#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!

#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...)