Updated on 03.31.10

# Mental Math and Good Spending Choices

Earlier today, I linked to an article at Free Money Finance that included a quote from Mary Hunt:

Get into the habit of quickly calculating the annualized cost of things and you’ll achieve an effective way to get mindless spending under control.

I can see how a tip like that could be useful, but I’m really awful at mental math and it seems unreasonable to futz around with a calcluator to do the math. How do you do this kind of math?

First of all, I’ll admit that I’m good at mental math. It was something I practiced a lot when I was very young and I can still do things like add a series of numbers or multiply two multi-digit numbers in my head. Thus, I usually do the math in a strange fashion in my head that really is hard to explain or make rational to others.

Instead, I asked a few people on Facebook and Twitter how they did this kind of math and they all responded with more or less the same technique.

First, they figured up how much a week of such purchases costs. If you do this thing once a week, it’s easy. If you do it more than once, double it or triple it – whatever’s appropriate. If you’re unsure about the pennies, round to the nearest dollar. So, if you get a coffee and a bagel for \$5.46 three times a week, round the amount to the nearest dollar (down to \$5) and multiply that amount by three, giving you \$15.

Next, add two zeros on the end. That’s easy enough. If your current amount is \$15, your new number is \$1,500.

Finally, divide that number in half. If you can’t do it quickly, feel free to adjust the number from the second step. So, for example, if you have a hard time dividing \$1,500 in half (it’s \$750), just add \$1 to the original \$15 and divide that resulting number in half – \$1,600 divided in half is \$800. I suggest adjusting up if you rounded down in step one or adjusting down if you rounded up in step one.

That’s it – you have a very quick thumbnail of how much this expense costs you over the course of a year.

What if the expense is monthly? Slap a zero on the end and you’re getting close, but it’s a bit higher than that, too.

The thing to keep in mind is that this is a rough estimation, just to let you know the approximate amount you’ll be spending on this routine if you keep it up. Being able to come up with a rough estimate quickly is key. This way, you can do the math in your head while standing in line, giving you time to rethink the whole thing.

What’s the real benefit for doing this? If you do this type of calculation, you can quickly put your impulse spending in context. \$750 a year spent on bagels and coffee could be half of an extra house payment. Paying off the house sooner makes it easier and more attainable for you to jump into the career you’ve been dreaming of for years. It might also open the door to having a child sooner than you think.

If you decide to go ahead with the purchase after doing this calculation and weighing the options, that’s great – you’ve weighed the options and chosen the option that provides the most value to you. However, denying yourself that opportunity often puts a big restriction on your big dreams.

Yep, a bit of mental math can make all the difference.

1. jim says:

If you’re serious about getting your finances in order, then messing with a calculator shouldn’t be something that gets in your way. Using tricks to approximate is good, but the key is doing it. If you’re going to let the use of a calculator or lack of math practice be your crutch, then you have bigger problems.

2. Chapeau says:

One of my favorite bits of mental math is “how many hours do I have to work to pay for this?” I have a second job. After taxes, I earn about \$7/hour at that job. So your bagel and coffee would “cost” me about 45 minutes at the second job. So not worth it. I’d much rather be out digging in the yard. That snack/piece of clothing/pair of shoes is a lot less desirable if I know it’s going to cost me 2 Saturdays doing what I enjoy.
That math, since it’s a job I don’t really love, earning just above minimum wage, is also more convincing than the math with the full-time job. If I only have to work 15 minutes to buy something, it’s not quite as undesirable. But it still works. Telling my husband that the “great buy” he found will mean I’m away from home for 2 more nights a week really puts it in perspective for him (and me).
On the other hand, don’t do the math to figure out how many hours you’ll have to work for something you just bought. Do it before you buy.

3. Nicole says:

Nice!

I like leaving 20% tips because there’s fewer math steps involved. (Just have to chop off 2 zeros and multiply by two rather than chopping off the two zeroes, remembering that number, dividing it by two and adding to the number you remembered). I like lazy mental math.

Chapeau– since the 2nd job is your marginal job, you’re actually doing the economically “right” calculation. A lot of people use their average wage to do these, but if you only make \$7 for each additional hour, that’s the marginal wage, which is the right comparison.

I never did understand the people who spent money on the overpriced vending machines or fastfood during break at the minimum wage job I had in high school– that was like a full hour of work going down the drain.

4. David says:

Suggest always rounding up rather than down to nearest dollar. If you round down \$5.46 * 3 and call it \$15 a week, \$750 a year, you are deluding yourself because the true figure is \$851.76 annually. Of course, even if you round up and call it \$16 a week, \$800 a year, you are still underestimating, because \$5.46 * 3 is \$16.38, not \$16, and there are 52 weeks in a year, not 50. But perhaps you don’t buy coffee and bagels on your annual vacation.

Another compelling argument in favour of rounding up, not down, is that prices almost invariably go up, not down. Furthermore, if you get into the habit of rounding up then you increase your chance of ending the year under budget, not over it.

Numbers in this post calculated in my head. If they are wrong, go ahead and embarrass me.

5. Jeannette says:

Chapeau,
You bring up one of the most viable methods to really understand what something “costs” on a visceral (as well as financial) level.

If more of us actually computed, as you advised– before buying, what something costs us in terms of time, etc. we’d probably spend a lot less.

Instead, I think a lot more folks rationalize the cost of something by how much “pleasure” or usage they’ll get out of something. Sometimes, that is truly a legit way to evaluate cost. Sometimes, not so much.

It’s a lot easier to say “no” to purchases when you are say, saving up so you can leave a lousy job…but often people overspend when they are miserable, rather than belt tightening so they might be able to take a less lucrative but less soul-leeching job.

It reminds me of people who have high-income jobs but travel all the time and are away from their families and very isolated and disconnected. Their families may have lots of nice stuff, but most kids would rather have their parents around and actively present in their lives. Same for a partner/spouse.

6. Ruby Leigh says:

Hi – I will be printing this article for an Extra Credit assignment in my Math Class. I teach Basic Math to adults. I hope that’s okay with you.

7. et says:

And be sure your base price estimate includes tax and the tip where applicable. I’ve gotten caught too many times at the end of a vacation needing more cash than estimated because I didn’t include the added tips. Rounding up more generously would also cover some of the added maintenance/ care/utility costs on certain purchases.

8. Corey says:

@Nicole (#3), you said: “I like leaving 20% tips because there’s fewer math steps involved. (Just have to chop off 2 zeros and multiply by two….)”

Well, I hope you really only chop of one zero. Otherwise, there are probably a lot of waiters and waitresses out there who were not too pleased with their 2% tips. ;)

9. Nicole says:

Corey yeah yeah.

In my defense, I was chopping off two zeroes off of numbers in the CPS while I was writing that post (since they report hourly wage without the decimal)… but yes. Good catch. Just keeping you on your toes. ;)

10. Bill says:

I try to think of the cost of something in before tax dollars. In the 25% tax bracket, I need to earn \$1.33 for every dollar I spend. So I need to earn \$2.00 to buy a \$1.50 coke from the machine. However I need to earn \$667 to buy a \$500 laptop.

11. Jules says:

This is what summers spent adding 4236 + 8972 and multiplying and long division lead up to: doing quick mental math.

12. I think that’s an even quicker process than mine. I usually mulitply times four for the monthly amount, then multiply times ten and times two and add those together for the annual amount.

Getting proficient in at least a little “mental math” goes a long way to understanding your finances in the “big picture”.

13. J says:

The “annualized cost” is something I especially like to apply to things with contracts or monthly fees. Like cell phones with data plans. I just can’t justify the \$800-1000 per year on that.

14. Moby Homemaker says:

Really good post!!!
I get a rounded monthly figure…then multiply by 12–to get the annual expense.
I’m sure there’s an easier and better way–but it seems to work for me.