Photo courtesy of David Drexler

On Wednesday, I showed you how to calculate the amount of money you’ll need in retirement — based on a variety of variables, including your pre-retirement income, the percentage of that income that you can live on in retirement and the number of years you expect to be in retirement. I even suggested that you find three or four goals for this — low, middle and high amounts — so that you have some realistic flexibility.

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.

]]> http://www.mathforgrownups.com/benchmark-your-retirement-savings/feed/ 0 http://www.mathforgrownups.com/saving-for-retirement-how-much-when/ http://www.mathforgrownups.com/saving-for-retirement-how-much-when/#comments Wed, 10 Oct 2012 09:00:58 +0000 Laura http://www.mathforgrownups.com/?p=3177

Photo courtesy of Philip Taylor

With a presidential election comes big speeches about Social Security and Medicare. But if you’re a cynical 40-something (or younger) like me, you’re not planning on being able to depend on those programs being viable in 20 or more years. Nope, I figure my ability to retire will rest entirely on my shoulders.

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.

]]> http://www.mathforgrownups.com/saving-for-retirement-how-much-when/feed/ 0 http://www.mathforgrownups.com/good-debt-bad-debt/ http://www.mathforgrownups.com/good-debt-bad-debt/#comments Wed, 30 May 2012 09:00:34 +0000 Laura http://www.mathforgrownups.com/?p=2584

Photo courtesy of Omar Omar

Today, I welcome Annie Logue, a terrific writer who specializes in business and economics. When she offered to write a guest post about the difference between good and bad debt (with a particular emphasis on student loans), I jumped at the opportunity. We decided that she would write the first half, and I would do the math at the end. If you have questions, she’ll come back and chime in.

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.

Photo courtesy of Ha-Wee

How about these scary statistics:

1. In the U.S. student loan debt is huge. Last year alone, students took out $117 billion in federal student loans. The Consumer Financial Protection Bureau estimates that the total U.S. debt has now exceeded $1 trillion. And this debit is not simply because new students are going to school. Nope, it’s also because folks with college degrees are behind in their loan payments, which increases the total interest costs. (The New York Federal Reserve estimates that 1 in 4 people with student loan debt is behind in their payments.)

2. The cost of a college education is rising fast. From the 1999 school year to the 2009 school year, tuition and room and board at public institutions rose 37% and at private insituations rose 25% (adjusting for inflation).

All of these statistics — and more — have some economists worrying that student loans are the new economic bubble. Like the tech and real estate bubbles, if this one bursts, the country could be in for another deep recession, this time with the federal government holding the bag.

So what the heck are colleges, parents and students doing to slow down this fast-moving train? Elgin Community College (ECC) in Elgin, IL is getting proactive, requiring financial aid counseling to students who are seeking federal student loans.

“The feedback has been positive,” says Amy Perrin, ECC’s director of financial aid and scholarships. “Students have expressed appreciation for educating them on the loan basics, budgeting, percentage interest rates and expected monthly payments.”

But student expectations are still a big issue. “We’ve had several students walk in with an inflated idea of what they ‘want’ to borrow — and walk out with a better understanding of what they ‘need’ to borrow,” Perrin says.

Student loans aren’t free money. And unlike other debts, these loans can follow a person forever, since they cannot be discharged in bankruptcy. It’s not just the math that trips students up.

“There seems to be a conflict between the Department of Education’s regulations and the student’s reality,” Perrin says. “The loan advising meeting covers many concepts, including creating a budget, interest rates, monthly payments, the student’s rights and responsibilities, and the consequences of default. After meeting with the staff, they should have a good understanding of the basic financial concepts of borrowing a student loan.”

So how can math help? A solid understanding of interest payments is critical here, and although there are online calculators that can help students estimate the total cost of these loans, students must have some basic math skills in order to use them. Perrin also suggests that parents and schools work harder at developing financial literacy skills.

“Parents can definitely play an important role in educating their children on basic financial concepts such as budgeting, how to open a checking account, why having a savings account is important and explaining ‘wants’ vs. ‘needs,’” she says. “Additionally, high schools should infuse financial literacy concepts into their classroom curriculum to further communicate the importance of wise financial decisions. High schools can partner with colleges to offer financial aid awareness events for parents and students.”

This student loan debt isn’t going anywhere any time soon. Unless we turn on our math brains and really deal with the numbers behind these scary statistics, our country could end up in another ugly economic place. Here’s hoping that other colleges require students to attend these programs–so that college degrees can actually mean something more than a monthly debt that must be paid off.

I’ll be the first to admit that my understanding of student loans is limited. So if you have questions, I completely understand! Post them here, and I’ll find the right expert to answer them. 

Photo courtesy of Hiroh Satoh (cho45)

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 calculators out 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.)

Photo courtesy of LifeSupercharger

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! 

Photo courtesy of taxfix.co.uk

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 value each 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!

Photo courtesy of Diana Parkhouse

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.

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.

Photo courtesy of Håkan Dahlström

Earlier this week, we took a look at one of the big personal finance decisions out there–buying a car. But the price of the vehicle alone isn’t the only consideration. Unlike a blender or sofa, your shiny new mode of transportation will tap your budget year round. But by how much?

Generally speaking, car ownership involves four additional costs: fuel, maintenance, insurance and taxes. (Some states and municipalities don’t have a property tax on vehicles, so you might be off the hook for that last one.) Problem is, these costs aren’t like your mortgage or cable bill. They can be hard to predict and aren’t due at the same time each month.

So how can you plan for these? Well, just like any other irregular or unexpected costs, it’s a good idea to  put something away each month for car expenses. The trick is figuring out how much you’ll need. Let’s start by estimating the annual costs for each of these items.

Fill ‘er up

With gas prices rising and falling like the barometric pressure on a spring day, budgeting for fuel sure ain’t easy. But you can get a rough idea of what to expect, and then tweak that amount as the year goes on.

You’ll need to consider several variables for this one: the miles you travel in a given year, your vehicle’s miles per gallon, and the cost of gas where you live. This is going to be an estimate, of course. Unless you’ve got a wicked crystal ball, you won’t be able to predict any of this for sure–but you can get close.

If you’ve been keeping records of your miles traveled, you can take a look at the previous year to predict this number. Of course if you’re like me, those records don’t exist. So figure out a rough estimate based on your commute (if you have one), annual trips and even carpool. You should add on for errands and other around-town trips. For reference, the U.S. Department of Transportation estimates that on average, Americans drive 13,476 miles per year.

Now calculate the amount of gas you will likely consume. Let’s say your car gets 32 miles per gallon, and you expect to drive 14,500 miles this year. To find out how many gallons of gas you’ll use, divide:

14,500 ÷ 32 = 453.125 gallons

And the last part is simple: multiply this number by the cost of gas per gallon. In my area, we’re averaging about $3.85 per gallon, so for the sake of this example, let’s use that number.

453.125 • 3.85 = 1,744.53

The annual cost of gas for this fictional vehicle is estimated at $1,744.53.

Maintenance and Repairs

While maintenance can be pretty predictable, repairs are something that you can’t foresee–just like you didn’t see that light pole behind you in the Giant parking lot. But you can budget for these.

Again, if you keep good maintenance records, you can review these to see what you have paid in past years. Your mechanic may have these on file, as well. Remember, most maintenance is based on the number of miles driven, so if you add a long commute, you can expect these costs to rise. The kind of car you drive also matters. And of course, older cars will likely require more maintenance and repair.

If you haven’t tracked these expenses, you will probably have to make a good guess. Ask your dealer or mechanic about this. Or start with $2,000 per year and see what you have left over in December.

Whatever you do, don’t forget your Emergency Fund. This is where you’re big, unexpected repair costs will come from, like an accident that isn’t covered by insurance.

Speaking of Insurance

If you’re driving in the good old U. S. of A. and you don’t have “Farm Vehicle” stamped on the bumper of your truck, you will need to pay insurance. Again, this is a cost that depends on several variables, including your age, your driving record, and much more. But once you choose your insurance policy, that number will be set in stone, as long as you keep your driving record squeaky clean.

The Tax Man

Some states (and some municipalities) require personal property taxes on vehicles. Problem is, these payments are not usually monthly. Sometimes they are only charged annually, and in some places, residents pay these taxes quarterly.

To budget for taxes, take a look at what you paid last year. Or look up a property tax calculator for your state.

Month by Month

Let’s say you’ve found all of these annual costs. Now it’s time break them down, so that you can put away some cash each month.

Fuel = $1,744.53 per year

Maintenance = $2,000 per year

Insurance = $1,566 per year

Taxes = $2,867 per year

First add these to find your total annual costs:

1,744.53 + 2,000 + 1,566 + 2,867 = $8,177.53

Now divide this total by 12 to get your estimated monthly costs.

8,177.53 ÷ 12 = $681.46

So, based on this fictional numbers, socking away $682.46 for car expenses should cover the annual cost of owning and maintaining this fictional car. (Your milage may vary.)

Do you have any tricks for covering these unpredictable costs? Share your ideas or questions in the comment section.

]]> http://www.mathforgrownups.com/the-real-cost-of-car-ownership/feed/ 0 http://www.mathforgrownups.com/dealership-or-want-ads-deciding-between-a-new-or-used-car/ http://www.mathforgrownups.com/dealership-or-want-ads-deciding-between-a-new-or-used-car/#comments Wed, 09 May 2012 09:00:43 +0000 Laura http://www.mathforgrownups.com/?p=2488

Photo courtesy of Elsie esq.

When you’re looking at your personal finances, the big expenses stand out. That means purchasing a car is a huge consideration, and deciding between new and used can make your mind turn to mush. Do dealer and automaker incentives–like free financing or cash back–make a big difference? Sometimes yes, sometimes no.

Today, I’m bringing you an excerpt from my book, Math for Grownups. Use this math, and you can make an educated vehicular purchase, speedy quick.

Used cars are generally less expensive than new ones, unless you’re deciding between a pre-owned Hummer and a brand new Hyundai, of course.

But how do dealer and automaker incentives stack up to buying used?

Check it out!

Roxanne is trying to decide between two cars. Her local dealership has a current model priced at $25,000, including tax. But online she saw the same car—pre-owned—for $15,000. The used car is in excellent condition and certified. Plus, the warranty transfers, so price is her only real consideration.

The dealership is offering free financing. And the automaker has a $2,000 cash-back program. That means she’ll pay exactly $23,000 for the car and no interest at all.

But to finance the used car, she’ll have to get a loan. To compare the prices, she’ll need to find out how much she’ll pay in all for the used car. That means she needs to know what interest on a loan will cost.

In order to calculate that, she’ll need to know the principal (the amount she is borrowing and the basis of the interest calculation). That means the principal is $15,000. She’ll also need to know the interest rate. Her bank is offering a 6% interest rate on car loans, for a period of 4 years. The interest is compounded annually, so once a year, the interest rate is calculated and added to the loan amount.  Thus compounding interest means that in every year for the term of the loan, except the first year, Roxanne is paying interest on the interest she paid the year before (and the year before that . . . and you get the idea).  

Roxanne can use an online calculator, or she can turn to a really simple formula:

A = P(1 + r)ⁿ

Okay, breathe. It only looks hard. It’s not difficult at all if you remember the order of operations—that is, what you do first, then second, and so on.

First, do anything inside the parentheses. Next, take care of exponents—those are the little numbers at the right top of another number. They tell how often to multiply the bigger number by itself.  (Thus 4² means 4 Ÿ 4, and 16⁵ means 16 Ÿ 16 Ÿ 16 Ÿ 16 Ÿ16.) Then multiply or divide. And finally, add or subtract.  In other words, Please Excuse My Dear Aunt Sally, or PEMDAS:

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

Ready to apply this formula?  With PEMDAS, you can do it!

A is the total amount she’ll owe

P is the principal

r is the interest rate per compounding period

n is the number of compounding periods

Roxanne’s principal (or the amount she’s borrowing) is $15,000, so P = $15,000. Her interest compounds yearly, so her rate is 6%. To make it easier to multiply, she can convert that percent to a decimal: r = 6% = 0.06. And because the compounding period is annual, and the length of the loan is 4 years, n = 4.

A = $15,000(1 + 0.06)⁴

First add the numbers inside the parentheses.

A = $15,000(1.06)⁴

Now calculate the exponent. Remember, 1.06⁴ = 1.06 •Ÿ 1.06 Ÿ• 1.06 Ÿ• 1.06.

A = $15,000(1.26)

Last step!  Just multiply.

A = $18,900

So, Roxanne would pay $18,900 total if she finances the purchase of the used car.

That’s a heck of lot less than the $23,000 she’d pay for the new car. And she hasn’t even figured in her down payment yet.

Why does that change anything? Because after making a down payment, she would be paying interest on less principal (remember, that’s the amount she’ll be borrowing). How would a $1,500 down payment affect her decision?

For the used car, she’d finance $13,500 instead of $15,000.

A = $13,500(1 + 0.06)⁴

A = $13,500 •Ÿ 1.26

A = $17,010

So the total she’ll pay for the used car is $17,010.

And for the new car?  She just needs to subtract her down payment from the adjusted price: $23,000 – $1,500, or $21,500.

Judged on the basis of price alone, the new car doesn’t seem so minty fresh.

Do you have questions about using this formula? What about questions about buying cars and fitting the payments into your monthly budget? (On Friday, I’ll talk about the year-round cost of owning a car, a consideration that is critical at the buying stage. And later this month, we’ll take a closer look at compound interest.)