The actually is a problem with calculating Tax on a line item basis. The problem lies in rounding errors. Rounding must ALWAYS be the final step AFTER ALL OTHER CALCULATIONS.
Otherwise any variations propagate through the calculations. Example: $26.755 + $4.255 = $31.01 without line rounding $26.76 + $4.26 = $31.02 with line rounding This type of error compounds with an increase in line items, and is why Taxes are always solely calculated upon the final total and never on subtotals of any kind. While this example is just one penny, I have seen Eros of as much as 5% on larger orders.
Under the General Accepted Accounting Procedures (G.A.A.P.), effectively law in much of the world, you are required to maintain all digits up through the total, then apply taxes, then and only then are you allowed to round.
All this is based upon strict mathematics and a principal known as "Significant Digits" which determines the meaningful level of precision that is possible. Rounding anywhere before the final number always adds in significant and needless errors.
Kevin Yip
@Reply 2 years ago
There were rounding rules in the industry of my old job as well. In the 1990s when we first started sending financial data electronically, anything that had rounding errors would be rejected by the computer at the other end, which enforced industry rules. Another challenge was that sometimes we had to explain to our customers why the total shown on the invoice didn't add up to the line item amounts (due to rounding rules being enforced), but those were rare instances. Most of the times, our line item amounts came from an integer multiplying a 2-digit number (quantity multiplies price), and that always yielded a 2-digit number. So the grand total would always be 2-digit with no rounding needed. Rounding would only become an issue when decimals multiply decimals: 2-digit x 2-digit = 4-digit; 4d x 4d = 8d, and so on.
I've been teaching this stuff for like 30 years now, and when I first started back in the 90s, I didn't know better and I was teaching Excel and Access to a bunch of accountants, no less, and they were the ones that told me that you should round off calculations on each line so you don't run into errors with the subtotal and a total at the end, so that's how I've been doing it this whole time. And in the 20 plus years that I've been teaching online, you are the first person to say something to me about this, so I'll definitely look into it, but that's how I've always been taught. You take your line item, multiply by the quantity, and then if there's a fraction, you round off each line item total. So if you're buying 3.1 gallons of paint at $1.01 per gallon, your line total should be $3.131, which we round to $3.13.
In accounting, the generally accepted practice for handling rounding in transactions, such as tracking orders in a database, is to maintain accuracy at each line item level before applying any rounding. This means that for each line item, like buying 3.1 gallons of paint at $1.01 per gallon, you should calculate the exact total (which would be $3.131 in this case) and keep it as is without rounding at this stage.
When you calculate the final total at the bottom of the invoice or statement, that's when rounding is typically applied. The total amount is usually rounded to the nearest cent in U.S. currency (or to the smallest unit of currency in use). This approach ensures that the sum of the detailed line items reflects the true total amount before rounding, providing a more accurate and fair representation of the total cost.
For Excel or Access databases tracking such transactions, it's important to set up your calculations to follow this method. This ensures consistency and accuracy in financial reporting, which is critical for both internal tracking and external reporting, such as for tax purposes or financial audits.
Remember, the specifics can vary depending on the company's accounting policies or the requirements of the jurisdiction in which the business operates, so it's always a good idea to consult with an accounting professional if in doubt.
So, it looks like in this example, you're correct. Maybe it was just something that the accounting firm did or their particular practices. But I've been teaching it that way ever since, so I will definitely bring this up the next time I re-record this course. Thank you for the feedback.
As I always say in my lessons... I'm not an accountant or a lawyer. I'm a computer nerd LOL
Michael OlsenOP
@Reply 2 years ago
Glad I could contribute.
As an Engineer and Mathematician, I am very aware of how over simplified many mathematics rules are in the general populace. Rounding is perhaps one of, if not the, most over simplified and misused. Just remember that rounding introduces a small degree of error; therefore it should always be the very last thing we do.
If you have any other questions about maths, especially common practice vs strict rules, please do not hesitate to ask.
You are a wonderful teacher Richard and I am learn tons going through your courses on MS Access. I have spent most of my career dealing with dbase and extremely formal SQL. Last time I actually used MS Access was in the late 1980s ('87 or '88). So your courses are a MAJOR help in my current position where I am having to develop an Access Database from scratch.. I especially like how you show a common "wrong" way (letting us know in advance), and the sow a much better method. I have actually recommended to the Canadian Government that they contact you to purchase your classes for their many departments that require, or would benefit from, small to medium localized databases. You have already saved my office well over $500,000.00 by making my database far simpler for my coworkers to use and search.
Well, I appreciate the help, thank you very much, Michael. I'm glad you are enjoying my videos. And please do let your associates in the Canadian government know that I grew up in Buffalo, New York, so I spend a lot of time in Ontario. Toronto is one of my favorite cities. Rush is my favorite band. And I've been to many Blue Jays games (to watch the Yankees, of course. LOL.)
Kevin Yip
@Reply 2 years ago
Computer users also have to be aware of "floating point errors," an inherent mathematical flaw in all computing devices that has existed forever, and still does today. If you do a simple math in Access such as 0.1 + 0.2 - 0.3, you don't get the correct answer (see picture below), because the computer can't achieve the precision required for the operation, even with 32- or 64-bit processing.
Kevin Yip
@Reply 2 years ago
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