I’m on vacation! (Can you tell?) So this week’s schedule is way off. But when I saw that Lee Doyle, owner of BTO Self Serve Yogurt in Colorado had sent along her Math at Work Monday responses, I decided to spend just a few moments during a delicious hotel breakfast of Cheerios and milk to post the interview. Then I’m back in the car, headed to Cincinnati to my cousin’s wedding.
There’s nothing better than a cool treat on a hot summer’s day, and since I was a little girl, the options have expanded exponentially. From popcicles to snowballs (a Maryland-only experience) to frozen yogurt — ice cream isn’t the only sweet, cold treat available. At the Doyle’s Highland Ranch location of BTO Self Serve Yogurt, you can create your own delicious treat. But first, the math:
Can you explain what you do for a living?
I am responsible for creating and making all the yogurt at the shop, buying ingredients for recipes and estimating useage of product and toppings weekly.
When do you use basic math in your job?
I use math all day, everyday. Since I create and follow recipes, I use addition, subtraction, liquid and dry measurements, fractions, estimation, equivalency charts multiplication, division, just about every kind of basic math you can think of. For example, if I am creating a new recipe, I use one cup of our basic yogurt and add a teaspoon or tablespoon of various flavors to come up with a new flavor I like. Then I have to write a recipe using a gallon of basic yogurt, because all our recipes are based on one fluid gallon.
Do you use any technology to help with this math?
When I shop for ingredients, I use a calculator constantly to determine price per ounce to be sure the ingredients are within our pricing guidelines.
How comfortable with math do you feel?
I always liked math and feel very comfortable using it. In high school, I took algebra, trigonometry and solids but did not take calculus.
Do you have questions for Lee and Jack? Ask them in the comments section. And of course stay cool with a sweet treat, like frozen yogurt.
I am not a particularly athletic or physically active person. If given a choice between a hike through the woods or a book and a hammock, the good read always wins out. I start and stop exercise routines at least once a year — usually more. But I do have a bicycle, and once a year, I sit atop that tiny seat and pedal my way through 14 miles of parks in Baltimore.
That was yesterday, and today I’m paying for it, big time. Not only do I have a funny-shaped sunburn on my back (from the one cool exercise shirt that I have), but my legs and feet and rear end are screaming: “What the hell??” Still, I know I’ll do this next year, too. Because it’s the one time a year that it’s worth hoisting three bikes on top of our car and driving 15 minutes away to explore the city parks.
Of course, I think about the math involved. Between birdwatching and listening to my almost 12-year-old complaining, what else is there to do? Here’s what I came up with.
1. I woke up yesterday morning with one thing on my mind: I do not want to spend all day on a bike. But would it be all day? Not likely. So I went to the interwebs to help me estimate the time I’d actually be cycling. Here’s what I found:
For the kind of biking I was about to do, an average speed is about 10 miles per hour. I didn’t even bother with a formula; this information was enough to help me estimate that I’d be pedaling for about 90 minutes or so. (I figured I’m slower than average, we’d have one 5-minute break, and we were biking 14 miles, not 10.)
How did I do with my estimate? Not bad. We pushed off at 9:00 a.m. and were munching hamburgers and hotdogs by 11:45 or so.
2. I once thought that the pedals and brakes and chain were the most important parts of the bike. But it turns out that the seat height has more to do with a comfortable ride than most anything else.
Last year, I spent the first half of the course on a seat that was way, way too low. My thighs were burning by the time we hit the rest spot. Luckily, there was a bike tech there who showed me how to adjust my seat and where. I thought I would fall off the precipitous height when he was done, but the rest of the ride was a breeze, comparatively speaking.
Here’s how it works: The leverage of your pedaling is controlled by the seat height. If your seat is too low, you’ll work way, way too hard to get up even the most modest hill. In other words, when your seat is adjusted properly, you’ll get the most efficient pedal stroke. (And your rectus femoris muscle will thank you.)
There are formulas and online calculators that can help you figure this out. But as a once-a-year biker, I rely on a simple idea. When sitting on my bike, I position my feet at 12:00 and 6:00. If my leg is completely extended in the 6:00 position, my seat is at the correct height.
There’s tons more math in cycling, I’m sure. But as a novice, these little calculations and estimates are enough for me. By next year, I’ll forget how sore I am today — and the trouble it is to get our bikes into the rack — and hit these trails again.
Are you a cycler? What math have you used to help keep your pedaling efficient or manage your rides? Share your ideas in the comments section.
Wait! Isn’t it Monday? Where is Math at Work Monday? It’ll be back, I promise. I had some scheduling problems with some sources, so you may see an interview later this week. Don’t worry!
Whether for graduation or summer camp or a great trip, a memory book or journal can be a nice way to remember a special time. And since I’m currently addicted to Pinterest, I’ve been browsing tutorials–from simple booklets to fancy, bound books. And then there are flower-pressing books and books constructed with homemade paper. The options are endless. (And they’re all so inspiring!)
From my days as my high school yearbook editor, I know that there’s a little formula used to find the number of pages that a book can have. If you need to have a certain number of pages (at least), you’ll need to employ that tidbit of information. But first you must know how many pages you’d like to have in your book.
Your teenager is headed off for a two-week long camp in the woods. She loves to write in a journal, and you’d like to make her a special book to take with her. If she uses three pages per entry, how many pages does her journal need to have?
Let’s assume she’ll be journaling every day of her two-week stay. And let’s assume that she’s leaving on the last day. So that means she’ll journal for a total of 13 days (that’s two weeks, minus one day), and she’ll need a total of 3 • 13 or 39 pages.
But here’s where you’ll need a little book-making insider information. Books are actually made up of signatures, which are sets of folded paper. You can put as many pieces of paper you want in a signature, and you can put as many signatures you want in a book — but the resulting page count will always be a multiple of 4.
(Don’t panic if you don’t remember what a multiple is. Look carefully at the word. You’ll probably notice that multiply is a root, which may cause you to think of multiplication. You’re on the right track. A multiple is a product of two numbers. So the multiples of 4 are: 4, 8, 12, 16, 20, etc. That’s because 4 • 1 = 4, 4 • 2 = 8, 4 • 3 = 12… well, you get the picture.)
In your book, the number of pages must be a multiple of 4, and you need at least 39 pages. Your first question: Can my book have exactly 39 pages? Nope. That’s because 39 is not a multiple of 4.
You need to find a number close to 39 that is a multiple of 4, and you have two obvious choices: 36 (4 • 9) and 40 (4 • 10). Of course, you’re going to chose 40; otherwise, your daughter won’t have enough pages in her book. (Better to have too many than not enough.)
Now you can decide how to create your signatures. I leave those details to the experts. Besides, you need to choose a book style first. Take a look at these great resources I found on Pinterest. Pick one, and have fun!
I grew up a few miles from the Appalachian Trail in Southwest Virginia and my grandparents lived in the Shenandoah Valley, near Big Meadows a popular stop-off for trail hikers. While I’ve never had any inclination to take the entire trail from Georgia to Maine, I have done a few tiny sections — an hour or two hike each.
It’s way too late in the year to start a thru-hike (doing the entire trail), but a section hike would be perfect for a lazy summer day. These are generally less than 5 miles, though you could string together two or more for a weekend adventure. And if you’re nowhere near the Appalachian Trail, just choose another trail to explore.
But how much time should you allot for your hike? This is an important consideration, since it will determine the time you set out (there are no lights on the trail, so once the sun sets, it’s black as pitch) and what you’ll need to bring (food and water are essentials if you’re planning to be gone more than an hour or so).
Experienced hikers can probably gauge how long it will take to hike a given number of miles. But if you’re like me, you don’t have a clue. That’s where pace counting comes in. The length of your stride will tell you how many steps it will take you to go a certain distance. From that, you can get a good estimate of how long it will take you to complete the hike.
To measure the length of your stride, you’ll need two pens, a tape measure and a long hallway or sidewalk. Place one pen at the end of the hallway or sidewalk and stand with your feet together and hells against the pen. Now, walk 10 steps, taking normal strides. After the tenth step, bring your feet together again, and place the second pen behind your heels. Measure the distance between the pens, using the tape measure. Then divide by 10 to find your stride length. Ta-da!
Another method is to estimate your stride based on your height. There’s a simple formula for this, but you’ll first need to have your height converted to centimeters. If you’re a man, multiply your height (in cm) by 0.415; women will multiply by 0.413.
Once you have your stride length, you can use this to estimate the number of strides you’ll take when hiking a particular distance. Let’s say your stride is 28 inches long, and you’re hiking the Chestnut Knobsection in Virginia, which is 2.6 miles round trip. How many steps will you take in that hike?
Ultimately, you’re going to divide the total hike by the length of each stride. But that means you need to have these measurements in the same unit. In other words, you need to convert 2.6 miles to inches. There are 63,360 inches in a mile, so the entire hike is 2.6 • 63,360 or 164,736 inches. Now divide, to find the total number of strides:
164,736 ÷ 28 = 5,883
So on this hike, you’ll be taking a total of 5,883 strides. Still, you don’t know how long the hike will take you, right?
For that step, you need to know how long it takes you to walk a certain number of strides. Let’s go back to the where you found your stride length. If you timed how long it takes you to walk 10 paces, you can easily find the time, right? All you need to do then is use a stopwatch while you take 10 paces. Let’s say that value is 6 seconds. A little bit of math will get you closer to your answer.
First, divide the total paces by 10. Why? Because your time is based on 10 paces, not one.
5,883 ÷ 10 = 588.3
Now multiply this answer by 6 or the number of seconds it takes to walk 10 strides.
588.3 • 6 = 3,529.8
So, it will take you 3,529.8 seconds to hike this section of the trail. It’s probably easier to understand, if you convert this to minutes or hours.
3,529.8 ÷ 60 = 58.83 minutes or just under an hour
Of course this estimate assumes a lot of things: that the terrain is easy to maneuver and that you’re not going to stop to look at the view of Burkes Garden. In other words, you can bet that you’ll be on the trail for longer than an hour, especially if you’re there to metaphorically or literally smell the flowers.
Still, you can use these calculations to estimate the time it will take you to complete any number of hikes. Once you know your stride length and the time it takes for you to walk 10 paces, the math is pretty simple.
What kind of hiking do you love to do? How have you used math to help you plan a hike or other outdoor activity? Share your stories in the comments section.
Whether a day or sleep-away, camp is a perineal part of summer for many families. So today, I introduce you to Joelle Kelenson, Director of School Age Programming for the Jewish Community Center of Northern Virginia. She uses math, and she doesn’t even run a math camp!
Can you explain what you do for a living?
During the school year I am in charge of managing the before and after school program at the Jewish Community Center of Northern Virginia. The program encompasses 150 children and 30 part-time teenage and college staff. I am responsible for ensuring that our program is up to the health and safety standards of our license, that the children get a healthy snack, training the staff to ensure the well being of all children, that all supplies are purchased, and that all information is communicated with parents. During the summer I switch hats and become the assistant camp director. I develop programming and curriculum for our summer camp, supervise the units heads and specialists and ensure that camp is running smoothly.
When do you use basic math in your job?
I use very basic math in my job like counting how many children are in a room to ensure proper ratios. I also use math to add up staff hours for payroll. In addition I manage a budget of $160,000 so I need to use math to make sure I’m on top it and know where I’m at spending wise.
Do you use any technology to help with this math?
I use a calculator to do my payroll and a formulated Excel spreadsheet to help me manage my budget. I’m also not very good at math so I often use my fingers to count. 🙂
How do you think math helps you do your job better?
If I didn’t use math in my job, my program wouldn’t be up par, we would run a defict and our staff would probably get paid more than they actually worked. Math helps me stay on top of things and manage things.
How comfortable with math do you feel?
Over time I’ve gotten better and more comfortable using math. Most of my math is basic, it was the math of managing the budget that at first made me nervous, but now I’m getting better with it.
What kind of math did you take in high school?
I grew up in Montreal and took advanced math called 436 and 536 in my junior and senior year. I was never good at math. It didn’t come naturally to me and I hated it, but I worked hard and did well in the classes — except that midway through my senior year, I gave up and barely passed my senior math class. As a result I was forced to drop out of the sciences like physics and chemistry and take more social science classes.
Did you have to learn new skills in order to do the math you use in your job?
I did not need to learn anything new but rather refresh myself on the basics. I did however learn the benefits the Excel formulas and how they are helpful!
Thanks, Joelle, for being our Math at Work Monday interview today. If you have questions for Joelle, ask them in the comments section. I’ll make sure she sees them and has a chance to respond.
I grew up in the 70s and 80s with teacher parents and in a small town that I could roam pretty much at will. Summer was both amazing and boring. School was out, and I could stay up late (at least until the sun set). These were the months when we traveled — sometimes on a big trip, but always for a week to Virginia Beach, where we would rent a big house with all of my cousins, and I would get brown as a berry. I remember riding my purple bike with the banana seat and long handlebar streamers. Or spending my days at the pool and nights at the local movie theatre. Instead of canned green beans or tomatoes, we’d have at least three sides of fresh vegetables every night at dinner, and I could pick the raspberries in my yard as I mowed the lawn.
Life was slow and easy in the summer. And that’s exactly what I strive for now. I’m not as tolerant of the heat as I once was, but I’d much rather be barefoot and sleeping with the overhead fan on high. I try to knock off of work a little early each day, and I visit the farmer’s market every single Saturday morning.
So even though it’s not officially summer yet, June is dedicated to the math of summer. I promise not to sap all of the fun out of the most relaxing month of the year, but I will point out the math that is around you — from the vegetable garden to the pool, and from bike riding to watching the temperatures rise. In Math at Work Mondays, you’ll meet summer camp coordinators, a summer sweets maker, a pool manager and more.
A note about kids and math over the summer: I know that some parents worry about their kids losing math skills while on vacation. While this month’s content can certainly be used to keep kids engaged with the math side of their brains, I’ll devote all of August to this important task. And you can always visit me at Mom’s Homeroom, sponsored by Kellog’s Frosted Mini-Wheats on MSN.com, for great advice. (More articles and Q&As are coming soon!)
I hope you’ll join me in exploring the math of summer. If you have questions you’d like to see answered or themes that you’d like me to explore, please drop me a line or comment below. I’m always looking for great ideas to explore.
Meanwhile, enjoy the warmer months. Let’s dive into summer!
Today, I welcome Annie Logue, a terrific writer who specializes in business and economics. When she offered to write a guest post about the difference between good and bad debt (with a particular emphasis on student loans), I jumped at the opportunity. We decided that she would write the first half, and I would do the math at the end. If you have questions, she’ll come back and chime in.
Annie Logue
Economists recognize that debt can be good. It smoothes out consumption over a lifecycle, they say; if most people had to save up enough money to buy a house, for example, they would never be able to do it. By taking on mortgage payments while they are working, people can buy a house, live in it, and then pay it off before retirement so that they can live rent-free then. By taking on debt, people have the use of a house while they are paying for it and after it is paid for.
Good debt, then, lets you enjoy the benefits of something before, during, and after the time that you pay for it. It gives you a long-term economic benefit, such as a place to live for the rest of your life.
By contrast, if you run up your credit card to buy a new outfit for a fancy party that you only wear two or three times, and then make the minimum payment on your card, you have bad debt. You took on debt for something that you could enjoy for only a short time – not during or after the years it takes to pay it off. The faster you pay this off, the better!
Student loan debt is usually thought of as good debt: you borrow money to get an education, which is a good thing, and it increases your lifetime earnings power. You can enjoy real personal and economic benefits before, during, and after you pay the debt off.
However, with the rising price of college, the shift in funding toward student loans, and the ongoing recession, many people are asking if college is still enough of a benefit to make the debt worthwhile.
The short answer is yes; the long answer is yes, but.
Georgetown University’s Center on Education and the Workforce has done extensive work on this issue. What they have found is that the degree matters; people with a bachelor’s degree, on average, make $2,268,000 over a lifetime, while those with a high-school diploma earn, on average, $1,304,000. However, occupation also matters, and many people earn more money than people who have a higher level of education. Someone with a Masters in English Literature is unlikely to earn as much over a lifetime as a police officer or a fire fighter.
We’ve seen the same thing in the housing market, by the way; people who borrowed what they could afford for houses that they intended to live in for a long time aren’t feeling especially pinched by the recent big drop in real estate prices. People who stretched and hoped to flip at a big profit have been suffering mightily.
It’s fine to borrow money for college, but those who do should be practical about it. They need to think about whether they are using that education to enter a field that is likely to make the debt pay off.
Doing the Math
What will a student loan cost in all? To assess whether even good debt will be a good idea, it can be helpful to consider the total cost of the loan and then compare that cost to the average total earnings over a lifetime. Here’s how that can be done.
Chloe is planning to attend a four-year public university. She estimates her tuition, plus room and board to be $15,000 each year. She received a $10,000 scholarship, which will be divided throughout the four years. If she takes out a federal student loan to cover the rest of the costs, how much will her college education cost in all?
First off, she needs to figure out the amount she will borrow each year. Her scholarship is $2,500 each year ($10,000 ÷ 4 = $2,500), which means the annual total that she will borrow is $15,000 – $2,500 or $12,500. She plans to complete her degree in four years, so the total that she’ll borrow is $12,500 • 4 or $50,000.
Remember, this amount is only the principal, or the amount Chloe will borrow. More complex calculations are necessary to find the total amount of the loan, which depends on the interest rate and her monthly payment.
Chloe’s interest rate is 6.8%, and she’d like to pay off her loan in 20 years. Using an online calculator, she finds that her total loan will cost $91,600.68, with a $381.67 monthly payment.
But 20 years sounds like a very long time. What would she need to pay each month in order to pay off her student loan in 15 years? The online calculator spits out $443.84. By paying the loan off earlier, her total cost is only $79,891.81.
So for an extra $62.17 ($443.84 – $381.67) each month, she can save a total of $11,708.87 ($91,600.68 – $79,891.81) in interest over the life of her loan! But even with the second option, she’ll pay a total of $79,891.81 – $50,000 or $29,891.81 in interest.
So how does Chloe’s total student loan debt compare to the amount of money she’ll earn over a lifetime? Let’s take a look. With a college degree, she can expect to earn a total of $2,268,000. If she pays off her student loan in 15 years, she’ll have paid a total of $79,981.81. What percent of her total expected earnings went to her loans?
$79,981.81 ÷ $2,268,000 0.035 or 3.5%
Not a bad return on investment. The trick of course is to get a decent job after graduation and stay on top of those monthly payments.
When I started doing Math at Work Monday interviews, I thought of it as a little experiment. Would people I talk to actually recognize the math they do? Would they feel confident in their math skills? Would the the math they need to succeed in their careers get in the way? I had a theory: Most people don’t realize that they’re doing much of the math they need for an average day.
Now that I’ve got about a year of Math at Work Monday interviews under my belt, it’s a great time to take a closer look. Did my hypothesis stand up? Reading through these interviews again, I’ve noticed five interesting themes.
1. Everyone does math in their jobs. Okay, that’s a duh conclusion, right? But when you consider the number of school kids who ask, “When will I ever use this stuff?” it’s not necessarily a foregone conclusion. In other words, if kids think that by avoiding science, they’ll avoid math in their careers, they should think again.
Kiki Weingarten, a NYC-based executive, corporate and career coach uses math to help her clients understand the financial implications of a career change. Criminal profiler Mary Ellen O’Toole looked for patterns and used statistical analysis to help solve crimes.
2. Many folks don’t know that they’re doing so much math — until someone asks them about it. This has come up over and over again. I’ll ask someone to do a Math at Work Monday interview with me, and they’ll say, “Why would you want to talk to me? I don’t use math in my job.” But once they think about it — even a little — many of them are surprised by the sheer number of numbers in their jobs. From managing their business to practicing their passion, math is everywhere.
Painter Samantha Hand said that she didn’t realize how much math she uses, until we talked about it — then she started making big connections, including using proportions to help paint to scale. When I asked my sister, Melissa Zacharias to participate, she first said that she didn’t really use math. She soon discovered plenty of places that math is useful in her job as a speech therapist who works with adults.
3. Math is particularly prevalent in the visual arts. So much for the myth that people are either artistic or mathematically minded! In fact, math is required in a variety of different aspects of art, from working with materials to managing sales to envisioning the final design. That’s one of the reasons that I devoted an entire month to math in the arts. (And we didn’t even scratch the surface!)
From noted jewelry artist Shana Kroiz to glass artists Ursula Marcum and Beth Perkins, it became clear that the connection between math and art is undeniable. Even museum curator Ann Shafer uses math.
4. Using math tools is fine, but many people depend on their brains. I expected people to tell me that they depended heavily on computers or calculators to do the math they needed. But most folks admitted that they do a heck of a lot of mental math — from basic addition to finding percents.
Kim Hooper uses a calculator to check some figures, but as a copywriter, she also does “margin math,” a grownup version of showing her work. Executive vice president, Gina Foringer uses mental math to quote labor percents for new contracting jobs.
5. People generally like the math they do at work. Of course they don’t always think of the math they do as math (see #2), but the folks I interview feel confident in the skills they need to perform their jobs well. This includes those who say they didn’t do well in school math classes or that they feel like they’ve never really “gotten it.”
Costume designer, Katie Curry says that she doesn’t feel comfortable with math outside of the calculations she needs to draft a creative design (though she can balance her checkbook, of course). When hair stylist Nikki Verdecchia opened her salon a few years ago, she worried that the math would get in her way, but she quickly became comfortable with the calculations she needs to make her business work.
So there you have it — the unscientific results of my unscientific experiment. As I suspected, people don’t mind doing the math in their jobs, and that’s because they don’t even realize that they’re doing math. We’ll see if that trend continues in the upcoming year of Math at Work Monday interviews.
What about you? Do you like the math that you do at work? Are you now realizing that there’s more math than you originally thought? Share your ideas in the comments section.
1. In the U.S. student loan debt is huge. Last year alone, students took out $117 billion in federal student loans. The Consumer Financial Protection Bureau estimates that the total U.S. debt has now exceeded $1 trillion. And this debit is not simply because new students are going to school. Nope, it’s also because folks with college degrees are behind in their loan payments, which increases the total interest costs. (The New York Federal Reserve estimates that 1 in 4 people with student loan debt is behind in their payments.)
2. The cost of a college education is rising fast. From the 1999 school year to the 2009 school year, tuition and room and board at public institutions rose 37% and at private insituations rose 25%(adjusting for inflation).
All of these statistics — and more — have some economists worrying that student loans are the new economic bubble. Like the tech and real estate bubbles, if this one bursts, the country could be in for another deep recession, this time with the federal government holding the bag.
So what the heck are colleges, parents and students doing to slow down this fast-moving train? Elgin Community College (ECC) in Elgin, IL is getting proactive, requiring financial aid counseling to students who are seeking federal student loans.
“The feedback has been positive,” says Amy Perrin, ECC’s director of financial aid and scholarships. “Students have expressed appreciation for educating them on the loan basics, budgeting, percentage interest rates and expected monthly payments.”
But student expectations are still a big issue. “We’ve had several students walk in with an inflated idea of what they ‘want’ to borrow — and walk out with a better understanding of what they ‘need’ to borrow,” Perrin says.
Student loans aren’t free money. And unlike other debts, these loans can follow a person forever, since they cannot be discharged in bankruptcy. It’s not just the math that trips students up.
“There seems to be a conflict between the Department of Education’s regulations and the student’s reality,” Perrin says. “The loan advising meeting covers many concepts, including creating a budget, interest rates, monthly payments, the student’s rights and responsibilities, and the consequences of default. After meeting with the staff, they should have a good understanding of the basic financial concepts of borrowing a student loan.”
So how can math help? A solid understanding of interest payments is critical here, and although there are online calculators that can help students estimate the total cost of these loans, students must have some basic math skills in order to use them. Perrin also suggests that parents and schools work harder at developing financial literacy skills.
“Parents can definitely play an important role in educating their children on basic financial concepts such as budgeting, how to open a checking account, why having a savings account is important and explaining ‘wants’ vs. ‘needs,’” she says. “Additionally, high schools should infuse financial literacy concepts into their classroom curriculum to further communicate the importance of wise financial decisions. High schools can partner with colleges to offer financial aid awareness events for parents and students.”
This student loan debt isn’t going anywhere any time soon. Unless we turn on our math brains and really deal with the numbers behind these scary statistics, our country could end up in another ugly economic place. Here’s hoping that other colleges require students to attend these programs–so that college degrees can actually mean something more than a monthly debt that must be paid off.
I’ll be the first to admit that my understanding of student loans is limited. So if you have questions, I completely understand! Post them here, and I’ll find the right expert to answer them.
Need to make a big purchase, like a house or a car? Take out a loan. Want to go to college? Take out a loan. Need to cover other expenses, like home renovations or an adoption? Take out a loan. Want to consolidate your debts? Take out a loan.
Loans are a fact of life in our country. They’re convenient and useful. They can also be really dangerous to financial health.
And the math behind loans can be pretty daunting (which is why there are some great loan calculatorsout there on the interwebs). That’s where a teeter-totter comes in. (Stay with me on this my literal friends; it’s a metaphor.)
A formula or equation is like a teeter-totter — that piece of playground equipment that requires one person on one side and another on the other side. (You may call it a see-saw, but I think teeter-totter is a funnier word.) If an adult sits on one side of the teeter-totter, while a child is on the other side, what happens? Unless the adult is really small or the child is really big, the child will be up in the air right? In other words, the teeter-totter will not be balanced.
That’s exactly how many mathematical formulas and equations work. If you have one large variable, the outcome will likely be larger. If one of your variables is reduced, the outcome will be smaller.
(Okay, so this really depends on the operations that you’re using, which is what some of you smarty-pants math readers have already noticed. Still the idea of balancing the equation holds.)
This means that simply thinking about math concepts that define these loans can help you make smart decisions. Here’s how — without any numbers at all!
Know thy variables
As with any math application, the variables matter — big time. These are the pieces of the problem that can change from situation to situation. (Yes, they’re the letters in a formula or algebra problem, but don’t let that scare you.) Because there are so many different kinds of loans out there, paying close attention to these variables is critical.
So what are they?
1. First off, there’s the principal or the total money borrowed. This amount completely depends on what you need the funds for. You might borrow $5,000 from your home’s equity to purchase new appliances for your kitchen. You might borrow $25,000 to start a graduate or undergraduate degree. Or you might take out a $250,000 mortgage to buy a new house.
2. Next comes the interest rate or the amount that you’ll be charged periodically for the privilege of borrowing the money. Sometimes, like with federal student loans, this rate is already set. But most of the time, you can shop around for the best interest rates.
3. Then there is the term of the loan or the amount of time you’ll have to pay it off. Again, this depends on the loan itself. You may choose a 10-year, 15-year or 30-year mortgage. Your car loan may be due in full by the end of three years.
How low can you go?
These variables matter, because they determine three things: how much you’ll be paying for the loan in all, how much your monthly payments will be and how long you’ll be paying off the loan.
For most situations, it’s a good idea to keep all of these variables as low as possible. The smaller the loan, the quicker you’ll pay it off. The lower the interest rate, the less you’ll pay in all, and the shorter the term, the less interest you’ll pay.
All of this works because of math. But this is one of those situations when understanding the concept behind the math is as useful as doing the calculation itself. If you can remember how formulas work (generally speaking), you can see why it’s important to keep the variables as small as possible.
— A large loan increases the total interest (not necessarily the interest rate) and time it takes to pay it off.
— A high interest rate increases the total interest paid.
— A longer term increases the total interest paid.
Balancing the teeter-totter
Here’s where the teeter-totter comes in. If you want to pay off the loan in a short period of time, your interest rate and/or your principal must be low. If you want to borrow a large sum of money, you’re term is probably going to be longer (unless, of course, you can make really large monthly payments).
In other words, whatever you do to one side of the teeter-totter will have an effect on the other side of the teeter-totter.
Pick and choose
But one or more of your variables may be set. For example, you won’t be able to negotiate a lower college tuition (unless you choose a different school), and if you are living on a fixed income, the monthly payment you can afford will likely dictate the term of your loan.
So that’s when you need to consider how to lower the other variable(s). This is where the math comes in. If your principal is constant, try to lower the interest rate or term. If your term is set in stone, look at borrowing less or shop for a lower interest rate. And if you can’t get a smaller interest rate, consider lowering your principal or shortening the term of your loan.
See? You don’t necessarily need to scribble down the math to have an idea of how to choose a good loan. Yes, you will need to do the math at some point. But considering the basic variables in a loan can put you on the right path for making good financial decisions.
Does the teeter-totter metaphor work for you? How can you see it in other math applications? Share your stories in the comments section! (And if you have questions about the math behind loans, ask those, too.)
Any college student who receives financial aid knows the drill. Folks in the financial aid office look carefully at many of the numbers that define a college student’s life — from income to GPA. Financial aid is reserved for those who need the funds the most and maintain good grades, while moving through a degree program in a reasonable amount of time.
Financial aid is also one big reason that some people are able to attend college — and ultimately land a good job in the hopes of remaining financially stable. Julia Dennis just left her job as a financial aid professional for a community college in North Carolina. She offered to share how she used math in her job.
Can you explain what you did for a living? I awarded financial aid (grants, loans, scholarships, and work study) to college students.
When did you use basic math in your job? Mostly adding and subtracting, but also some division and a small amount of multiplication. Here’s an example.
Students are federally required to maintain a 2.0 or higher cumulative GPA and at least a 67% cumulative completion rate. Being able to look at the number of completed versus attempted classes and know at a glance whether the student hit the 67% mark is decidedly helpful. (When it’s close, I always break out the calculator or adding machine to be certain.) The student also is required to complete their degree in 150% of the allotted time for their program. In other words, if their program is 100 credit hours, they have to complete their degree by the time they have finished attempting no more than 150 credit hours. Math is helpful for that as well.
Did you use any technology to help with this math? Some things I can do without it. For the numbers that look close, I always use a calculator or an adding machine.
How do you think math helped you do your job better? Sometimes students are right on the line. Being able to do the correct calculations to determine their eligibility for aid means the difference between that student going to school or not. In my job, the usefulness of math is a no-brainer.
How comfortable with math do you feel? I’ve always been comfortable with math. I scored higher on the math portion of the SAT than the English, which was weird because English was my favorite subject. I am one of those weird people who actually enjoys balancing the checkbook. I like the preciseness of it.
What kind of math did you take in high school? I took Algebra II, Geometry, Trigonometry and Pre-Calculus. I can’t say I loved it, but I did pretty well at it.
Did you have to learn new skills in order to do the math you used in your job? No new skills required. Most financial aid math involves things you learned in grade school.
Anything else you want to mention? If math is something you enjoy, then being a financial aid professional is something you might want to consider as a career. On the other hand, it’s important to be good with people too, since so much of being a Financial Aid Counselor or Director is having to give people bad news. You have to be prepared for lots of misplaced anger and a fair amount of stress and overtime.
Stay tuned for more details about financial aid math, along with repaying student loans!
If you’ve ever been in the market for a house, you know what the real estate agent asks first. It’s not the number of bedrooms or neighborhood or whether or not the home has a detached garage.
“What is your price range?”
Because whatever you have to spend will dictate the size of your house, where it is located and its amenities. Like it or not.
But how do you know how much you can spend?
Luckily, there are a few guidelines that can help you set this price before you even call on the agent. The following three rules use math to set your home-buying budget.
The Total Price Tag: Five times your annual gross salary
Remember how the diamond industry once told young men that an engagement ring should cost the equivalent of two months income? Of course that is simply a marketing plan. But there are similar and reliable guidelines for home buying.
These days, experts recommend spending no more than five times your gross salary on a home.* Let’s say that you gross $32,450 each year. Five times that is the most you should be spending on a house.
5 • $32,450 = $162,250
With that salary, you should spend no more than $162,250 on a home.
Of course the economy should be taken into consideration. If you’re concerned about losing your job, either purchase a much less expensive home or skip home buying until things get more stable. And if you have extra expenses, like college tuition or medical care for an ailing relative, put those in the mix as well. You might consider subtracting these large expenses from your gross salary, before multiplying by 5.
*It’s worth it to mention that the experts disagree on this multiplier: some suggest 1.5 times your gross salary, while others shoot for 2.5, 3 or 5 times. It’s always best to err on the side of caution, but any of these multipliers are much better than simply taking a wild guess.
Month to Month: A percent of your monthly income
Another way to consider this purchase is by looking at the monthly mortgage payment. (You may want to do both!) Financial planners advise homeowners to spend 28% to 33% of their monthly income on housing costs — that means rent or mortgage, and maintance.
It’s okay to look at a ball park figure here. Let’s say you bring home $1,995 each month. Using the percents above, you can reasonably spend 28% to 33% of this on housing.
0.28 • $1,995 = $558.60
0.33 • $1,995 = $658.35
So all things considered, you can budget between $558.60 and $658.35 each month on housing. (Your real estate agent can help you estimate your monthly mortgage payment, which will include taxes, interest and sometimes insurance.)
Maintain and Repair: A percent of the home’s value
But what about those maintenance and repair bills? Owning a house means fixing the furnace if it goes out, getting the gutters cleaned and repairing a leaky roof.
Lucky you: real estate experts have come up with another little guideline that will help you estimate these expenses. The cost of home maintenance can be estimated at 1% to 2% of the home’s valueeach year. Let’s say you are considering a home priced at $155,000.
0.01 • $155,000 = $1,550
0.02 • $155,000 = $3,100
Does this mean you will absolutely spend no more than $3,100 each year in home repairs? Nope. Some years you may not come close, and in other years, you may exceed this amount by thousands of dollars. And as the value of your home increases — as you hope it will! — the cost of repairs and maintenance will increase as well. Still this little benchmark can help you figure out if you can afford the home you have your eye on.
So there you have it. Three rules that can guide your home purchasing process. Do a little math, and you could make a very smart home purchase.
Do you have questions about these figures? Have you used these or similar guidelines in budgeting a home purchase? Post a comment!
