The Math of Ten Bucks

(or how to tell the difference between frugality and being cheap)

I got into a debate with a Republic Wireless customer recently. I know, people are sick of me talking about them; but this isn’t a post about Republic, it’s a post about math. Specifically, it’s a post about math defending why you should spend a little time learning about your communications technology, being willing to pay for what you actually need, and choosing the Cheap and Good options from the modified Engineer’s Iron Triangle instead of Cheap and Easy, especially when we’re talking about recurring monthly costs. We shall do this by simply examining the math behind $10.

By: frankieleon
By: frankieleon

Why examine ten dollars? Well, the math is relatively easier to understand. It’s also a common threshold amount for a lot of people to defend poor service choices as it’s “cheap enough” to not care if it’s good. This latter defense for putting up with low quality services really deserves closer examination to see how true it really is.

For the sake of argument and to keep things simple, we’re going to pretend that inflation doesn’t exist with this math. We’re also going to paint in very broad, average statistical strokes for US citizens primarily (that is the majority audience for this site) using the slightly dated but still seemingly reasonably accurate median annual individual income from the 2003 US Census Bureau study ($32,140), the average number of hours worked by individuals per year in the US according to FRED in 2011 (1703.55 hours), the average number of hours worked per week according to the Bureau of Labor Statistics in 2012 (34.5 hours), the average paid tax rate of an individual’s income from a 2010 Tax Foundation study (11.81%), and the average life expectancy of US Citizens from the 2013 WHO study (79 years). Hope you don’t mind.

The Math

Let’s extrapolate some raw numbers first:

$32,140 – 11.81% = $28,344.27 annual take-home pay after taxes per person
$28,334.27 ÷ 1,703.55 = $16.64 an hour take-home pay after taxes per person
$16.64 ÷ 60 minutes = 28¢ a minute take-home pay after taxes per person
$10 ÷ 28¢ = 36 minutes of labor to earn ten bucks after taxes

Okay, we’ve now established that $10 is equivalent to 36 minutes of labor for the average American, give or take.

Now, let’s say our hypothetical John Doe is 30 years old, he wants cell phone service, he thinks $10 a month is a good deal, and we’ll pretend that there’s no additional taxes on that cost. Let’s first examine the math of what it will take to pay for that $10 service for the rest of his life.

79 years – 30 years = 49 years = 588 months = $5,880 paid in cellphone bills until he dies. Now, let’s find out how much of John’s remaining work life will be needed to pay for this cheap, $10/month cellphone.

$5880 × 36 minutes ÷ 10 = 21,168 minutes = 352.8 hours
352.8 hours ÷ 34.5 hours worked a week = 10.226 work weeks

That’s right, it will take 30 year old John over ten weeks of his work life just to pay for this “cheap” $10 recurring cost for the rest of his living days.

It certainly gives that little portrait of Alexander Hamilton a bit more weight, doesn’t it? On the flip side, let’s pretend he’s not actually living hand-to-mouth and look at it from a financial investment standpoint as John saves and invests his unspent money every month and gets a modest and safe 4% annual return on his investments across the rest of his life.

$10 × 12 months = $120 year
$120 ÷ 4% SWR = $3,000 of permanently invested money
3000 × 36 minutes ÷ 10 = 10,800 minutes = 180 hours
180 hours ÷ 34.5 hours worked a week = 5.217 work weeks

Old John there still has to work over five weeks to save up enough money to let his investments work for him to pay for his phone service for the rest of his living days. This bit of math shows the power of saving your money and investing, but when you think about a $10 recurring monthly cost, don’t think of it as ten bucks… in John’s case, he should be thinking about that money spent as representing somewhere between five and ten weeks of his life.

The Rationale

Now that we know what that recurring $10 subscription represents in the bigger picture, ask yourself these questions:

What if this $10/month service was buggy, had problems, and didn’t reliably provide the very services you’re paying for, and have decided you either need or want as a desired quality of life thing?

What if this service had terrible or non-existent customer support and you constantly had to fiddle with it and pester other people because it was a closed system with glitchy software?

What if there were alternatives that didn’t have these problems that cost the same amount or just a little more, and it only took you a couple hours of your life up front to learn how to comparison shop, configure, and continually find and use these other options for the rest of your life for this trouble-free service?

Would you tolerate anything less than simple, trouble free usage from anything you’re paying for with five weeks or more of your work life that you will never get back?

I wouldn’t.

Given the average going rate per 1GB of mobile data is around $10 per month as well, the “math of ten bucks” argument can easily be extended towards the cost and usage of mobile data as well.

Anyway, this is what separates the frugal from the cheap. If anyone says $10/month is their threshold for “good enough” to tolerate ongoing problems and shortcomings of a service, they either don’t actually need the service they’re paying for or they don’t sufficiently respect their own time and resources.

So ask yourself, do you want to be frugal or cheap?

Leave a Comment