months or years. The longer time
periods will usually result in more accurate calculated averages, and
calculated predictions. DO NOT use
time periods that are significantly different than current business
conditions, in terms of gross revenue, expenses, and profits, if you want
calculated averages and predictions that apply to current business
conditions. 











For the gross
revenue you entered above, enter the time period that it was earned, in terms of a start
date and an end date. (For example,
gross revenue earned from 1/1/2010 to 10/18/2010) To do this,
delete the sample dates in the white boxes on the lower left and lower
right. Then enter the start date in the box on the lower
left, and an end date in the box on the lower right. The
dates must be entered as Month/Day/Year, such as 10/26/2010.





START DATE: Delete the date in this white box, and enter the
start date for the gross revenue you entered. 

from to 

END DATE: Delete the date in
this white box, and enter the end date for the gross revenue you
entered 




Note for above
START DATE and END DATE: The
calculations are carried out from 12 AM of the start date, to
12 AM of the end date. For example, if 10/25/ 2010 is a start
date and 10/26/ 2010 the end date, the calculations are for one day or 24
hours. 




Calculated results are presented below in red
words and numbers 














Note: An AVERAGE
MONTH as the terminology is used here, is
30.4368499 days 









The above is based on the average monthly
revenue divided by 30.4368499 DAYS 









The above is based on the average monthly
revenue divided by 4.34812141 WEEKS 











The above is based on total revenue you entered,
divided 








by the number of AVERAGE months, in
the time interval you entered. 











The above calculation is based on 12 times the
average monthly revenue 





The following calculations are projections, (or
forecasts, or predictions) based on the calculated rate of
revenue. 










The above calculated prediction is based on 3
times the average monthly revenue 









The above calculated prediction is based on six
times the average monthly revenue 









The above calculated prediction is based on 12
times the average monthly revenue 









The above calculated prediction is based on 24
times the average monthly revenue 









The above calculated prediction is based on 36
times the average monthly revenue 
























































Calculator 2, for the Average Rate
of Expenses 


































Calculated results are presented below in red
words and numbers 









Above calculation is based on the average
monthly expenses divided by 30.4368499 days 









The above is based on average monthly expenses
divided by 4.34812141 WEEKS 









Above based on entered expenses divided by
number of months in time period you entered 









The above calculation based on 12 times the
average monthly expenses 





The following calculations are projections, (or
forecasts, or predictions) based on the calculated rate of
expenses. 










The above calculated prediction is based on 3
times the average monthly expenses 









The above calculated prediction is
based on 6 times the average monthly expenses 









The above calculated prediction is
based on 12 times the average monthly expenses 









The above calculated prediction is based on 24
times the average monthly expenses 









The above calculated prediction is based on 36
times the average monthly expenses 
























































Calculator 3, for the Average Rate of Profit,
Based on: 




Average Monthly Revenue Minus Average Monthly
Expenses 





















The numbers used by this device to calculate
the rate of profit are obtained from Calculators 1 and 2, and they are
presented below: 










Important Note: If the rate
of revenue is less than the rate of expenses, the calculations on this
device will show a negative rate of
profit, which is the rate of financial
loss. This is expressed with a negative sign right after the
number. For example: Average Monthly Rate of Profit = $ 225.23





Calculated results are presented below, in red
words and numbers. 























The above is based on the average monthly
profit divided by 30.4368499 DAYS 









The above is based on the average monthly
profit divided by 4.34812141 WEEKS 









The above is based on the average monthly gross
revenue minus the monthly expenses 









The above calculations based on 12
times the average monthly profit 




The following are predictions
of future business performance, based on the
calculated rate of profit, for the time period you entered in Calculator
1. 









The above calculated prediction is based on 3
times the average monthly profit. 









The above calculated prediction is based on 6
times the average monthly profit. 









The above calculated prediction is
based on 12 times the average monthly profit. 









The above calculated prediction is based on 12
times the average monthly profit. 









The above calculated prediction is
based on 36 times the average monthly profit. 


























































Calculator 4, for Rate of Personal
Income from the Business 




This device uses the time period you entered in
Calculator 1, and the average monthly rate of profit, from Calculator 3,
to calculate Your Rate of Personal Income, from the business. (This does not calculate
other income sources.) 




In the white box
below, enter the percentage of the profit that
you keep for personal income. This
excludes money that you
put back into the business, as well as any money that must be shared with
partners, investors, or stockholders.
If you are NOT sure of the percent of profit that you keep for
personal income, or if the business did NOT make a profit, or if you
receive a salary and/or bonuses from the business, LEAVE THE FOLLOWING WHITE BOX BLANK. 





% 































Enter in the white box below, the TOTAL number
of hours you worked 









Hours of work for business for above time
period = 

hours 



The following red words and numbers are
calculated results. 







































The above is based on the average monthly
income divided by 30.4368499 DAYS 









The above is based on the average monthly
income divided by 4.34812141 WEEKS 









Above: based on % of monthly profit, OR entered
income divided by months in time period 














The calculations below, are predictions of your
future income, from the business, based on the rate of your income, for
the time period you entered in Calculator 1. 



















The above calculated prediction is based on 6
times your average monthly income 









The above calculated prediction is based on 12
times your average monthly income 









The above calculated prediction is based on 24
times your average monthly income 





































































Calculator 5: Rate of Return on
the Business Investment 




The calculation for rate of return, (as
presented here) involves the yearly profit divided by the money value of
your business, which is multiplied by 100 to provide the yearly rate of
return in a percentage. The calculations are also carried out
with the monthly, weekly, and daily rates of profit, which provides (a
less conventional), monthly, weekly and daily rate of return.
(The rate of profit is obtained from Calculator 3, but you have to
enter the money value of your business as explained below.) 




If the business is just breaking
even, and not making any profit, the rate of return is zero, regardless of
the money value of the business. If the average rate of
expenses are greater than the average rate of revenue, the business is
losing money, which is a negative rate of profit. This device
will display a negative rate of return, with a negative sign right after
the number, such as $1000. For example, if your business is
worth $100,000, and the calculator indicates a Average
Yearly Rate of return= 10% it means
your business is costing you $10,000 a year. 




The money value
of a business is generally an estimate. This can
be based on the book value of the business, derived with conventional
balance sheet calculations, or even by an estimate of the money you
invested in the business. A less conventional alternative is
to use the amount of money you believe you can get for the business if you
sold it. This can simply be called the resale value of the
business, or the market value. However, this CALCULATOR CARRIES OUT SIMULTANEOUS CALCULATIONS
FOR BOTH THE BOOK VALUE, AND THE RESALE VALUE OF A BUSINESS. 




IMPORTANT TWO
PARAGRAPH NOTE: The book value and
resale value of a business will usually provide very different results
when used to calculate the rate of return on the total business
investment. These results can have very different
implications. For example, if the rate of return is very low
based on resale value, it might be more profitable to sell the business,
even if the rate of return based on the book value is very high.
(This sometimes happens when the land owned by a business has
increased greatly since the business was established. For
example, farm land that was originally purchased for $100 an acre, now may
be worth over a million dollars an acre, because of suburban
development.) 




When the calculations are based on
a resale value that is higher than the book value of the business, the
mathematical result will indicate a lower rate of return. The
following greatly simplified example will clarify this: If
100 acres of farmland was originally purchased for $100 an acre its book
value would be $10,000. If we assume the this land provides
an average profit of $5000 per year. Thus, the rate of return
is: (100%)*($5,000/$10,000)=50%. A 50% rate of return is very high.
However, if the resale value of the land is now $1,000,000 an acre,
the total value is $100,000,000. Thus, the rate of return,
based on the resale value of the land is very low, as follows:
(100%)*($5,000/$100,000,000)=0.0050% Thus, from a purely financial perspective,
selling the land for $100 million, would be the best choice, because even
a bank with provide a higher rate of return than 0.0050% 




BOOK VALUE: In the white box
below, enter the book value of the business. This can be based on balance
sheet calculations, or even an estimate of the money you invested in the
business. 









RESALE VALUE (THE MARKET VALUE): In the white box below, enter the amount of money you believe
you can get if you sold your business. 









Note the rate of return on an investment is
generally presented in terms of a yearly rate. However, this
Calculator presents the rate of return in terms of a daily, weekly,
monthly as well as a yearly rate. 




The four calculations below are based on the
BOOK VALUE of the business 



















(Book Value) Above is based
average Monthly Rate of Return divided by 30.4368499 DAYS 









(Book Value) Above based on Average Monthly
Rate of Return divided by 4.34812141 WEEKS 









Above based on average monthly profit divided
by Book Value
(Multiplied by 100 %) 








(Book Value) Above based on 12 times the
Average Monthly Rate of Return 


The four calculations below, are based on
RESALE VALUE of the business 





(Resale Value) The above based average Monthly
Rate of Return divided by 30.4368499 DAYS 





(Resale Value) Above based on Average Monthly
Rate of Return divided by 4.34812141 WEEKS 





Above based on average monthly profit divided
by Resale Value
(Multiplied by 100 %) 





(Resale Value) Above based on 12 times the
Average Monthly Rate of Return 












Calculator 6, for Dual Cash Flow Calculations:





One ) For Upcoming Billing
Period, and Two) Based
on Averages 




This device calculates CASH
FLOW, in terms of three rates, which are:
the rate of expenses,
the rate of available money to pay the
expenses, (usually called cash and the
rate of remaining funds. This
involves money that is entering a business at a specific rate, and money
that is leaving the business at a specific rate. The rate of remaining funds is money
remaining after expenses have been paid. (The following
paragraphs will provide some additional information on cash flow, as
calculated by this device.) 




As the
terminology is used here the rate of remaining
funds is the same as the profit, ONLY
WHEN the profits are calculated in terms of
actual money (cash) received from customers. This excludes
money owed to the business by customers, because it cannot be used to pay
business expenses. In addition, we cannot be certain that all
customers will pay their debts. 




The rate of
remaining funds is NOT the same as profit, when
the profit calculations include money that customers owed to the business,
or when the expenses are paid from a separate fund, which is not related
to the revenue earned by the business. (Expenses may be paid
from a separate fund when a business has a rate of expenses that is
greater than its rate of revenue, which often happens with new businesses
that are in the process of establishing a customer base.) 




The rate of
remaining funds may have a zero rate, a
fluctuating rate, as well as a positive or negative rate.
When positive, cash flow is positive, and expenses are less than
available funds. When the rate of remaining funds is
negative, cash flow is negative, and expenses are greater than available
funds. 




If this
Calculator indicates a negative number for the rate of remaining funds,
such as $10,000, it means the cash flow is negative. That is the available money is NOT enough to pay
for all the expenses that are due on or before the upcoming billing
period. With the above example, $10,000 means that the
business needs an additional $10,000 to pay expenses that are due on or
before the upcoming billing period. 




This calculator
carries out two variations of cash flow calculations, involving: A BILLING
PERIOD, and AVERAGES. In section 1 of this Calculator, the
cash flow for an upcoming billing
period is carried out. This involves
entering expenses that are due on or before the upcoming billing period,
and available funds to pay the expenses. In section 2,
Average Cash Flow, is calculated. This is based on gross revenue,
expenses and profits for the time period you entered in Calculator 1,
which ideally should involve many billing periods to obtain a good
average. For the average cash flow calculations in section 2,
numbers are NOT entered by the user, because all the needed data is
obtained from Calculators 1, 2, and 3. 




The two sets of
cash flow calculations provide calculated results and data with very
different implications. For example,
a negative cash flow for a billing
period, may NOT be a serious problem, especially
if the average cash flow is positive. In such a case, credit can be
extended, and/or shortterm loans might be available, etc.
However, an AVERAGE cash flow that is negative is often a serious
problem. This is especially the case, if the averages are
based on 12 or more months of expenses and gross revenue, and when there
is no reasonable evidence suggesting that the situation will
improve. 



SECTION 1) Cash Flow Calculations for Upcoming
Billing Period 



ENTERING MONEY
INTO THE CALCULATOR TO PAY EXPENSES:
In the white boxes below, enter the total amount of money that will
be available to pay the bills, and any other expenses, that are
due on or before the upcoming billing
period. The Calculator adds the
funds entered in these boxes, and presents the results below the boxes in
red type. If no numbers are entered in these boxes, this
device will use the average monthly gross
revenue, from Calculator 1, as available
cash. This is usually not a good alternative, unless there
are substantial reserves of cash, to cover any discrepancies. 




Optional: In the white boxes below
enter a descriptive word or phrase, to indicate source of the
money. 

In the white boxes below, enter the money that
is available to pay the expenses that are due on or before
the upcoming billing period. 































































































































































ENTERING EXPENSES:
In the white boxes below, enter the bills, and any other expenses,
that are due on or before the upcoming monthly billing
period. The Calculator adds the expenses entered in these
boxes, and the result is presented below the boxes in red type.
If no numbers are entered in these boxes, this device will use the
average monthly expenses from Calculator 2, for the calculations.
This is usually not a good alternative, unless there are
substantial reserves of cash, to cover any discrepancies. 




Enter a descriptive word or phrase, in the white
boxes below, to identify each expense, such as electric bill. 

In the white boxes below, enter the Expenses
that must be paid on or before the upcoming billing period. 














































































































































Calculated Conclusion Based On Numbers Entered
In Section 1 





























SECTION 2, Average Rate of Cash
Flow, Based on the Average Monthly Rates of: Revenue,
Expenses, and Profit 





You do NOT enter numbers in this section,
because all the needed data is automatically obtain from Calculators 1, 2
and 3. 



































































































































































Calculator 7, Average Hourly Rates
of Revenue, Expenses & Profit 


Based on the Number of Hours
Business is Opened per Month 



This device, calculates the average hourly
rates of revenue, expenses, and profits, based on the NUMBER of HOURS the
BUSINESS is OPEN PER MONTH. To carry out the calculations,
numbers are obtained from Calculators 1 and 2 . The calculations also
require information about the days and hours of business operation, as
explained below. 




In the white box below, enter the
number of days per month that the business is opened. If you
do not have exact figures, you can use an average or an estimation.
Enter 30.4368499 days for the average month if the business is
opened every day of the month, but if it is closed on Saturday and Sunday
enter 21.741days. 



Number of DAYS business is
opened per month = 

days per month 



In the white box below, enter the number of
hours that the business is opened per day, on the average. If you do not
have exact figures, use an estimate. 



Number of HOURS business is opened per day =


hours per day 



The calculated results are in red words and
numbers. 


























Note: The above calculations are rounded down
to two decimal places. This can occasionally result in
insignificant rounding errors of plus or minus 0.01. The
following are the same calculations, but they have NOT been rounded
down. This will prevent rounding errors from occurring at the
second decimal place. These results may have OVER nine
decimal places. This greater level of precision can be
confusing, and generally has no practical purpose when calculating money,
but it is presented here for its theoretical value. 










































Calculator 8, Carries Out Calculations, based
on Time of Day 




To Evaluate Business Performance During
Operating Hours. 




The previous seven devices on this page,
performed calculations based on PAST business performance, and they provided financial averages
and calculated forecasts. THIS
CALCULATOR IS DIFFERENT. It was designed to provide feedback
while a business is in operation. The calculations involve
hours, minutes, and seconds, from the time the business opened, and
related revenues and expenses. Whenever you enter numbers,
this device accesses the time and date from your computer, to carry out a
set of time based calculations, involving revenue, expenses and
profits. This provides useful feedback on current
business performance, whenever data is entered. 




Note: The time and date presented by this
software is the TIME THAT A CALCULATION TOOK
PLACE, which happens when numbers are entered or deleted, or
when the software is first opened. Pressing the calculation or update buttons on the
online JavaScript version of the
software, will also result in recalculations,
which will update the date and time. If these buttons are not
pressed, and if no data is entered or deleted, and the software is left
open, there will be no calculations, and the time
and date will NOT change. 




The results
provided by this Calculator are only valid from the time the business
opened until closing time. If there are any calculations
carried out after closing time, the results will not be valid. 




INSTRUCTIONS: To use this Calculator, you must enter the time
that your business opened today. This is done with the hour
and minute settings, highlighted in red, on the bottom of the following
Time Readout Box.
If your business opens the same time every day, you will
only have to set the time once. If your business opens
at 9:00 AM, you can skip this step, because the Calculator is already set
at this time. 




Time Readout Box 










Note: The three readouts below,
with red type and yellow background, are ONLY correct after the opening
time of the business has been set, and they will be valid until the
business closes for the day. 















Note: the above, hours with decimals, is used
for the calculations 


















Set Hours 

Set Minutes 







To set the hour ? 



? To set minutes 






Button ?


Button ?





To set the time the business opened, there are
two red boxes above this paragraph. The box on the left is to
set the hours, and the box on the right is to set the minutes.
For the spreadsheet version of this software left click on a red
box and you will see a small silver or gray button.
Left click on this button, and a dropdown menu will open, with
numbers. For the ONLINE JavaScript version
of this software, a dropdown menu will open as soon as you LEFT CLICK ON
A RED BOX. 




When the dropdown opens, scroll
through the menu, until you find the number that corresponds to the hour
or minutes you are looking for. When you find the correct
number, left click on it, and it will appear in a red box, in white
type. The above step must be performed twice, once on the
left, for hours and again on the right for minutes. 




After completing all of the above,
the date and time the business opened will be displayed just above the red
boxes, highlighted in light yellow. If this is NOT the case,
you made an error. If you need further clarification read the
following example. 




AN EXAMPLE TO
CLARIFY THE ABOVE: If your business
opened at 9:53 AM, access the dropdown menu for setting the hour, by left
clicking on the red box on the left. When the menu opens,
scroll through the numbers looking for 9 AM, When you
find 9AM, left click on it. Then 9:00 AM will
appear in white type, in the red box on the left. The next
step is to access the dropdown menu for the minutes, by left clicking on
the red box on the right. When the menu opens, scroll through
the numbers, and when you find number 53 left click on
it. After this, the number 53 will appear in white type, in
the red box on the right. When all of the above is completed
the date and time the
business opened will appear above the two red boxes, and it will look
similar to the following: The
Business Opened on Tue, Nov 23, 2010 at 9;53 AM 




Note: If your business day extends
into the following day, this device will carry out the correct
calculations automatically, based on the opening day and time.
A example is the business opened on Mon, Nov, 22nd at 12 PM, and it
closed on Tues, Nov, 23rd at 4 AM. Situations like this, will
NOT interfere with the calculations, as long as they are less than 24
hours. However, this software was designed to reset to zero,
when the timing mechanism reaches 24 hours. 




If your business is open 24 hours
a day, you can set the opening time as 12 AM, or any other time you find
convenient. For example, if you choose 9 AM as the opening
time, the calculator will indicate that the business was opened 23 hours
and 59 minutes at 8:59 AM. At exactly 9 AM it will indicate
zero hours. 




ENTER REVENUE:
In the white boxes on the lower
right, you can enter a descriptive word or phrase
to indicate the source of specific revenue, such as computer sales.
However, this is optional, and it may be unnecessary to use the
white boxes on the lower right. 




In the white
boxes on the lower left, enter the revenue that
the business earned from the time the business opened until now.
This time period is indicated below in red type. (If
the revenue is in two or more quantities, the Calculator will
automatically add the money, if you place the numbers in separate
boxes.) 
































































































from 11/23/10, 1:51 AM 





NOTE: If you fail to enter
any numbers in the white boxes above, the Calculator uses the average
hourly gross revenue from Calculator 7 for the calculations.
This alternative is NOT recommended, because it defeats the primary
purpose of this Calculator, which is to provide feedback of CURRENT
business performance. 




EXPENSES: This Calculator accesses the average hourly expenses from Calculator 7,
and uses it for the calculations. The average hourly expenses
is multiplied by the number of hours the business was opened for the
calculation below. If this does NOT reasonably approximate
the expenses for this time interval, enter the expenses that were incurred
in the white boxes below. However,
in most cases, it is best to let the Calculator use the average expenses,
because it is usually too cumbersome to evaluate all the expenses based on
hours and minutes from the time the business opened. 





OPTIONAL: You can enter a
descriptive word, or phrase, for each expense in the white boxes below (on
the left). 
OPTIONAL: In the
following white boxes (on the right), you can enter expenses for the time
period indicated below in red type. If no numbers are
entered, the average expenses from Calculator 7, will be used, which is
usually a better option. 






























































































The following is a computer generated report
for the business performance from the time the business opened, to the
time that calculations were last carried out. 





























































































TECHNICAL CONCEPTS 


Topic 1) Rounding Down And
Rounding Errors 





Topic 2) The Timing Devices In This Software,
And Related background Information 







Topic 2) Creating Timing Devices That
Automatically Transmit Elapsed Time Directly Into Formulas for Rate
Calculations 




TOPIC 1) ROUNDING DOWN AND ROUNDING ERRORS 



SUBTOPIC) CALCULATED RESULTS ROUNDED DOWN: MOST of the calculated results displayed in
this software are automatically rounded down, unless otherwise
noted. The money calculations are rounded down to two decimal
places, and the time calculations are rounded to the nearest minute.
This is done to avoid confusing people with unnecessary levels of
mathematical precision. This can sometimes result in very
small rounding errors, with a discrepancy of plus or minus 0.01.
However, in some cases, rounding numbers down can actually remove
rounding errors, as explained below. 




SUBTOPIC
ROUNDING NUMBERS DOWN MAY REMOVE ROUNDING ERRORS: When rounding errors occur more than two or
three zeros to the right of the decimal point, rounding down to the second
decimal place may eliminate the errors. As an example, let us
assume that the nine on the end of this number 99.9999 is a rounding error.
Rounding down to two decimal places results in 100.00, which
obviously eliminates the error. 




SUBTOPIC) WHEN
NOT TO ROUND DOWN: However,
calculated results that are going to be used for additional calculations
should NOT be rounded down, because that may increase rounding
errors. This does NOT necessarily apply to manual
calculations, because it may be excessively timeconsuming to perform
calculations with numbers that have many decimal places, with pencil and
paper. 




SUBTOPIC)
COMPUTERS CAN MAKE ROUNDING ERRORS:
Rounding errors can occur when the computer converts decimal
numbers to binary, or vice versa, and/or when DIVIDING numbers with many
decimal places. However, computers usually do not make rounding errors
with addition and subtraction, especially when the numbers have less than
15 digits. Computers are most likely to make rounding errors
with division, and when the root of a number is calculated, such as square
root or cube root. 




SUBTOPIC)
DIVISIONS IN THIS SOFTWARE: There
are many divisions carried out by this software. For example,
Calculator 8 is dividing by the number of hours that a business is opened,
which changes every time a calculation is performed. This can
involve numbers with 14 or more decimal places, such as 12.07234722228412
hours. However, the rounding errors that result from these
divisions are not likely to be any greater than plus or minus 0.01.
In general, rounding errors are usually insignificant, and can be
ignored, except for certain types of highly specialized
calculations. 





Topic 2) The Timing Devices In This Software,
And Related background Information






SUBTOPIC) DESCRIPTION Of THE TIMERS: There are several timing devices in this
software, which are located in Calculator 8 and 9. These
devices calculate the total time from the time of day that the business
opened to the instant when a calculation is performed. The
devices are timers, as opposed to clocks, because they measure elapsed
time. 




I created a number of variations
of these timers for experimental purposes, and to demonstrate their
potential utility. Only two were required for the money
calculations. The nonessential timers are in Calculator 9,
which was set up for demonstration and experimental purposes.
These devices measured time with one or more of the following
units: hours, minutes, seconds, milliseconds, microseconds, and
nanoseconds. The timers are controlled with the settings in
Calculator 8, and designed to reset to zero when they reach 24 hours. 




All of the timers I created for
this software measure time with a high degree of precision.
Four of the timers provide readouts down to one tenbillionth of a
second (1/10000000000 of a sec.). Needless
to say, this level of time precision should be considered experimental, in
terms of the current state of consumerbased computer
technology. (To see these timers,
scroll down to Calculator 9.) 




The question remains are the four
timers discussed above, really measuring one tenbillionth of a
second. I do NOT have the equipment to check the timers for
this level of precision. Based on limitations of Microsoft
Windows, Excel, and my computer, my guess is probably NOT.
However, they appear to have a very high level of precision
nevertheless, and their behavior is very interesting.
Specifically, the four timers produced exactly the same results
down to one tenbillionth, with my computer. This applies to
the Excel and the online JavaScript versions. 




SUBTOPIC)
LIMITATIONS OF TIME PRECISION:
Milliseconds are the smallest commonly used units with most
programming languages, especially when creating
software for conventional desktop and laptop computers. Spreadsheet software also has similar
limitations. The builtin time formatting mechanism in
Microsoft Excel can be set with custom formatting code [S].000 to display
time down to 1/1000 of a second (1/1000 of a second = one
millisecond). There are other limitations with this mechanism
that can limit the precision and versatility of timers created with
Excel. 




SUBTOPIC)
CIRCUMVENTING THE TIME FORMATTING MECHANISM IN MICROSOFT
EXCEL: The design techniques I used to create the timers, discussed
above, provides an interesting and highly desirable utility. These devices measure time in numbers, such as
4.764313578 hours. This circumvents limitations of Excel's
formatting mechanism for time. Thus,
numbers can be automatically fed directly into formulas for calculated
results, without user intervention.
This is especially useful for most rate calculations, because time
is one of the factors in rate formulas. 




SUBTOPIC) RATE
FORMULA THAT FUNCTIONS WITH THE TIMERS:
Rate multiplied by time equals
D, is a basic linear rate formula, which can also
be written as: RT=D or Rate*Time=D. This simple formula is very useful, and it works well with the
timers and automatic calculation mechanisms in this software. With this formula, D can represent revenue,
expenses, profit, an employee salary, units of work, distance, fuel,
weight, mass, volume, or anything that changes
with time, at a constant or average rate.
The rate, and D in this formula can be positive or negative.
For example, a negative rate of profit. The time in
this formula is positive, except perhaps with certain types of specialized
calculations, such as for computer simulations. 




SUBTOPIC)
AUTOMATIC HOURLY RATE CALCULATIONS REVENUE, EXPENSES, AND
PROFITS: The rate calculations carried out by
Calculator 8 and 9 use the method described in the two preceding
paragraphs. That is a timer measures the number of hours the
business has been opened, (elapsed time), which is automatically fed into
three formulas to calculate the hourly rates of revenue, expenses, and
profits. 




SUBTOPICS)
FORMULAS AND TECHNIQUES USED TO CREATE THE TIMERS: There are many ways of
creating the softwarebased elapse timers. discussed above.
In the following paragraphs I describe formulas and techniques I
devised to create the timers in this software with Microsoft
Excel. I also provide related
background information about how Excel measures and formats time.
However, this brief discussion will NOT provide the detailed
information needed to create timers. (If you are an expert in
the technical aspects of spreadsheets, and have related programming
knowledge, you probably will figure out how to make similar timing
devices, after reading the following.) 




EXCEL'S METHOD
OF MEASURING TIME: To understand how the timers I created for this software
function it is necessary to understand how Microsoft Excel keeps track of
time. Excel uses the number format
based on days (as discussed a few paragraphs above) to measure time,
INTERNALLY. Excel generally converts this to the standard
time format before displaying the time to the user.
Specifically, Excel keeps track of time (including dates) by
counting the number of days from a specified point in time, which is
Sunday, January 1, 1900 at 12:00 AM. to the present point in time. This
includes tiny fractions of a day, beyond the 9th decimal place. 




Based on the above, it is apparent
that Excel defines Sunday, January 1, 1900 at 12:00 AM as DAY ONE.
Thus, when working with Excel's timing mechanism, we can think of
Saturday, December 31, 1899 at 12:00 AM as DAY ZERO. However,
Excel does not think exactly as we do. That is, if you enter
a 0 in a cell, that has been formatted with a date and time code, such as:
dddd, mmmm dd, yyyy, h:mm:ss
AM/PM , Excel displays: Saturday, January 00, 1900, 12:00:00
AM. There is of course no such date,
but from a purely mathematical perspective, it serves as the zero point,
for the time and date calculations. 




(The following example will
clarify the two preceding paragraphs.) I am writing this
material on Sunday, November 28, 2010 at 12:16:39 AM. When
Microsoft Excel displays this date and time to the user, INTERNALLY the
software processes only one number, which is: 40,510.011557754600
days. The first five digits of this number are the number
Excel counted, from DAY ONE, 1/1/1900 to 11/28/2010. The
decimals (.011557754600) is a fraction of a day, which represents the
time:12:16:39 AM. The display of the number
(40,510.011557754600) in terms of a date and time is initiated by
formatting code, which is discussed several paragraphs below. 




Microsoft Excel will automatically
count the number of days from 1/1/1900,12 AM to the present point in time,
down to a tiny fraction of the day, with this formula:
=NOW(). This formula (NOW()) can be used to display
the current date and/or time, when placed in a cell that is appropriately
formatted. A similar formula is: =TODAY()
However, this formula does NOT calculate fractions of a day, as a
result it cannot display the time. It is generally used to
display the date. Both of the formulas, recalculate whenever
a worksheet is reopened, or when ever data is entered or deleted.
For example, if you enter the TODAY() formula on November 7, and
reopen your spreadsheet a week later, it will display November 14. 




Based on the descriptions in the
four preceding paragraphs, the method Microsoft Excel uses to measure time
might sound strange to some people. However, similar methods
are used by most programming languages and spreadsheet software.
With this method, conventional mathematical principles and
operations can be applied to time and dates. This provided
the versatility I needed to create the timers and related formulas, which
involve addition, subtraction, multiplication, and division.





SUBTOPIC)
MICROSOFT EXCEL'S FORMATTING CODE:
The numbers Microsoft Excel sees internally, and uses for
calculations, are not necessarily the same as the symbols displayed to the
user. The idea to keep in mind is
the symbols that Excel displays to users is an interpretation of the
numbers, based on the formatting code.
This can be quite confusing for individuals that do not have
extensive training and experience with the technical aspects of
spreadsheet software, especially if they are dealing with time
calculations. Presented below, there is a good example of a
problem that is potentially confusing, because the formatting code is concealing the numbers used for the
calculations. 




This is an
example of a simple problem that may be confusing as a result of the
formatting code. Let us assume, you
have the =NOW() formula in a Microsoft Excel spreadsheet, and it is
displaying the time of day in your locality. However, you
want it to display the time it is in Paris, which is a plus sixhour
difference from the time in your locality. The logical, BUT
INCORRECT answer is to add 6 to the formula, as such: =6+NOW().
The INCORRECTNESS of this simple logic is NOT apparent, because the formatting code hides the numbers
use for time calculations. Excel
calculates time and dates in days, and the correct reasoning is: 6 hours
is one fourth of a day. That is 6/24=1/4. Thus,
the CORRECT solution is to add one fourth to the formula, which results
in: =(1/4)+NOW(). 




NOTE: The above problem can be
very difficult to solve, because the underlying logic is concealed, but
when the underlying logic is revealed, (time based on days) it is very
easy to solve. This represents a general principle that
applies to many types of problems, in the physical, biological, and social
sciences, as well as to the challenges and difficulties we all face in
everyday life. Specifically, it can be difficult or
impossible to find a satisfactory solution or resolution to problems, if
the underlying logic, causeandeffect sequences, and other relevant data
are not known to the problem solver. 




This suggests a strategy that can be helpful in
solving certain types of problems. This involves initially
searching for the underlying causeandeffect sequences, dynamics, the
logic, that relate to a problem and its solution. If this
does not result in success, problems with many unknowns can sometimes be
solved by a trial and error process, or by experimentation. 




As examples, I am presenting four
variations of Microsoft Excel's formatting code, in relation to time and
dates. When the formatting code is in a number format, such
as #,##0.00000000000, the
NOW() formula displays
the number of days from
January 1, 1900 12AM, to the exact point in time when data was last
entered. The result will look similar to:
40,513.55754826390. This number was calculated by the NOW()
formula, and when the formatting code is changed to [$409]h:mm AM/PM;@ the number is
displayed as 1:22 PM. When this number is placed in a cell
that has been formatted with the following code: dddd, mmmm dd, yyyy, h:mm AM/PM the date and time will be displayed as:
Wednesday, December 01, 2010, 1:22 PM. Excel's default
formatting is General, and with this code the NOW() formula displays the date and time
as: 12/1/2010 13:22. 




Keep in mind that Microsoft
Excel's formatting code is essentially a type of computer language, and
there are a limitless number of ways of displaying numbers, time, and text
with this code. The formatting code provides great
versatility. This includes the functionality of
controlling the number of decimal places in numbers, and combining money
symbols or even words with numbers. However, it can also be
quite confusing for the casual spreadsheet user. If you want
to learn how to use Microsoft Excel's formatting code see the following
websites. (These sites provide basic information.) 



http://www.bettersolutions.com/excel/EVD243/QM215412021.htm



http://office.microsoft.com/enus/excelhelp/numberformatcodesHP005198679.aspx



http://www.google.com/search?hl=en&q=Microsoft+Excel,+formatting+code&tbs=vid:1&tbo=p&source=vgc&num=100





Topic 3) Creating Timing Devices That
Automatically Transmit Elapsed Time Directly Into Formulas for Rate
Calculations 





SUBTOPIC) CREATING A DEVICE TO RECORD THE
OPENING TIME OF A BUSINESS: The first step
in creating the timing mechanism in this software, was to create a device
for the user to enter the opening time of the business. This
device must also convert the entered time into a number that can be used
as a zero point, for measuring elapsed time. I created this
device with two lists, one for hours, and the other for minutes, which are
displayed in two dropdown menus, in Calculator 8. The list
for the hours are in a conventional AM/PM time format, ranging from 12 AM
to 11 PM. The list for minutes is in a
conventional number format, and they range from 0 to 59. 




SUBTOPIC) NAMING
THE CELLS WITH THE MINUTES AND HOURS:
The cell used for the dropdown menu for
the hours was named HourBox, and the cell use for the dropdown menu for
the minutes was named MinBox.
(HourBox, and MinBox, are the red cells in Calculator 8.)
As a result of the naming process, HourBox can represent hours, and
the MinBox can represent minutes in the following formulas.
Note, if the above is not kept in mind, the formulas presented
below, will be very confusing. 




SUBTOPIC)
CREATING A FORMULA TO DISPLAY THE OPENING TIME OF THE
BUSINESS: The minutes in the
dropdown menu, displayed in MinBox are in a conventional number
format. However, the hours displayed in HourBox are in
Excel's time format, which is based on fractions of a day.
Thus, I converted the minutes to fractions of a day, by dividing
the cell that displays the minutes, which is MinBox by 24 and 60.
This obviously result in (MinBox/24)/60 (This is the
same as MinBox/1440) Now a single formula can be created, by
adding the above to HourBox, which results in the following:
HourBox+(MinBox/24)/60 (or HourBox+MinBox/1440).
For convenience this formula was renamed
to StartTime. 




The formula derived above (
StartTime ) calculates in fractions of the day, which is the same method
that Excel uses internally to calculate time and dates. Thus,
when this formula is placed in a cell formatted with any variation of
Microsoft Excel's time code, such as [$409]h:mm
AM/PM;@ the time the business opened will be
displayed, such as 12:00 PM. The StartTime formula, with a
number format code, such as the following:
#,##0.0000000000000000 displays the time the business opened in a
fraction of a day, with decimals, such as 0.5000000000000000.
(This number is the same as 12 PM.) 




Thus, the StartTime formula
described above, provides one number representing the opening time of the
business, which is used as the zero point, to calculate elapsed
time. The StartTime formula, can also display the time the
business opened in a conventional AM/PM time format, with appropriate
formatting code. 




SUBTOPIC)
DERIVING A FORMULA THAT PROVIDES READOUTS OF CURRENT TIME IN FRACTIONS OF
A DAY: The next step was to derive a
formula that would measure a 24hour period in terms of fractions of a
day, with a range of 0 to 0.99999999999 days. (This is
equivalent to 12 AM to 1 1:59:59 PM.) I created the formula I
needed, with two of Excel's formulas, ( NOW() and TODAY() ) and with the
reasoning presented below. 




As previously explained, Microsoft
Excel's NOW() formula measures time in days from 1/1/1900 12 AM to the
point in time when a calculation takes place. For example,
40,523.60210752310 days is Saturday, December 11, 2010, 2:27 PM (displayed
with formatting code: dddd, mmmm dd, yyyy, h:mm AM/PM;@ ). To
create the elapsed timers, I need a formula to calculate the fraction of a
day that represents the time. With the above example, I
needed 0.60210752310, but I do NOT need the 40523 days. The
derivation of the formula, I needed is presented below. 




The TODAY() formula measures time,
without fractions, by counting the days in whole numbers, from 1/1/1900 12
AM, to 12 AM of the current day. For example, if the NOW()
formula calculated 40523.60210752310 days, the TODAY() formula, would
calculate 40523 days. Based on the above, the required
formula can be created with the NOW() formula minus the TODAY() formula.
This results in: NOW()TODAY(), which is the formula I needed.
For convenience I renamed this formula to: TimeIS. 




The TimeIS
formula, explained above, calculates the fraction
of the day that has expired. For example, at 12 AM, it
calculates 0, at 12 PM it calculates 0.5, and that 6 PM it calculates
0.75. The TimeIS formula can also display the time in conventional style,
with appropriate formatting code, such as [$409]h:mm AM/PM;@. 




SUBTOPIC)
CREATING A FORMULA THAT MEASURE ELAPSED TIME, WITH THE TWO FORMULAS
DERIVED ABOVE: The StartTime formula, and TimeIS
formula, were derived and explained in the previous paragraphs.
The StartTime formula displays the time the business opened, and
the TimeIS formula displays the current time, but the goal here is to
create a formula that measures the elapsed time. To explain
how this can be achieved, I will use an example. Let us
assume that the StartTime formula indicates an opening time of 6 AM, and
the TimeIS formula indicates that the current time is 11 AM.





We want to know the number of hours the
business has been opened. This can be obtained by subtracting
the opening time (=StartTime) from the current time (=TimeIS) which
results in 5 hours. Thus, the formula needed to measure the
elapsed time is obviously TimeISStartTime. 




The formula derived above
(TimeISStartTime) displays the time the business has been opened in
fractions of the day, which works well with Microsoft Excel's time
formatting code. However, it is necessary to have a formula
that provides the elapsed time in hours, with decimals. This
is needed to automatically calculate the hourly rates of revenue,
expenses, and profits. Thus, I multiplied the
TimeISStartTime formula by 24, which results in
(TimeISStartTime)*24 For convenience this formula was
renamed to DecimalHours. 




The formula derived above
(DecimalHours) calculates and displays the number of hours the business
was opened in a single day, starting from 12 AM, to 11:59
PM. However, if the business opens and closes on
different days, the DecimalHours formula will not provide a
calculation. For example, if a business opens at 12 PM, and
closes at 4 AM the following day, the DecimalHours formula will calculate
4 minus 12 equals a negative 8 hours 




When the DecimalHours formula
produces a negative result, it means that it is off by 24 hours, which is
one day. With the example presented in the previous
paragraph, we incorrectly obtain negative 8 hours, but if we add 24 hours
to the calculated result, we obtain the correct answer, which is 24 hours
minus eight hours equals 16 hours. That is, with our example
the business opened at 12 PM and closed at 4 AM, which is 16 hours.





Based on the information presented
in the preceding paragraph, a more versatile elapsed time formula can be
created. To do this, I simply created a statement for the
computer. In English words it states when the operating hours
of the business extends from one day to another, at 12 AM add one
day. The actual formula was written as
IF(DecimalHours<0,1,0) In terms of the computer it simply states if
DecimalHours produces a negative result, present 1, but if this is not the
case, present 0. This formula
(IF(DecimalHours<0,1,0)) was renamed to NextDayFix.





With the formula derived above (NextDayFix) and
the formulas explained in the previous paragraphs (TimeIS and StartTime )
another formula was created, that can calculate elapsed time from one day
to another, which is NextDayFix+TimeIsStartTime. This
formula calculates elapsed time infractions of a day. Thus,
it was multiplied by 24, to calculate elapsed time in hours.
(NextDayFix+TimeIsStartTime)*24. For convenience, this
formula was renamed to TimeBasedHours. 




Thus, the formula derived above
(TimeBasedHours), provides a number output, in hours. The
output from this formula can be fed into any formula that requires elapsed
time for its calculation. In this software the TimeBasedHours
formula is used to calculate the hourly rate of revenue, expenses and
profits. 




SUBTOPIC) THE
ABOVE IS GENERAL TECHNIQUE THAT HAS POTENTIAL UTILITY WITH OTHER TYPES OF
SOFTWARE The general
methodology The primary point of all of the above, is a
general methodology, of creating softwarebased timing devices that can
feed their output directly into formulas, to obtain automatic calculated
results. However, the way I derived, structured and named
formulas presented above, was based on convenience. There are
many ways of creating similar formulas that measure elapsed time.






















Calculator 9, For Experimentation and
Demonstration Purposes 


AN EXTREME LEVEL OF MATHEMATICAL
PRECISION, BASED ON CALCULATOR 8: I am presenting some of the
calculation devices from Calculator 8 reconfigured to provide a greater
level of mathematical precision, at the end of this section.
(About 15 paragraphs below, in red type.) The
reconfigured devices provide calculations with a number of decimal
places. The length of time the business was opened is
calculated either with many decimal places, or with very tiny units of
time. However, this higher level of mathematical precision does NOT
provide any additional utility with money calculations, but it has
theoretical value, as well as practical utility with other types of
calculations. 






































































Currency Symbol Settings Device 




The pink box below displays the currency symbol
that is used by the eight Calculators. If you do NOT see the currency symbol you need
in this pink box, scroll down and follow the four steps below to change
the currency symbol. 



































Step 1) Currency Box One 






If the currency you are calculating is the
euro, enter the letter E in the
white box below. However, if the
currency you are working with is NOT the euro, make sure that the white
box below does NOT contain ANY letters or symbols. 




Enter E in white box for euro 
For Euro only 

For Euro only 
Enter E in white box for euro 




If you are not using the euro the
white box above must be empty. 






Step 2) Entering a Currency Symbol 





In the white box below, delete the blue symbol,
and enter the currency symbol for the money you are calculating.
Alternatively, you can enter an abbreviation for the currency,
which cannot be over four letters. If you are using the euro,
you can leave this box blank, and enter the letter E in the box above. 














\ 









Step 3) LeftRight Placement Settings 






The white box below controls the placement of
the currency symbol, which can be on the left or right of the
number. Left click on the box, and enter the word left or
right. To do this first left click on this white box, and
then type in the number, or use the dropdown tab on the lower right of
the box. 

















Note: If your calculations involve the euro or
the US dollar, the word Left
should be entered in the white box above. If you used an
abbreviation or word for your currency, you might prefer to have it placed
on the right of the number. 






Step 4) Spacing for Currency Symbol 






The number in the white box below determines if
there is a space between the currency symbol and the number.
For zero spaces enter 0, and for one space enter 1.
Before entering a number left click on the box. Then
you can type in the number, or use the dropdown tab on the lower right of
this white box. 

















Note: The above should be set at 0
for the US dollar ( $ ). The spacing for the
euro is automatically set, and it is not affected by this setting.
If you used an abbreviation or word for the currency, you might
prefer one space. If you want one space enter 1, but if you
do not want any spaces enter 0 

