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Math of Homebuying: Three easy rules for budgeting

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!

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In Math at Work Monday

Math at Work Monday: Stephen the Realtor

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.

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In Home

Pretty as a Picture: Using math to hang your art

Today, I bring you an excerpt from my book, Math for Grownups.  Enjoy!  (Now you have your weekend project planned for you.)

Hanging pictures can be a tricky business. If you’re not careful, your foyer can look like a hall of mirrors—with crooked photos of your wedding party alongside drawings that your kid made in kindergarten. Not to mention the holes in the drywall from when you realized that you hung your college diploma so high up the wall that only a giant could read it.

Not exactly the look you were going for?

You may not want to face it, but a tape measure, pencil, and yes, even a level, are your best buddies in home decorating. And hanging anything on your walls is no exception. Let’s look at this in a bit more detail.

Mimsy Mimsiton is thrilled to have finally received the oil portrait of her dear Mr. Cuddles, a teacup poodle who is set to inherit her large fortune. The painting will look fabulous above the marble fireplace in the west-wing lounge of her mansion.

But drat! The museum curator Mimsy has on retainer is in Paris, looking for additions to Mimsy’s collection of French landscapes. (She’s redoing the upstairs powder room and wants just the right Monet to round out the décor.)

But the painting must be hung before Mr. Cuddles’s birthday party. His little poodle friends would be so disappointed not to see it! There’s no way around it; Mimsy’s poor, overworked House Manager must hang the painting herself.

Luckily, House Manager is no stranger to the DIY trend, and Butler will be there to help. The two meet in the lounge, where the painting has already been delivered—along with a stepladder, a tape measure, and a pencil. Once House Manager marks the spot, Handy Man will come along to safely secure the painting to the wall.

House Manager and Butler get to work. First they measure the painting: With the gilded frame, it’s 54″ tall and 60″ wide.

Next, they turn their attention to the space above the mantle. House Manager climbs atop the ladder, while Butler holds it steady. From the ceiling to the top of the mantle is 84″.  The width of the mantle is 75″.

Climbing down from the ladder, House Manager notes that the painting will certainly fit in the space allotted. She knows from experience that it is to be centered over the mantle. However, Mimsy will have a fit if the painting is centered vertically—between the ceiling and the mantle. No, the bottom of the painting must be exactly 12″ above the mantle.

So how high should Handy Man install the picture hanger?

To find out, House Manager must add 12″ to 54″ (the height of the painting). The top of the painting should be 66″ above the mantle.

House Manager grabs her tape measure again and removes the freshly sharpened pencil from behind her ear. Then she climbs the ladder. Starting at one end of the mantle, she measures 37½”—which is half the width of the mantle. She makes a barely visible pencil mark at that point.

Then from there, she measures up the wall to 64″. Again, she carefully makes a faint pencil mark.

If House Manager stopped here—leaving that small mark for Handy Man to hang the portrait—she’d probably be out of a job. That’s because she’s merely marked the top of the frame, not where the hanger should be secured.

She descends the ladder and goes back to the portrait. Turning it around, she notices the picture wire that has been stretched from one side to the other. She hooks her finger under the center of the wire and pulls up gently—creating an angle, as if the picture wire were hanging on a nail. Now an angle is a two-dimensional figure formed by two lines (called rays) that share a common point. Hereʼs an easier way to remember this: An angle looks like a V.

If she can measure the distance from the top of the frame to the vertex—the point where two sides of an angle meet—she’ll be in business.

There’s just one more thing to consider: Is the vertex of the angle too far to the left or too far to the right?  For the painting to hang straight and be centered on the mantle, the vertex must be located at exactly half the width of the portrait.

House Manager uses her tape measure to find the length of each leg of the angle. In other words, she measures the distance from one end of the picture wire to the vertex of the angle and then the distance from the vertex of the angle to the other end of the wire. If the vertex is centered properly, the legs of the angle will have the same length.

Moving her finger ever so slightly, House Manager centers the vertex of the wire angle—and measures from that point to the top of the picture frame: 9″.

She now can make the final mark for Handy Man. She climbs the ladder for the third time and measures 9″ from the mark she made earlier. Again, being very careful, she makes a tiny mark on the wall.

House Manager’s work is done. If anything goes wrong now, it’s Handy Man’s fault.

She folds up the ladder and gathers her supplies. Then she’s off to order beef cupcakes for Mr. Cuddles’s party.

Any questions?  Ask them in the comments section.

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