Math for Grownups (4 page)

Sure, your teacher may have been getting her jollies by insisting that the units matter. (Can’t you just hear her maniacal laughter?) But in the real world, if you’re not paying attention to your units, you could make a costly mistake.

Let’s say you want to compare the powdered lemonade with the stuff premade in the bottle. The powdered drink is measured in grams, but the liquid is measured in ounces. You need to compare like units (grams and grams or ounces and ounces), so what you really need to know is this: How many ounces does the powdered drink make?

Even if the items are packaged in the same units, you may need to be careful.

Take orange juice, for example. You can buy it as a concentrate or already mixed up and ready to go. The units represent different things, though. That’s because you’re probably not going to drink the concentrate without adding water. You’ll get a much more accurate comparison if you consider how much juice the juice concentrate makes.

Here’s how that works: Let’s say that the can of juice concentrate contains 12 ounces. If the directions say to add 3 cans of water to the juice concentrate, you’re adding 12 ounces • 3 or 36 ounces of water. But there’s one more thing to consider: You already have 12 ounces of concentrate. So when you mix the juice, you’ll end up with 12 ounces + 36 ounces or 48 ounces of juice. And that’s what you should use to find your price per unit.

This means you may need to look a little closer at the product label—to avoid comparing lemonade to lemons.

In your dreams, it’s the perfect match. You want to save big bucks on groceries, diapers, electronics, even a pretty fountain for the backyard. Your friendly warehouse club offers bulk packaging and, they say, rock-bottom prices.

All you have to do is fork over $50 for an annual membership and figure out where to store those 144 rolls of toilet paper.

But is warehouse shopping a good deal? The truthful answer is yes—and no. Buying in bulk won’t necessarily save you a dime. Let’s look.

Anabel is considering joining a warehouse club. She’s sick and tired of going to the grocery store once a week. Besides, with her husband’s compulsion to add to his DVD collection, they could save big on movies. And who knows, maybe she can pick out a nice piece of jewelry for him to give her for Valentine’s Day. Would joining the club be a good idea?

She’s able to check out the prices online, so she makes up a quick list of items that she buys regularly. She works out the per-unit price, just so she can compare apples to apples (so to speak).

Freezer storage bags at the warehouse store are $33.88 per 250 bags, at a price per bag of 14¢. At the local store, they cost $3.49 for 30 bags, at a price per bag of 12¢. Continuing in this way, Anabel assembles the following information:

At the warehouse club, she’d come out on top buying soup, soy milk, and bread. But the coffee and freezer bags are less expensive at her regular grocery store. Judging on the basis of this list, how much would she be saving at the warehouse store?

First, Anabel adds up the prices per unit at the warehouse store. Then she does the same for the grocery store. Finally, she subtracts to find the savings.

14¢
+
37¢
+
6¢
+
4¢
+
8¢
=
69¢ (warehouse store)

12¢
+
33¢
+
12¢
+
6¢
+
12¢
=
75¢ (local store)

75¢
-
69¢
=
6¢ (difference between local store
cost and warehouse store cost)

On these items, using the price per unit, she’ll save 6¢.

It might be helpful to think of this in terms of a percent savings, but how does she figure that out? Consider this: Anabel is saving 6¢ for every 75¢ she would have spent at the grocery store. In other words, she’s saving 6¢ per 75¢, right? And what does
per
mean? Divide.

6¢ / 75¢
=
0.08, or 8%

Based on these items only, Anabel can realize an 8% savings. If she can generalize that savings to her entire grocery list, how much can she save over a year?

Anabel knows she spends about $7,800 each year on groceries, so she takes 8% of $7,800. (But first she needs to convert the percent to a decimal.)

8% of $7,800

0.08•7,800

$624

$624 a year is not chump change.

There’s more to consider, of course. Anabel and her hubby are in the market for some big-ticket items. Accordingly, she makes another list and does the research.

Turns out that she can save on all of these items—sometimes a lot! But how much? As before, Anabel adds up the prices of the items and then subtracts to find out:

$499 (treadmill)
+
$195.52 (vacuum)
+
$599 (laptop)
=
$1,293.52

$899
+
$241.52
+
$630
=
$1,770.52

$1,770.52
-
$1,293.52
=
$477

Holy tightwad! She can stash a cool $477 by buying these items at the warehouse club. Added to the $624 she could save each year on her weekly shopping, Anabel can put away $1,101 just by shopping at the warehouse store.

But Anabel also has a $50 membership fee. When she subtracts that cost from her savings, she gets $1,051. The warehouse is still a great deal.

Just don’t tell her hubby. He might think they should celebrate with some new DVDs.

Predicting what you can save over the next year is a bit like developing a weather report. You might have some good models and some past data to base your forecast on, but in the end, just about anything can happen.

So if you’re looking for a sure thing, look elsewhere.

Let’s say you’ve estimated that you will save $300 a year by brewing your morning cup of joe instead of buying it on the way to work. But so many things can affect those savings. If you have to replace your $200 coffee maker, you’ve seriously eaten into your surplus. And if the coffee shop introduces a club card that can save you big bucks, you might just be better off stopping there in the
A.M.

And then there is the value of your time. You can calculate this using your hourly salary, or you can use your own logic. Does it take you 3 hours a week to save $15 clipping coupons and researching grocery sales? If your hourly salary is $35, the savings may not be worth it.

Then again, they may be.

If the premium ice cream tastes better than the store brand—and you can afford the difference—buy the premium. If you have a coupon for a large pizza, but you only need a medium, there’s no rule that says you can’t buy the medium at full price.

Math can be flexible and useful. But it won’t tell you what you
must
do. That’s because math is both a tool and a language. It facilitates a process and explains why something works.

So calculate your little butt off. Just remember that
you
—not the numbers on the page—make the final decisions.

At the Dealership: Leasing vs. Buying, New vs. Used— You Do the Math

Is that cloud of black smoke from your exhaust pipe starting to gag pedestrians? Are you tired of borrowing your brother’s beat-up truck to haul your yard-sale treasures home? Did you take an office job, after working from your living room couch for years, and now you have a commute to deal with?

You might just have to visit your friendly car dealership for a new set of wheels.

If the mere mention of this causes heart palpitations, you’re not alone. Dealers have a bad reputation for tricking buyers into getting behind the wheel of a vehicle they can’t afford. And whether or not this stereotype is true, understanding car-buying math will make you feel more confident about driving a new
or
used car off the lot.

Think the sticker price is what you’ll pay for a new vehicle? Think again. You might be able to negotiate a better deal, but even then, you’ll probably have a few additional costs to take into account.

Leather seats, a built-in GPS, or top-of-the-line treads may jack up the cost. These are called options, and they’re seldom included in the sticker price of the car.

Then there’s the destination fee. This may seem like a bogus charge, but it’s actually legit. When a dealership orders a new car from the automaker, it doesn’t suddenly appear on the lot by some kind of Harry Potter magic. Nope, the automaker must get your new car from their factory to the dealership—without putting any miles on it. Dealerships pass that cost on to you, generally to the tune of a few hundred dollars.

Even if you’re shopping at Uncle Alvin’s Used Car Extravaganza, there’s another thing to consider. Unless you live in Alaska, Delaware, Montana, New Hampshire, or Oregon, you’ll need to pay sales tax.

Sales tax is calculated as a percent of the price of the item. And when you purchase a car, it’s not like you’re picking up a magazine at the airport. The bigger the cost of the item being taxed, the higher the taxes you’ll pay. That’s why sales tax is a figure worth knowing before you sign on the dotted line.

And there’s one more thing to keep in mind: the title and licensing fee. The title proves that you own the vehicle. Paying the licensing fee gives you permission to drive it on public roads. These fees are imposed by the state, so there’s no getting around them. And a dealer will usually pass them on to you.

There’s no way to predict the title and licensing fee exactly, but you can bet that it’ll be between 1% and 1.5% of the cost of the vehicle. The good news (such as it is) is that you don’t need to pay taxes on this fee.

How does this all work together? Meet Bubba.

Bubba is ready to go off-road riding, but he has one problem—no truck. So he and his brother Larry are cruising the lot at Nevada Ned’s Monster Trucks, looking for a good deal on a great vehicle.

That’s where Bubba spies the most gorgeous four-wheel-drive pickup on the planet: fire engine red, an extended cab for his dog, Lady Bird, and a navigation system (so there’s no repeat of that bad scene with Larry and Lady Bird last year in the Nevada desert).

The base price is $38,020, without the navigation system. Here are the options:

The sticker also lists an $875 destination charge.

Bubba decides he’d like the navigation system and the bigger engine, but none of the other options. Because he’s buying the truck in Nevada, he’ll pay a sales tax equal to 6.85% of the purchase price. What’s the total price of the truck he wants to buy?

First, Bubba needs to find out how much the options will cost. For the options he wants, he’ll spend:

$2,430
+
$3,000
=
$5,430

Now he needs to add the cost of the options to the base price of the truck, plus the destination charge:

$38,020
+
$5,430
+
$875
=
$44,325