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Unless your last name is Trump or you were recently the last “Survivor” in Somoa, you’ll probably need a mortgage to purchase a home. Not many folks can afford to pay cash for a more than $100,000 purchase. But to get a mortgage, you have to prove that you can actually pay it off. And that means your lender will be looking at something called DTI or debt to income ratio.

Fortunately, this little calculation is pretty darned simple. Let’s see if you can figure it out on your own with these questions:

1.  What is your debt?

2. What is your income?

3. What is a ratio?

Of course, there are many ways to describe your debt (housing, housing + other debts) and many ways to describe your income (gross yearly, take-home monthly). But ratio? That’s simple.

A ratio is a way to compare two numbers, either by using a colon or a fraction. In this case, we’re looking for a number, so we’ll write the debt to income ratio as a fraction and then divide. But how do you know which is the numerator and which is the denominator?

Turns out that’s pretty simple, too. Look at the order: debt comes first, so it will be in the numerator; income comes second, so it will be the denominator. If you think of “to” as the fraction bar (or as division), this makes sense.

debt to income =

[pmath size=12]debt/income[/pmath]

You can’t get much easier than division, especially if you can use a calculator. But in order to divide, you need to define your variables. In other words, you need to know what “debt” means and what “income” means.

In this situation, income is your monthly gross income. If you get a weekly paycheck, you’ll have to multiply that amount by four. If you paid twice each month, multiply by two. And if you get paid once each month, you don’t have to do a thing.

The debt can be calculated one of two ways. Some lenders only want to know what your expected housing debt is. This amount will include your monthly mortgage payment, insurance and taxes But these days, lenders are looking at your entire debt, which also includes monthly payments for child support, student loans, car loans  and minimum credit card payments — plus your expected housing debt. (You don’t need to include regular monthly bills like energy and childcare costs.)

Let’s say your monthly gross income is $3,027. You’ve figured out that you can afford an $890-per-month housing payment (to include mortgage, insurance and taxes). In addition, you have the following regular monthly debts: minimum monthly credit card payments ($35), student loan payments ($150) and car payment ($300). What is your debt-to-income ratio?

Method One: Simply divide your expected monthly housing expenses by your monthly gross income.

890 ÷ 3027 = 0.29

So using the first method, your debt-to-income ratio is 29%.

Method Two: Add all of your monthly debts and then divide by your gross income.

890 + 35 + 150 + 300 = 1375

1375 ÷ 3027 = 0.45

Looking at all of your monthly debt payments, your debt-to-income ratio is 45%.

But what does this mean? In short, these numbers spell danger. Anyone with a 40-49% DTI is not doing well financially. (Over 50% is considered “living dangerously.“) Most lenders like to see no more than 28% of your monthly debt going to housing costs (mortgage, insurance and taxes), and no more than 36% DTI over all.

If the above scenario were real, it’s very likely you would not be offered a mortgage. (And if you were, run in the other direction. You probably don’t want that kind of debt.) The goal, of course, is to get your DTI as close to 0% as possible. But anything below 28% for housing only and 36% for all debt is within reason.

What’s your DTI? Are you surprised by this amount? How can you reduce it? Feel free to respond in the comments section.

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.)

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!

When we moved to Baltimore almost seven years ago, my family and I found amazing friends in our next-door neighbor Stephen Sattler and his partner Neil. So, it is really no surprise that Stephen has now found his calling as a Realtor, working primarily with relocation. Here’s how Stephen uses math in his work.

Can you explain what you do for a living?

Basically, I help my clients find shelter–which includes the buying, renting, selling, and ferreting out of places to live, after listening and then understanding what they’re trying to tell me.

When do you use basic math in your job?

The whole idea of proration is key to the real estate industry.  At the settlement table, the property’s monthly taxes, utilities, interest, and other financial considerations must be equitably split between both buyer and seller, as of that date.  The same thing holds true if you’re renting a house, especially if you’re beginning your term in the middle of a month.  Leases typically call for a yearly total of rent due, which means you just multiply the monthly rent by twelve. But calculating the first month’s rent can be tricky if you don’t know how to calculate the daily rate.  It sounds complicated, but all you have to do is divide the yearly rent by 365. Then you can multiply that by the days left in the month.

Stephen Sattler

Do you use any technology to help with this math?

I do have a fancy real estate calculator that helps with the more complex things like finding a monthly amortization amount at a given interest rate over a set period of time, but for the most part I hand-calculate the math I tend to use from day to day.

How do you think math helps you do your job better?

I wouldn’t really have a job unless I could apply math at its most basic levels:  settlement costs are a typically a set percentage of the sales price, prorated bills are due as of the date the property is transferred, and my income is always a percentage of the total sales price–which can change at each and every transaction.  I feel like I’m always taking quick, armchair calculations to figure out where things generally stand at the end of any given week.

How comfortable with math do you feel?  

I was one of those students in school who tended to excel more in the creative arts–writing, languages, history, and the like.   I have horrible memories of feeling I was the last person in math or science class to even generally grasp the problem being discussed, from algebra to geometry to even basic chemistry.  I don’t think I ever quite figured out how to balance a chemistry equation!

I turned 50 this year, which meant I could finally let go of what hasn’t worked for me in the past.  With GMATs and all the other truly stressful mathematical events I’ve had in my life, I was convinced that my brain just wasn’t wired the right way, or that I even had some sort of math disability.  Put me in a job I absolutely love, however, and help me see how math can help my clients find and then settle into the home of their dreams, and I’m astonished at how mathematically competent I now feel!

What kind of math did you take in high school?  Did you like it/feel like you were good at it?

I took everything mathematical a good properly-educated, college-bound boy was supposed to take, but my God was it absolute torture.  There were so many rules to understand and follow, and you couldn’t really reason or write your way out of a problem–like you could in an essay question in, say, English class–unless you knew how to manipulate the underlying mathematical formulae (which of course my feeble brain could barely even understand let alone memorize and apply).  It also didn’t help that all the math teachers at my school seemed to double as coaches for various sports teams in their after-school lives, and using the same motivational threats they used on the field (Yo–  what the &*^%$ were you #@!) thinking!) didn’t quite have the same result in the classroom with those of us who were not quite as macho about math.

Did you have to learn new skills in order to do the math you use in your job?

Actually, successfully using math as much as I do now in my everyday job has finally helped me feel I’m not the complete and utter dolt I always thought I was when it came to dealing with figures.

Do you have questions for Stephen about the math of real estate? Please ask them in the comments section. He can responded there or I’ll write another post addressing more complex issues.