A Novel Set of Software-Based 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 e-mail address  
  On this page there are eight software-based 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/Rate-Time-And-Business    
    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 short-term 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 drop-down menu will open, with numbers. For the ONLINE JavaScript version of this software, a drop-down menu will open as soon as you LEFT CLICK ON A RED BOX.    
    When the drop-down 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 drop-down 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 drop-down 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 time-consuming 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 ten-billionth 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 consumer-based computer technology. (To see these timers, scroll down to Calculator 9.)    
    The question remains are the four timers discussed above, really measuring one ten-billionth 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 ten-billionth, 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 built-in 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 software-based 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 six-hour 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, cause-and-effect 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 cause-and-effect 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/en-us/excel-help/number-format-codes-HP005198679.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 drop-down 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 drop-down menu for the hours was named HourBox, and the cell use for the drop-down 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 drop-down 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 24-hour 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 TimeIS-StartTime.    
    The formula derived above (TimeIS-StartTime) 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 TimeIS-StartTime formula by 24, which results in (TimeIS-StartTime)*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+TimeIs-StartTime. This formula calculates elapsed time infractions of a day. Thus, it was multiplied by 24, to calculate elapsed time in hours. (NextDayFix+TimeIs-StartTime)*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 software-based 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.    
                 
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        Step 3) Left-Right 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 drop-down 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 drop-down 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