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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.

Over the last three years, there has been no bigger news story than personal finance. And for good reason. Most economists agree that our home-buying habits (fueled by dangerous lending practices) contributed to the Great Recession. Plus, most Americans were completely caught off guard by our plummeting economy — left without adequate savings when we needed it the most.

Sadly, some things haven’t changed much. Take a look at these scary statistics:

— Forty percent of Americans say they are saving less this year than they did last year, and 39 percent say they have no retirement savings (Harris Interactive).

— But according to the same survey, 28 percent say they are spending more this year than they did last.

— The U.S. student loan debt is now \$870 billion (with a b), according to the Federal Reserve Bank of New York, and it is expected to reach \$1 trillion (with a t) very soon. This is way, way more than the country’s credit card debt and auto loan debt.

— Harris Interactive reports that 56 percent of all American households have no personal finance budget.

Last month was Math Appreciation Month — and it was also Financial Literacy Month. We couldn’t celebrate both at the same time, so May will be devoted to the math behind personal finance here are Math for Grownups.

Financial literacy has a lot in common with math. For many folks, the concepts are scary and somewhat mysterious. And in my experience there are many, many personal finance experts who prescribe a right and wrong way to approach money management. This month, I’ll take a look at both of these things.

We’ll consider the math behind budgets, credit card payments and savings. I’ll show you a few quick ways to estimate your financial health, and we’ll explore how you can apply your own methods to reaching financial stability (or teaching your kids the benefits of financial responsibility). Experts, including a mortgage broker, financial planner and more, will share how they use math in their jobs and even how you can harness your math know-how and become a better steward of your money. We’ll also look at lots of statistics. (What does the reduction in home values actually mean?)

Meanwhile, if you have questions about this subject you’d like to ask, share them in the comments section. I’ll be drawing up a plan for the month, and I’d love to hear what you think!

Buckle up — this is math everyone can use.

I’ve hit the age when many of my friends and colleagues are managing the realities of having aging parents. Luckily, I’m not there yet — my mom is still very active, both physically and mentally. But many of us in our 40s or 50s are probably at least thinking about how we might manage our parent(s) affairs if/when they are unable to handle things on their own.

My friend and fellow writer, Beth, faced this problem last year, when she, her husband and her mother moved to another state. Beth’s mother needed a little more supervision, and so Beth and her husband arranged for her to live with them. That brought up some emotional and practical questions, which Beth shared in an online writing’s group that we both belong to. She gave me permission to share them here:

Mom lived independently until we combined households. She wants to pay us a monthly fee that covers “room and board.” The question is: How to figure a fair and reasonable amount.

It’s been a long time since [my husband] and I had a roommate. In those days, we simply divided the big stuff by three (rent, utilities, cable), and each person was responsible for his/her own food. That doesn’t seem fair in the current situation for a variety of reasons (not the least of which we’re talking about my MOM, not some friend).

I feel I’m making this unnecessarily complicated. Can anyone help me sort this out? I bring it up because Mom talks about it constantly. She seems to feel the amount she’s paying is too low, and I keep putting the brakes on changing the dollar figure until we have better data about our expenses.

Naturally, I think math can help us find some simple solutions to emotional problems. So I offered this:

I have a really easy and non-biased way to look at this. Calculate your total household costs — mortgage, utilities, food, etc. Then divide this by three. Each of these is a share.

Next, you can decide how many shares each person should have. For example, your mom may have only a half-share, based on what you think she can afford or how much she eats, etc. Take half of a share, and that’s her monthly rent.

Naturally, I like taking a mathematical approach, because it can help reduce the emotions. And if any of the variables go up or down — utilities, for example — you can adjust the rent really easily.

And that seemed to do the trick for Beth. In fact, she took things even farther, considering fair market value, as suggested by another group member:

Here’s how we solved the problem in the end:

1. I drew up Mom’s current monthly budget.

2. I drew up a list of household expenses that apply to her (including the mortgage payment). I didn’t include things like pet expenses or [my husband’s] fuel for commuting, obviously, because those are our sole expenses.

3. I used Laura’s methodology to divvy up the total household expenses into three full shares. Then I calculated partial shares: 3/4, 2/3, and 1/2.

4. I used [another member’s] data about the fair market value of a studio apartment in [my county] for comparison purposes.

5. Then I sat down with Mom and first explained her current budget. Next, I went over the household expenses.

6. I told her about the fair market value of a studio apartment and explained how that related to our attempt to determine what was a fair amount for her to pay us each month.

7. I showed her the share information.

8. I showed her how each share amount would affect her net income. Even at a “full share,” she still retains about 45% of her net income for “mad money,” and that’s without touching any investments. (I didn’t point that out to her, in terms of trying to steer her. I think what I wrote kind of reads that way. I just used a calculator to show her what each share amount would leave her, in terms of disposable income.)

9. I had written all these figures down on paper, so I stepped away to giver her time to peruse the numbers for awhile and consider what SHE wanted to do.

10. After a few minutes, she called me back and said she’d decided to pay a full share. She’s the type of person who likes to “pay her own way,” and she’ll still have plenty of mad money left over. She also was very happy she wouldn’t need to dip into any investments.

It’s important to note that this cut-and-dry approach didn’t erase all of the feelings in Beth’s situation. She was very nervous talking to her mother, and her mother felt responsible for paying a full share. See? Feelings.

Another interesting aspect is how flexible this process can be. With some simple parameters — the value of a full share vs. a half-share, for example — Beth’s family can alter the process depending on where everyone is financially. And if her mother needs more resources or Medicare helps to pay for things, the entire formula can be changed.

Just a bit of math helped Beth gain some perspective and offer her mother tremendous autonomy. The process also set them up to avoid conflict later on. Nice work, math!

Photo Credit: VinothChandar via Compfight cc

I’m currently reading The Organized Mind, by Daniel Levitin, and I can’t wait to share a review with you when I finish. He offers some really terrific math to help when medical decisions are tough. Four-square decision tables anyone?

What do you think of the process Beth worked out? (I also offer this approach as a way to divvy up the cost of a beach house among several family members.) Have you used math to help you come to a difficult or emotional decision? Do you think this approach would work for a young adult who hasn’t flown the nest? Share your stories in the comment section.

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!