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 =

debt/income

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.

The post Can You Afford a Mortgage? Debt to income ratio appeared first on Math for Grownups.

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.

The post Spring into Good Personal Finance Habits appeared first on Math for Grownups.

Today, I’m guest posting at Tinfoil Tiara on the CantonRep.com.

It’s not likely that our nation’s poor math skills caused the housing crisis or the Great Recession, but it’s likely being confident in math can help you stay out of debt and put more money in the bank.

Every day, I meet people who tell me that they’re no good at math.   That’s an understandable sentiment, given the way math is taught. But the cold, hard truth is you have to do math.

Read the rest of my post here.

The post Check and Double Check: Math can help keep your personal finances in order appeared first on Math for Grownups.

Even better is monitoring this savings along the line. Knowing what you should have already stashed away at age 30 or 40 or 50 can help you stay on track. If you’re behind, you can ratchet up your savings. If you’re way ahead, you can plan to quit your career a little earlier (or just bask in the really soft cushion you’ve created). Keeping an eye on these benchmarks helps you create a better plan.

But these calculations will naturally include a variety of assumptions — from how much you’re putting away in savings to the interest rates or return on investments. There’s no good way to really predict these, but retirement ratios have gotten pretty good reviews from some financial experts.

Retirement Ratios

Charles Farrell (not the silent film star) of Northstar Investment Advisors created a set of multipliers, outlined in his book, Your Money Ratios, that make it really simple to estimate these benchmarks. (In this case, multipliers are merely numbers that you multiply by. In essence they’re parts of proportions.) Like my suggestion to have several goals, Farrell developed bronze, silver and gold standards. (Bronze is 70% of income, retiring at 70 years old; silver is 70% of income, retiring at 65 years old; and gold is 80% of income, retiring at 65 years old.) His website and book detail these standards and benchmarks in really handy tables.

Basically, Farrell offers multipliers for each standard and each age. Pull the multiplier from the table, multiply it by your salary and — viola! — you have easily calculated a good estimate for how much you should have already saved by that age and for that standard.

Let’s look a simple example: retiring at age 70, with 70% of your income. And let’s say you earn $50,000 a year.  Here are four multipliers from Farrell’s tables: 30 years old at 0.45, 40 years old at 1.6, 50 years old at 3.5, 60 years old at 6.5 and 70 at 10.

30 years old: $50,000 • 0.45 = $22,500

40 years old: $50,000 • 1.6 = $80,000

50 years old: $50,000 • 3.5 = $175,000

60 years old: $50,000 • 6.5 = $325,000

70 years old: $50,000 •10 = $500,000

It’s not at all clear how Farrell came to these multipliers. (And I’m certain, like KFC’s secret recipe, he’s going to keep much of that to himself.) But, mathematically speaking, there’s something interesting to notice here. Your benchmarks are 10 years apart, but the difference between each goal is not a constant number. In other words, the difference between each consecutive year is not the same number.

Why is that? Well, if you think of the graph of compound interest, you’ll come to the answer quickly. Because compound interest is a curve, it increases quickly. This is a great thing when you’re dealing with savings. (It’s not so good with credit.) And if you look at the difference between each benchmark, you’ll see that over time, you’re retirement investments and savings are increasing by more and more.

And this should make perfect sense, if you look at the multipliers. These are not increasing in a constant way, either.

1.6 – 0.45 = 1.15

3.5 – 1.6 = 1.9

6.5 – 3.5 = 3

10 – 6.5 = 3.5

Each difference is slightly larger as you go up in age. If you were to graph the age and multiplier (or even product) on a coordinate plane (x-y axis), you’d have a curve.

The bottom line is this — as you age, you want your nest egg to increase exponentially, rather than linearly. In other words, you want your total to increase quickly, so that you can reach your retirement goals before you’re too old to take advantage of them.

What do you think of this process? How would having these benchmarks help you monitor your retirement savings more closely? Do you think it would be helpful to use these multipliers in your planning? Share your responses in the comments section.

The post Benchmark Your Retirement Savings appeared first on Math for Grownups.

But what does that mean? How much will I need to squirrel away for my golden years? Turns out the experts offer some advice.

First off, you won’t need 100% of your salary when you retire. Depending on their situations, most retirees live on between 70% and 80% of their pre-retirement incomes. Once you decide on that percentage, you can easily calculate the amount you’ll need to have on hand when you retire.

(Editor’s note: A reader let me know that it’s unclear what I mean by savings. For our purposes here, I’m discounting Social Security and pensions, since most of us don’t have pensions and there’s no guarantee that Social Security will still be around. At the same time, I am including investments like IRAs and 401K plans. These have largely replaced pension plans and are the most often recommended ways to save for retirement. Now back to our regularly scheduled program.)

Let’s say that you earn an even $50,000 each year. You’re a conservative sort, who figures that having 80% of that each year is a better cushion. Find 80% of $50,000 to find your annual retirement income. (In case you’ve forgotten, of means multiplication in this situation. So you’ll need to multiply 80% — or 0.8 — by $50,000 to get your final answer. Using a calculator works just fine.)

80% of $50,000

0.8 • 50,000 = 40,000

In this scenario, you’re shooting for $40,000 in the bank for every year you are retired. And that’s where the tricky part comes in. There’s no way to know for sure how many years of retirement you’ll actually have. People are living longer, which is one reason that the actual retirement age is creeping up.

But let’s assume that you are expecting the average 20-year retirement. (That sounds heavenly!) The rest of the math is incredibly simple. Just multiply the annual retirement income by the number of years:

$40,000 • 20 = $800,000

Yep. You read that right. With a modest $50,000 annual income, it’s reasonable to expect you’ll need $800,000 in the bank before you can spend your days volunteering at the hospital gift shop or planting daisies. (This is why most folks can’t afford to retire.)

So with just these simple calculations, let’s play with the numbers. What if you reduce the percent to 70% and keep the retirement time the same?

0.7 • 50,000 = $35,000

$35,000 • 20 = $700,000

What about keeping the percent the same and reducing the retirement time to 15 years?

0.8 • 50,000 = $40,000

$40,000 • 15 = $600,000

Let’s try one more idea: reducing both the percent and retirement time.

0.7 • 50,000 = $35,000

$35,000 • 15 = $525,000

This exercise isn’t really a waste of time. (I promise.) With these four figures, you have several goals to shoot for — lowest, middle and highest goal. (Of course, having even more than $1.2 million is just fine.) And with those three goals comes more flexibility in your savings options. If you shoot for 70% of your pre-retirement income and plan to spend 15 years in retirement, you’ll need $525,000 in savings. If you shoot for 80% and 15 years, you’ll need $600,000. At 70% and 30 years, you’ll need $700,000, and at 80% and 30 years, you’ll need a cool $800,000.

Of course deciding where to invest or save your hard earned cash is a whole ‘nother ball of wax. But knowing what you’re shooting for is a great start. Otherwise, you could miss the retirement boat completely.

Come back on Friday to get the scoop on benchmarking your retirement savings. In order to meet your goals, how much should you already have in savings at 30 years old? 40 years old? We’ll check the math.

Were you surprised to see these figures? Where they higher than expected or lower? Share your thoughts in the comments section.

The post Saving for Retirement: How Much? When? appeared first on Math for Grownups.

You probably know that simple interest is, well, simple. That’s because it’s linear. (Stay with me here. I promise it’s not too hard.) In other words, simple interest can be described as a line. Now in mathematics, lines are very specific things. They go on forever, for one thing. For another, they’re straight. So while I might casually use the word “line” to describe a squiggly while I’m doodling, that’s a huge no-no in math. Among the Pythagorii and Sir Isaac Newtons, there’s no such thing as a “straight line.” By definition, a line is straight, not curved.

Because simple interest is linear, it increases (and decreases) steadily. Remember graphing linear equations? Take a look:

The graph above is an example of simple interest. As time goes on (or as you look to the right on the “time” axis), the money, $, increases. And it increases very steadily. If you can remember back to your algebra class, you know that each point on this line is found by taking the same steps — x number of “steps” to the right and y number of “steps” up. This is consistent. In other words, you don’t take 2 steps to the right and 1 step up and then 2 steps to the right and 4 steps down. (If you were really paying attention in algebra class, you might remember that this is a way of describing slope, which indicates the steepness of the line.)

Now curves are different. And, yep, you guessed it, compound interest is a curve. Here’s a general example:

If you looked at three points on this graph, you would find that the way to get from the first to the second to the third is not a consistent series of steps. There would be a pattern, yes, but it wouldn’t be the same each time. This is what we call a non-linear equation, because, well, it’s not linear. (Duh.)

But what can these graphs tell us? It’s not as hard as you might think. Take a look at the graphs themselves. As time increases, so does the money, right? (In other words, as you move to the right along “time” the graph moves up along “$.”) But with the curve, the $ gets bigger faster. It takes less time for the money to increase along the curve than it does along the line. (Follow me? If not, take a closer look at the graphs.)

That’s because of one simple fact: with compound interest, the interest is accrued on the principal (or original amount) and the interest. Each time the interest is calculated, the interest from the previous time period is added to the amount. On the other hand, with simple interest, the interest is accrued on the principal alone. That translates to a steady increase over time, rather than a sharp increase, like with the curve.

So what does this matter? Well, it depends on whether your spending or saving. Since with compound interest, the amount accrues faster over time, this is a good thing for savings or investments — but a bad thing for credit. And it’s the other way around for simple interest.

(Of course that is all moot, since unless you’re borrowing from good old dad, simple interest is pretty hard to come by.)

The point is this: if you can remember that simple interest is a line and compound interest is a curve, you will likely remember how simple and compound interest are figured — slow and steady or speedy quick.

Do you have questions about compound or simple interest? Is there another way that you remember the difference? Share your ideas in the comments section.

The post Real Savings Has Curves: The difference between simple and compound interest appeared first on Math for Grownups.

For the first time in my life, I’ve hired a business coach. With her help, I’m streamlining my schedule and processes — looking for ways to work smarter, so that I can work less. As a result, I’m on a real savings tear in all aspects of my life — looking to spend less money and carve out more time.

And math has helped. Between considering whether to invest in new accounting software to actively assessing my weekly hours, I’m doing the calculations that help me make these decisions. Especially in this economy, I know that I’m not alone. We’re all looking for ways to cut down on our monthly bills and put more away in savings.

For the month of October, we’ll consider many aspects of savings — money, time, energy, even lives — and how math plays a role. We’ll find intuitive ways to squirrel away these important resources, just in time for a long winter, when we can sit back with a great book and enjoy the fruits (or nuts) of our planning and hard work.

Got questions or suggestions? Please share them in the comments section!

The post Squirreling Away for Winter: Saving with math appeared first on Math for Grownups.

You probably find it pretty darned easy to encourage literacy.  In fact, there are countless magazine articles and books and workshops out there on this very subject.  And so all good parents read to their kids every night, play word games with them, give them magnetic letters for the fridge.

But what about math?  If you’re like most parents, the idea of working math into the day probably seems down right daunting.  Scary even.

It’s not as hard as you think, especially if you’re willing to give into your children’s demands for a regular allowance.  Money is an instant math lesson—and can motivate even the most reluctant student (adult or child).

Here’s how:

The Even Split: If you want to use allowance to encourage savings and charitable giving, you’re at least half way there.  One way to do this is to require kids to split their allowance into three equal accounts: spending, saving and giving.  If your five year old gets $3 per week, $1 goes in each pot.  But what about the kid who gets $6 a week?  Or worse, $10 a week?  Pose these questions, and let your child figure it out.

The lesson: Factoring and division

Percent, Per Week: For a more complex math problem, consider uneven distributions, say 20% spending, 20% giving and 60% saving.  Or encourage your child to put aside a certain percent of savings for a particular goal, like a new iPod.  Or enforce a different distribution around the holidays, when she buys gifts for her friends.  If she can’t do the math, she doesn’t get paid!

The lesson: Percents

Accounting for Savings: If you have a little investor on your hands—and some of us do—show him how to create a simple register for recording his savings and spending.  He’ll get a first-hand look at how his stash can grow (or shrink).

The lesson: Addition and subtraction

Project Savings: Your child will inevitably want something she can’t afford.  In that situation, help her figure out when she’ll have enough money in savings.  Can she wait that long?  If not, consider giving her a loan, with interest and a regular payment plan.  Show her how the interest is calculated and even help her figure out the total interest on the loan.

The lesson: Using formulas and problem solving

Math may be hard for you, but with a little bit of creativity allowance can help your kids practice their skills—and become a little more savvy with their own money.  Now all you have to do is remember your kids’ payday.

How have you used allowance as an impromptu (or regular) math lesson? Share your stories in the comments section.Save

The post The Arithmetic of Allowance appeared first on Math for Grownups.

First off, here’s the problem that we considered on facebook last week:2 • 3 + 2 • 5 – 2 = ?The answer choices were 38 and 14.I would say that the responses split pretty evenly. Lots of folks chose the incorrect answer first and then realized their mistakes.

So what’s the correct answer? 14. Why? Because of the order of operations. A lot of us learned the order of operations — or the set of rules that establishes the order we add, subtract, multiply, divide, etc. — with a simple mnemonic:Please Excuse My Dear Aunt SallyORParentheses, Exponents, Multiplication, Division, Addition, SubtractionORPEMDAS

(Before going further, I must acknowledge that there are some problems with this approach. First off, it doesn’t really matter if you add before your subtract or multiply before you divide. Those operations can be done in either order with no problem. Second, many teachers are approaching this differently, a topic that I’ll explore in September.)

If you do the operations in the wrong order — add before you multiply, for example — you’ll get the wrong answer. And that’s how people got 38, instead of 14. They simply did the math from left to right, without regard to the operations.CORRECT2 • 3 + 2 • 5 – 2 = ?6 + 2 • 5 – 2 = ?6 + 10 – 2 = ?16 – 2 = 14INCORRECT2 • 3 + 2 • 5 – 2 = ?6 + 2 • 5 – 2 = ?8 • 5 – 2 = ?40 – 2 = 38

All of this is well and good, but what does it have to do with the real world? How often are you faced with finding an answer to a problem like the one above? And that’s exactly what one reader asked me. So I promised to explain things using a real-world problem.

Thing is, you do these kinds of problems all day long, without even thinking of the order of operations. And that’s because you’re not writing out equations to solve problems. You’re simply using good old common sense.

Let’s say you’re going back-to-school shopping with your child. He’s chosen a pair of pants that are $15 and five uniform shirts that cost $12 each. But the pants are $5 off. What’s the total (without tax)?

You probably won’t write an equation out for this, right? (I wouldn’t.) Instead, you’d probably just do the math in your head or scribble some of the calculations on a scrap piece of paper or use your calculator. So here goes:

First the shirts: there are five of them at $12 each. That’s a total of $60, because 5 • 12 is 60.

Now for the pants: all you need to do here is subtract: 15 – 5 = 10. The pants total $10.

Finally, add the cost of the pants and the cost of the shirts: $10 + $60 = $70.

The above should have been super easy for most of us. And — surprise! surprise! — it used the order of operations. Here’s how:15 – 5 + 5 • 12 = ?The order of operations says you must multiply before you can add:

15 – 5 + 60 = ?

Then you can add and subtract:

10 + 60 = 70

There are other ways to set up this equation. In fact, I would use parentheses, simply because I want to keep the pants’ and shirts’ calculations separate in my mind:

(15 – 5) + (5 • 10) = ?

The result is the same, because the process follows the order of operations — do what’s inside the parentheses first and then add.

UPDATE: A reader asked if I’d also show how this problem can be done wrong. So here goes! When you do the operations in the wrong order, you won’t get $70.15 – 5 + 5 • 12 = ?10 + 5 • 12 = ?

15 • 12 = 180

That’s more than twice as much as the actual total!

Try this with your kid. You can make it more complex by figuring out the tax. And there are lots of different settings in which this works — from shopping to figuring the tip in a restaurant and then splitting the tab to dividing up plants in the garden.  Just about any complex math problem that involves different operations requires PEMDAS. And that’s something all kids need to know about.

When have you used PEMDAS in your everyday life? Did this example spark some ideas? Think about the math that you did yesterday — or today — and share your examples in the comments section.

*Have you liked the Math for Grownups facebook page yet? What’s stopping you? We’re having great conversations about the math in our everyday lives. And I ask questions of my dear readers. Come answer them!

The post Back-to-School Shopping: Applying the order of operations appeared first on Math for Grownups.

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.

The post Good Debt, Bad Debt appeared first on Math for Grownups.