#Household math, #Investing - The Rule of 72

Question

I've heard of something called the Rule of 72 but I have no idea what it is.

Answer

It's a quick calculation used to figure out how what factors are needed (in terms of time and average return) needed to double your money.

Analysis

There are two basic factors that play into how an investment (or group of investments, such as a mutual fund portfolio) will do over a substantial number of years:

• the average rate of return, and 
• the number of years the investment is held.

So let's say for a minute that I have an investment and I anticipate making 6% per year on it and I plan on holding it for 12 years. Well... so what - is there some way to get an easy to understand number from these two details?

This is where the Rule of 72 comes in. It gives a quick answer to the question of "How long will it take to double my money". We take the average rate of return without the percentage mark (so in this case 6) and multiply it by the number of years to be held (in this case 12) and then multiply them together:

6 X 12 = 72

And so at the end of 12 years we can anticipate that our money would have roughly doubled.

We can work this another way - if we wanted to know the number of years we had to hold an investment for it to double at a 6% average return, we can divide 72 by 6 to get 12 - which is to say that every 12 years we can anticipate our investment doubling.

This becomes a very powerful tool when young people are first looking at putting some money away for retirement. For instance, if at age 25 someone puts $10,000 into a retirement account and anticipates 6% return per year, we know that every 12 years the money will double. If the person wants to access that money at age 60, it'll double 60 / 12 = 5 times. And so the value of that 10,000 will have become $320,000.

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Questions and comments always welcome!

#Budgeting, #Household Math - Tracking spending...

Question

My budget has been written up and everything looks good. So I'm done, right?

Answer

Ummm... no. Now it's time to execute the plan that you've created.

Analysis

It's absolutely fantastic that you've gotten your budget squared away and things look good on paper. Think of the budget as a financial plan - it lays out what you intend to spend over the given month. Now it's time to act on that plan.

There are many ways to accomplish this - some people prefer a more detailed level of bookkeeping while others prefer way less detail. Whatever system works for you, that's the one you should use.

For the more detailed people, receipts are going to be your friend. When you buy something, make sure to get a receipt. If you don't get a receipt, perhaps carry a piece of paper or small notebook to notate what was spent. When you get home, make sure to record those expenses onto a spreadsheet or perhaps a bookkeeping program such as Quickbooks.

For the less detailed people (and I fall into this category), figure out how much you can spend each day and put that amount of money into your wallet. That is what you can spend and when it runs out, your spending for the day is done.

As you track your actual daily expenditures, you may have to tweak your budget to have it match your spending. Alternatively, you may have to tweak your spending to stay within budget.

In the process of recording your expenses, you can record expenses that will have an impact on your tax reporting. This will significantly reduce the stress of doing your taxes at tax time.

This post is part of a series on budgeting - Budgeting 101

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Questions and comments always welcome!

#Budgeting, #Household Math - Credit Cards...

Question

What is your opinion of credit cards?

Answer

Analysis

I've tried writing the first sentence to this analysis a few times but eloquence is abandoning me. Elegant writing will simply not produce what it is that I'm trying to say, so I'll go with the simply statement of:

Credit cards are bad.

Actually... let me rephrase that. If you are a purchaser, they are bad. If you are a retailer, they're great. Why? Because studies have shown time and again that people who use credit cards are willing to spend more for products and services than people who use cash.

For whatever reason (this article proposes a few ideas), people spend more when using credit cards than when not. In fact, people are so programmed into this that even when paying by cash, seeing a sign that says that credit cards are accepted will help increase the spending of the average shopper.

One thing that the article above cites is that those who buy with credit cards will tend to focus on the benefits of the purchase. Those who buy with cash tend to focus on the costs of the purchase. It would seem that when the "burden" of paying for something is greatly reduced, now to the point of tapping the credit card on a reader or pulling up a QR code on a phone app for many purchases, it takes away the thoughts on the cost of the purchase. Purchasing in this manner, focusing on the benefits with little regard to costs, is Impulse Buying, and if it isn't the number one reason why people can't stay on a budget, it has to be in the top three.

Staying on a budget requires something that used to be called "sober consideration" - and maybe it still is. It requires a plan and then, far more importantly, execution of that plan. Credit cards act to circumvent that plan, making it far too easy to buy things and to add on to purchases already being made (ex. what's the cost of another drink when dinner is going to be expensive? What's the cost of buying that appliance insurance plan when the cost of the appliance is going to be so much?)

And so, bottom line - credit cards are an occasional necessity but as an integral part of daily life, credit cards are a financial disaster either waiting to happen (or already happening).

This post is part of a series on budgeting - Budgeting 101

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Questions and comments always welcome!

#Budgeting, #Household Math - Budgeting - Income

Question

I've done the budget process for expenses. Now what?

Answer

Let's now add income to the budget...

Analysis

It's time to add in the Income numbers into the budget and oddly enough this can be the harder part of the budgeting process.

With expenses, we want to identify all the expenses we incur over the course of a year, then display that on a monthly basis (we've done that part in prior posts). We use the Accrual Method to identify expenses as they are incurred so as to prevent surprises. Surprise expenses are no fun.

With income, we want to identify it as it's received - the Cash Method. One of the tendencies in budgeting is to project a rosy future where the promised raise at work is a sure thing, where that tax refund will be large, where a long lost relative died in the Congo ages ago and selfless lawyers have searched for years to find the heir - and it's you. We don't want to budget that in - if it happens, great and if it's periodic, we can budget it in (if the raise does indeed happen, adjust your budget!). Surprise income is a good thing.

For most people, income starts and ends with a salary. When we budget, we're going to want to budget the "take home pay" - not the gross pay. It's great that you have a job that pays $50,000 per year, but if you only take home $40,000 of that, that's what goes in the budget.

This also goes for people who receive pensions and other sources of periodic payments. Include what you know you are receiving. If and when an announcement comes that it's being changed, adjust your budget accordingly - if it's good news and the pension is going up, adjust the budget when you actually have that first payment in the bank. If it's bad news and it's going down, adjust the budget immediately and see if you'll need to change anything in your lifestyle.

Another common way to "overstate income" is to look to bank interest and other sources of investment income like that. Unless you have your finances set up to be living off of investment income (and we'll talk about that below), don't include it.

Ok - people who live on investment income, people who own a small business, or otherwise whose income varies. It's important to pick an income number that focuses more on the lean months than the rich ones - and it may be the case that budgeting into the expense side of things a "float" that income overages can go into and that reverse during the lean months. Doing something like that will require constant vigilance on that account - it's been set up to be there when income is lower, so you need to make sure it's nice and full when income is plentiful.

I've updated the budget example here:

https://docs.google.com/spreadsheets/d/1kCtMSNnKUXhvJT9yif5wtl5jbEsmyFz9mQ-IV62_U4g/edit?usp=sharing

and you'll note that we have a situation where the income is less than the expenses. We'll talk about that situation in the next post.

This post is part of a series on budgeting - Budgeting 101

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As always, questions and comments are welcome!

#Budgeting, #Household Expenses - Budgeting for Expenses - Putting in numbers...

Question

I've made my list of expenses. Now what?

Answer

Let's add some numbers! 

Analysis

In my last budgeting blogpost, I talked about identifying all the expenses and ways that money leaves your pocket. We want to look at the budget over the course of a sensible and useable timeframe, and that's usually one month.

The overall idea here is to budget for expenses using the Accrual Method - as soon as you are obliged to pay an amount, that should be recorded in your budget. This is why credit card payments will not make an appearance on this budget - we don't care how we pay for something, we only care that we need to pay.

Some items in our list of expenses are very easy to figure out monthly. Rent, mortgage payments, car payments, and the like are usually a single monthly payment and are easy to put into our budget sheet.

Some expenses are monthly but fluctuate. Electricity costs, for example, fluctuate based on the season (when it's colder, the costs go up). For costs that fluctuate, cycle, or otherwise change significantly over the course of the year, I'd recommend adding up the amount spent over the course of a year, then dividing by 12.

Other expenses are yearly. For instance, when paying insurance costs, I tend to pay a yearly lump sum, which results in a bit of a discount. Again, drop those costs into the yearly column and divide by 12.

And for costs that are every few months? Find the costs per year and divide by 12.

Here's an example:

https://docs.google.com/spreadsheets/d/1bDvJ0qpCvjIGNMs9AhliwCIlYY8XLLP8dnXbH1TxueE/edit?usp=sharing

This post is part of a series on budgeting - Budgeting 101

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Questions and comments always welcome!

#Budgeting, #Household Math - Budgeting Basics - Expenses

Question

How do I budget for expenses? 

Answer

This will take a few posts to do, but in this one we simply identify all the possible outlays you experience and put them in a spreadsheet.

Analysis

As we start preparing a budget, it's important to first identify where money goes. Do you pay rent or a mortgage? Pay for a car? Insurance? Gas? Or perhaps transit - maybe a daily fare or a monthly transit pass? Utilities? Cable? Phone (landline and/or mobile)? Food?

Let's first list out those items that you know about into a list (we'll be modifying the list, and so using a program like Excel (PC), Numbers (Mac), or Sheets (Google - it's free and can be used online). Here's a sample:

Mortgage
Condo Fees
Condo Insurance

Water
Electricity
Gas (Note: the heater and stove are natural gas)
Cable

Phone, landline
Phone, mobile

Groceries

Dining out

Auto payment
Auto insurance
Auto fuel
Auto maintenance, repairs


And perhaps you have other expenses that need to be added into this list. If you think of it, write it down!

Once you've done that, take a look at your credit card statement for the past few months. Do you see things there that aren't on the list? Clothing? Add it. Video games? Add it. Go ahead and put in all the categories you think of.

I've built a google spreadsheet to follow along with these posts (it's view only):

https://docs.google.com/spreadsheets/d/1ZxwZz7Nn5ZYVV-x6HgPavTP6wkfIswP8-NTvV9gTTR4/edit?usp=sharing

In our next step, we'll add numbers.

This post is part of a series on budgeting - Budgeting 101

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As always, questions and comments welcome!

#Budgeting, #Household Math - Budgeting... What's it good for?

Question

It's great that I read everywhere about the need for a budget, but what is it?

Answer

A budget is a tool that people use to figure out their financial health.

Analysis

I like this definition enough that I'll repeat it:

A budget is a tool that people use to figure out their financial health.

The most basic question that can be answered is "Am I living within my means?". More complicated questions can also be answered, such as "Can I afford that expensive thing?". Questions involving more involved financial questions, such as "At what age can I retire?", will probably require a Personal Wealth Plan of some sort - simply analyzing monthly spending probably will be insufficient to answer that kind of question.

The main idea behind the budget is to see where your financial strengths and weaknesses are. Where there are financial weaknesses, you can then develop strategies to deal with them. For instance, if it turns out expenses are higher than income, the budget can identify that that is the case and then steps can be taken to address it.

To budget, we look at the two sides of financial life - Money coming In and Money going Out. In future posts, I'll reference topics in the post about the Statement of Cash Flows for a business because there will be some overlap in concepts.

The first place to start is to think about your expenses and how often they occur. For most people, the big expenses occur once per month (rent/mortgage payment usually being the biggest of them all). And so, in general, it's best to work with a budget that looks at a monthly timeframe (we'll deal with non-monthly expenses and incomes in their respective sections).

I think the last thing to say about what a budget is is that it's something that can be quite individualized. Depending on how exacting you'd like to be can greatly affect the budget. What are the items you want to track? What are the items you don't want to track? Generally if there is a lot of guilt and shame involved, like perhaps the "amount of money spent at coffee shops" or "the amount of money spent online shopping", those are items that need the most attention!

In future posts, we'll talk about the How of budgeting...

This post is part of a series on budgeting - Budgeting 101

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As always, comments and questions are welcome!

#Accounting, #Household Math - Moving the accounting into the home...

Question

Do accounting principals apply to my personal financial life?

Answer

Absolutely! See below for a few ideas...

Analysis

Bookkeeping and accounting really only refer to the tracking of financially-related transactions over the course of the life of a financial entity. That entity can be a company, a government, or a person/family - to anything that conducts any sort of business, accounting applies. Of course, as the complexity of the entity increases, so do the challenges of recording those transactions and making sense of the resulting information.

One of the ways we see how this applies is in the preparation of tax forms. When filling them out, you are essentially asked to account for income that's been made (from various sources and it matters where money comes from because the tax treatment can change based on the source). Alongside that, you are also asked to account for specific types of expenses - say for instance mortgage interest - because those monies spent are treated as deductions (and again, the reasons for those payments will determine how the tax calculations are done). For most people, taxes are a nightmare requiring frequent sleepless nights, gathering information. However, if an accounting system is implemented and used throughout the year, the burden (physically and mentally) of filling out the forms would be greatly decreased.

Another place accounting shows up in a household is through budgeting (company's call it financial forecasting or some such other term). What is anticipated that will be made in income? What is anticipated that will be spent? Is the income number bigger than the expenses number???

And one more place I'll mention is in the area of Needs vs Wants - or the making of financial decisions. For instance, while there is a need for a car, does that mean you need the newest Mercedes? On the other hand, is it financially better to buy an old clunker, given that it'll need more repairs and work?

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Comments and questions always welcome!

#Household math - Which is the better value? Loose tea or tea bags?

Question

There's a lovely tea shop I go to sometimes. Which is the better way to buy tea, loose or in bags? The instructions say to use 3-5 g of loose tea in a pot. Here's a photo I took to help:

Answer

Financially, under my assumptions, the tea bags are a better way to go.

Analysis

First off, and probably to the dismay of tea lovers around the world, I'm going to assume that the tea experience from loose leaves and from a bag is the same.

In order to understand the financial aspect of this question better, we need to express the tea usage in terms of servings. I'll assume that 1 tea bag is a serving and that it's equivalent to the 3 - 5 grams mentioned in the question.

I'm also going to assume that the price points on the teas are for the same categories of teas (the selections of Lesser, Medium, and More Expensive teas are the same).

Let's chart out the cost per serving:

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As always, feel free to ask a question!

#Household math - Which size is the better option?

Question

While shopping online for tea I found a type of tea I like with 2 options for buying it: 16 bags for 134.30 of my currency and 24 bags for 169.89 of my currency. Which is the better option?

Answer

It's far cheaper to buy the bigger box assuming you are actually going to drink the tea. If you are more of a tea collector than a tea drinker, it's better to buy the smaller box.

Analysis

To answer this type of question, we need to set up equal terms so that we're comparing "apples to apples". One way we can do that with this problem is to look at the price per tea bag. We can set up the math for this in this manner:

Price / number of tea bags = price per tea bag

For the two options:

134.30 / 16 =  8.39 units of currency per tea bag

169.89 / 24 = 7.08 units of currency per tea bag

There is roughly a savings of 1.30 units of currency per tea bag, which is a big savings (when looking at this in percentage terms). To look at this problem in that way, we take the savings and divide by the better price per unit:

1.30 / 7.08 = 18.4%

And so the first method of buying the tea is wildly more expensive than the second.

The only caveat on this result is that, if you are like so many people who do more collecting of tea than of drinking it, then buying less is better. However, if you are intending to drink the tea, it's far better to buy the bigger box.

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Please feel free to ask a question!

#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.

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As always, feel free to ask a question!

#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.

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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...)