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!