#Accounting - What's a T account? Why use them?

Question

What's a T account? And why use them?

Answer

A T account is a simple but effective way to organize the activity in any given account.

Analysis

Let's first talk about accounts. An account is a way to gather similar activity in one place. For instance, over the course of a year, let's have Sample Co. have a number of sales throughout the year. We can sum up those sales to see the sales activity for the year. For an example, let's have Sample Co have sales of $100,000 for the year.

This $100,000 sales figure is made up of smaller sales throughout the year. We list them individually as they happen. A part of that list might look like this:

$500
$1000
$250
$300

and so on.

Some transactions will increase the balance of the account and some will decrease that balance. Take the account Cash for instance - as sales are made, cash comes into the company. As inventory is purchased, salaries are paid, and other outflows are accounted for, the balance of the account decreases.

One way to show this would be to list out all the transactions in a single list:

 $1,000
-$350
-$15
-$25
$300

and so on. Which can get messy.

Another way to look at the accounts is to put all the amounts that increase the account in one list and all the amounts that decrease the account in another list. To save space and to keep things organized, we can draw a T, put the account name above the crossbar of the T, and have amounts on one side of the T's vertical line increase the account and on the other side put those amounts that decrease it. It'll look something like this:


        Cash
------------------
$1000 |
           | $350
           | $15
           | $25
$300   |

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As always, if you have a question, please ask!

#Household math - Which is the better way to pay for an online school when dealing with referral credits?

Question

I'm looking at joining an online school website that has over 22,000 courses in all sorts of different topics (I'm interested in some portion of them that relate directly to my interests). The cost for joining this website is $15/month but if I join for a year, I pay $99. To make things more complicated, I have 2 coupons for 1 month off each (one is the usual offer from the website and the other is as a referral coupon - I got one and the person who referred me also got one). What's the best way to join the website?

Answer

It's best to subscribe for a year, unless you are going to receive 2 or more referrals every month. 

Analysis

This is an interesting question because of the twists and turns in what's available in terms of options. The key is going to be to put everything on equal terms so that we're comparing "apples to apples".

Let's look first at what happens if we look at the options without regard to the coupons. We're comparing the regular monthly cost of $15 vs the monthly cost of $99 over 12 months, which is $8.25 per month. Clearly it's better to pay less per month! But... what if you don't use the site for all 12 months? What's the number of months that'd you have to use the site on the yearly plan to have it cheaper than paying $15/month?

We can find that by dividing the yearly cost of $99 by the monthly cost of $15. This gives 6.6, or in other words, it's better to pay by the month if you'll use the site for 6 or less months. For 7 or more months, it's better to pay the yearly amount.

Now let's look at the coupons. When paying by month, the coupons give 2 free months (and so for the cost of 1 month for $15, you get 3 months). When paying by year, you get 14 months for the cost of 12. What that works out to be is, when paying monthly, $15 for 3 months is $5 per month. When paying yearly, $99 for 14 months, that's $7.07 per month. And so there appears to be a better financial result to pay for 1 month and pay $15, use the site for 3 months, then change over to a yearly plan. However, that ignores a couple of factors, and so the best way to calculate this is to calculate the monthly cost over the course of the annual plan, then look at the associated monthly cost.

Using the yearly plan, you get 14 months for $99. Using the monthly plan first and then paying for the year, you get 15 months for $15 + $99 = $114. To compare the two, we divide the $114 by 15 (to get the per month rate), then multiply by 14 to get to the same number of months under the yearly plan:

And so it's best to pay for the year and get the 2 free months added on.

The one exception to this would be if there is an expectation of receiving 2 or more referral codes per month. If that's the case, it'd be better to stay with the monthly plan until the likelihood falls off of getting those referral codes. At 1 referral code or less per month, it's better to pay yearly.

~~~~~

As always, feel free to ask a question!

#Accounting - Accounting requires organization, not advanced math...

Question

I want to study accounting but I'm afraid to do it because I'm not good at math. What are your thoughts?

Answer

The good news is that accountancy rarely goes beyond basic arithmetic (adding, subtracting, multiplying, dividing). In fact, accountancy is far more about organizing and classifying information rather than manipulating it. 

Analysis

As a for instance, let's take a sample transaction and look at how an accountant would treat it.

Stan's Superheroes (a store specializing in superhero collectables) sold a Baitman figurine (it's a knockoff of Batman - this one is of a cowled fisherman who fights crime on the docks) for $10. The customer paid cash. Stan originally bought the figurine for $3. How do we book this transaction?

And now let's watch how an accountant works through this question.

• Cash has increased by $10, so the account Cash is increased (Debit)
• Sales have also increased by the same amount, and so the account Sales is also increased (Credit)
• The inventory has decreased by the amount originally paid for the figurine, and so it decreases by $3 (Credit).
• The last account, which is the Cost of Goods Sold, increases by $3 (Debit).

Accountancy also gets into reasonableness. For instance, would it be reasonable to conclude that Stan's Superheroes makes $1,000,000 per year from sales of Baitman? Probably not - and it's the role of the Auditor (a type of accountant) to examine those types of situations.

Bottom line, most accounting does not involve anything more than basic math. If however you are interested in stretching your math muscles within the accounting world, Cost Accounting might be for you (it's a type of managerial accounting that does it's best to examine a business from top to bottom, in all its processes, and put them into financial terms so that the management of a company can make better business decisions).

~~~~~

Questions and comments welcome!

#Household math - How many times use a purchase to make it worthwhile...?

Question:

If I buy a table for 590 THB and I want to use it for art. Paying for a latte in a shop is approx. 60 baht per beverage and I consume anywhere from one to three lattes when I draw. How many days of drawing at home will it take for me to pay off the table?

Answer

A minimum of 4 art days out, a maximum of 10 art days out.

Analysis:

Let's first talk about Sunk Cost, which is the concept that once money is spent, it's gone. Nothing you do subsequent to buying the table is going to make the money come back. And so any decision you make concerning having coffee has no bearing on the cost of the table.

Now to the question at hand.

If we look at the number of lattes it takes to exceed the cost of the table, that's:

cost of the table/cost of a coffee = coffees equal to the cost of the table:

(on the 10th coffee, the coffees are worth more).

If we assume 1 coffee per art day, that's a maximum of 10 art days out.
If we assume 2 coffees per art day, that's 5 art days out.
If we assume 3 coffees per art day, that's 4 art days out.

~~~~~

Please feel free to comment or ask a question!

#Household Math - Credit or coupon for defective goods

Question

I bought some art supplies for $65 and found that a portion of them are defective. I was given a credit of $20. Later, I found that the remaining part of them are also defective. The retailer is offering me a 10% off coupon on a future purchase. Should I accept the coupon or should I try for another credit?

Answer

In all likelihood, unless there is a very large purchase you'd like to make, the credit will be better than the coupon.

Analysis

There are a couple of things going on here, but the most relevant question is: Which is better? A 10% coupon or a credit of some amount?

So let's talk about the results from each possibility.

The 10% coupon will offer some money back on a future purchase. For this to be worthwhile, we first need to assume that there will be a future purchase! If you are so disgusted by the quality of the product and the retailer isn't trusted, then the coupon would be absolutely worthless.

Let's assume there is an intention to order again. To get the most out of the coupon, you'll want to order as much as you can in order to get the maximum benefit (keeping in mind that you don't want to buy more than you reasonably need!)

The credit is an unknown quantity, but we can assume that the company will offer, at most, the remaining $45 of the original purchase price.

So how much do you need to buy using the coupon in order to have it equal the potential credit?

For this, we can set up an equation.

On one side, we'll have C, the credit. On the other, we'll have B, the amount you'll buy. Since we'll pay 10% less than usual, the amount of benefit we get from the coupon is 10% X B:

C = 10% X B

We can multiply both sides by 10 to get:

10 X C = B

So what does this say? Let's throw in a number - if the expected coupon is $20, we'd have to buy $200 worth of goods for the coupon to worth just as much. If we expect to buy more than that, then the coupon is better. If we expect to buy less, then the credit is better.

ANSWER KEY (alternate variables)

At 10% coupon:

C = $10, B = $100
C = $30, B = $300
C = $45, B = $450

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Please feel free to comment or ask a question!

#Admin - A new blog, a new beginning, a new conversation on math-y topics!

Hello one and all and welcome to Math Fact-orials!

In this post, the first of this blog, I'll talk quickly about me, this blog, what I hope to achieve, and all that.

About me

I love thinking and learning and sharing what I'm thinking and learning. Most recently, I was a Hero and Featured Answer Reviewer (Algebra, PreAlgebra, English Grammar) with www.Socratic.org, with (at the time of this writing, with roughly 2 weeks of life left in Socratic):

- over 890,000 views,
- 2400 answers, and
- 700 edits of existing answers.

But since that website is currently scheduled to be shuttered mid-August 2018, I've decided to start my own Question and Answer site (i.e. this blog) that will focus on things I find important/interesting/fun/etc.

Some more things about me:

- Formerly a Certified Public Accountant (in the USA) and a Chartered Accountant (in Canada)
- Holder of a Life Coaching certificate
- Spent a few years in the US Navy as a Supply Corps officer

About the blog

While I don't want to set anything in stone (this is a living blog after all, so it will morph and change as I do), there are a couple of areas I'll tend to focus on at the start: Combinametrics (or the number of ways of doing/arranging/organizing things) and something I'll call Life Math - this will encompass things like Business Math, Budgeting, Investing, Accounting, Financing, and all those non-sexy math topics that academics tend to shun. Life Math, by its very nature, is a bit more "squishy" than academic math - there typically are more "squishy" answers than in academic math. For instance, is a 10% discount on a shirt a good discount? It might be, but then again it might not be - it's up to the reader to decide. But in these kinds of questions and answers, I'll do my best to lay out some things to think about.

I intend to right about how to approach a problem as the first part of any blog post, and then to have an "Answer Key" below, which will show the various answers with changes in the starting facts. For instance, if a shirt that costs $30 has a 10% discount (with a final cost to the customer of $27 before sales tax), the same process will work if the shirt is $40 and there's a 20% discount (with a final cost of $32 before sales tax).

Questions are very welcome!!!

If you have math questions, please do ask! Post a comment (I approve all comments) and I'll be sure to respond and write on the blog in response. No names/specific locations will be used and so don't worry about anonymity!

And I think that just about does it - so Welcome! and I hope to hear from you.

Parz

Update, 22 Aug 2018

Through editing and updating the organization of the blog, I'm hoping it'll be more useful (and easier to find the information you are interested in!). Links, labels, and subjects are all being edited, reworked, and otherwise made better. Get ready for Math Fact-orials 2.0! (or maybe just 2!... - factorials and decimal points don't get along very well...)