Or just ride a bicycle instead...

I live in what I like to call an urbanized suburb: we still have parks and lots of houses, but along the main strip of the town there are a number of pharmacies, pizza joints, and a saturation of gas stations. There are two that I can walk to without breaking a sweat.

As a father of two with a brand new mortgage, one of the ways I try to cut down on expenses is to find the cheapest gallon of gas around. There's a web site that makes this an incredibly easy process, but it does not take into account things like savings card or other promotions. Our local grocery store offers $0.10 per gallon of gas for every $50 spent at their locations (and that goes to $0.20 for purchasing $50 in gift cards). Sunoco has a deal in some of their stores where buying a specific item can give you so many pennies off (and they can add up over time).

The supermarket promotion is the best, by far, but they are also the farthest away. The closest one is about 10 miles from home. Usually I can make up some other excuse to drive down there, and fill up on the way back, but other times I go there just for gas, and I always have the same thought going through my head:

"Am I LOSING money by driving all the way out here to try to SAVE money?"

Until now I've been blissfully ignorant of the answer. I'd rather pretend that I'm saving money instead of knowing that I'm not. But, this is another case of Math In Real Life, so it's time to bite the bullet.

There are a few things we need to know:

1. How much gas does my car use? This is traditionally measured in miles per gallon, or mpg.

2. How big is my gas tank? This is in gallons.

3. How much does the gas cost nearby and how much is it further away? These would both be in dollars per gallon ($/gal).

4. How far away is the "cheap" gas? This would be in miles.

So in my scenario, my car uses about 14 mpg in "city" driving. When you buy a car you usually see both city and highway mpg estimates: stopping and starting your car frequently obviously consumes more gas, and lowers your mpg. My gas tank is 19 gallons, which is a gigantic tank for a sedan...both a blessing and a curse.

The gas station up the road is charging $3.349/gallon. Yes, there's a hundredth's place (that's that little "9/10" you see on most gas station signs). I don't know how the gas industry gets away with the deception. I don't see Wendy's offering up a "$0.999" menu. Anyway, the discounted gas is going for $3.299/gallon. I get $0.20 off for spending $100 at the grocery.

Finally, the "cheap" gas is 10 miles away.

So, first thing's first: how much would it cost to fill up my tank at the nearby station? Assuming that the tank is bone dry (this has happened to me before), we're just doing simple multiplication:

19 gallons x $3.499/gallon = $66.50

Yowza. I'm old enough to remember when gas was under $1.00/gallon. Then again, I'm old enough to remember when leaded gas was available. Times have changed.

Next, let's do the same calculation on the cheap gas station:

19 gallons x $3.299/gallon = $62.68

That's already disappointing. Spending $100 at the grocery store saves me a whopping $3.82 at the pump. I already have some idea where this is headed.

Finally, how much did it cost me, in gas, to drive the 10 miles? More multiplication, but we're doing it two ways: using the "cheap" gas price and using the "nearby" gas price:

Cheap: $3.299/gallon / 14 mpg = $0.236/mile x 10 miles = $2.36

Nearby: $3.49/gallon / 14 mpg = $0.249/mile x 10 miles = $2.49

Wonderful. So I save $3.82 by driving the 10 miles to the cheap gas station, but it costs me at least $2.36 in gas to get there (or more, depending on where I last filled up).

Net savings: $1.33 - $1.46

I guess I'm a little glad that there were SOME savings, but obviously far less than I had expected. From now on I will let my discounts accrue until they're something meaningful, like $1.00/gal off or more, and gladly spend the extra $1.00 and change at the local station.

For more information on frugal living I've found a great blog with more tips and hints than math could ever teach you.

Kilo-what?

When you were a kid, I'm sure you remember your mom or dad begging you to turn off lights in empty rooms, that you were "wasting electricity". They probably used some parent-like phrase like "I'm not made of money".

Having worked in the electricity business for about a decade, I can say that your parents' intentions were in the right place, but there were far more energy-sucking things in the house they should have made you turn off.

While this country is still transition to the new CFL light bulbs, most of my house is illuminated by standard tungsten-heated bulbs. Let's take the bedroom, for example. I have a ceiling fan with four bulbs in it (60 watts each), and two lamps (40 watts each).

Watts are units of power that measures how quickly energy is converted to light. The higher the wattage, the faster energy is converted, and the brighter the light (which also means the bulb's life expectancy goes down as the wattage increases).

So in my bedroom example we have 320 potential watts. If you look at your electricity bill you'll notice that your costs are measured in dollars (or cents) per kilowatt-hour. A kilowatt-hour is how many thousands of watts are used in an hour...simple enough. If I never turned my lights off in the bedroom I'd be consuming 320 watts for 24 hours a day, for 365 days a year (I'd also get very little sleep):

320 x 24 x 365 = 2,803,200 watt-hours, or 2,803 kilowatt-hours (kWh).

The average cost of electricity in a residence is about $0.12/kWh (this number should not be used for commercial or industrial purposes; the cost is often much lower). So my annual cost to run my bedroom's lights would be:

2,803 kWh x $0.12/kWh = $336.36, or about $28 a month.

A 60 watt bulb, left on all day and all night, costs about $5.00 a month. If you left one of these lights on a completely forgot about it, chances are it would actually cost less than that, since most incandescent bulbs only have a 1,000 hour life expectancy. Switching your entire home to CFL bulbs would drastically lower consumption: most have wattage in the 10-15 watt range.

There are some energy hog items in your home that are, generally, not within your ability to control. Your refrigerator uses about 700 watts. Your hot water heater uses as much as 4500 watts (assuming it's an electric heater). Dishwashers require about 1200 watts.

The new "not made of money" item in the modern household is the computer.

When awake, your computer consumes about 270 watts. If you utilize the "energy saver" feature, it uses about 50 watts when asleep. I know, personally, that my computer is rarely not in use. My job requires a lot of overnight automated programs to run, so I have to leave it on and alert. I'd say, on average, my computer is on and working 20 hours a day, for 300 days a year.

270 x 20 x 300 = 1,620 kWh

The time it's actually shut down is arbitrarily small, so let's say for the remainder of the time it's asleep:

4 x 4 x 60 = 0.96 kWh

Rounding up my computer consumes 1,621 kWhs a year, or $194 in electricity.

That, in itself, is not a huge number, but I don't live alone. My wife has a laptop. My son has a laptop AND a desktop, and we have a spare computer in the playroom for my youngest and my mother-in-law. While these aren't in use as frequently as my computer, I'd say they all average about 1,000 kWh a year, or $120.

So $194 for my computer, $120 each for the other four computers, and I'm looking at an annual cost of $674, all thanks to technology.

You don't need to be a financial analyst to understand how quickly electricity piles up. Like I said, Mom and Dad had the right idea, but focus on the big ticket items. Use your energy saver utility on your computers (or shut them down). Don't leave electric heaters or a television on in an empty room. Don't take incredibly long showers (and try to avoid baths, since they use a lot more hot water than your typical 10 minute shower). And if you have to leave lights on in your house, switch to CFLs.

On a side note, it's important to check with your states deregulation laws when it comes to electricity and gas. In parts of PA we have the choice to switch suppliers, often at discounts of 10% or more off of the "primary" providers.

Jackpot!

The Mega Millions jackpot, as of Friday, December 16th, sits at $135 million. This is an astounding amount of money. Even the annuity option (26 annual payments of $5 million) seems like an awful lot of money. I've worked post-college for 9 years and I've made roughly $350,000 over that time. Over the next 30 years I'd have to have an average salary of about $150,000 annually in order to make $5 million before I retire. I don't think my boss is giving me that kind of raise next year.

The lottery is all about odds, one of the overarching concepts discussed in probability theory and statistics. Odds are calculated as relative probabilities: what is the chance that X will happen against the chance that X will not happen? Don't confuse odds with gambling odds, which relate to the payment of a specific event occurring, such as a 3:2 payout in blackjack or paying 1,000 credits for getting all 7s on a slot machine.

The classic example of odds is to flip a coin. The odds of that coin landing tail up are 1:1, or "even odds". In other words, there is an equal chance of it landing tails up or heads up. But keep in mind that odds still exist in the world of mathematics, and not real life. If you flip a coin ten times don't expect a result of five heads and five tails. You'd probably get four heads and six tails, or vice versa, or maybe even greater variances. Flip it a hundred times and you get closer to a 1:1 output. Flip it a thousand times and you've got too much time on your hands.

All state-run and national lotteries are required to make their odds public knowledge. The odds of winning the Mega Millions jackpot is 1:175,711,536. Those odds seem astronomical, but when you consider that there are about 310 million people in the United States, and roughly half of them are 18 or older, then logic would suggest that you would likely have a jackpot winner at every drawing (especially if you consider that most lottery purchasers buy more than one ticket for a drawing).

So why doesn't it happen? For the same reason flipping your coin ten times did not give you exactly five heads and five tails.

Probability is not constrained to any sort of pattern. You could flip your coin ten times and it could land on heads all ten times. Someone else could pick up that same coin, flip it ten times, and he gets all tails. Someone could, conceivably, buy lottery tickets for the next 75 drawings and win something all 75 times, and you could do the same and win nothing. In other words: just because X happens one time, doesn't mean that X won't happen the very next time.

Should you play the lottery? Any statistician would say "no way", but I disagree.

I remember, back in high school, the drudgery of applying for various academic scholarships. The application, itself, was relatively easy, but the essays drove me nuts. I had applied for a dozen scholarships and, as a result, had to write a dozen different essays, meticulously explaining why I want to go to college or what I want to do in life. I put much more effort into those essays than any paper I wrote for high school. Why? Because every scholarship offered the chance at thousands of dollars off of a college education, and that chance -- no matter how slim -- was worth the effort.

Playing the lottery requires virtually no effort, but it does require money. For most of us, a $2.00 sacrifice every drawing (there's two a week for Mega Millions) is probably a pretty small sacrifice, even if the odds are astronomically small.

My final word of advice: don't overdo it. Playing 5 or 10 or 100 tickets in every drawing does, statistically, increase your chances, but by how much? Instead of 1:175 million for a single ticket you're now at 1:35 million if you buy 5 tickets. That may seem like a huge leap in your favor, but it's still incredibly slim. Putting it in perspective: the odds of dying in a plane crash are 1:11 million.

Personally, I'll throw $2.00 away when the jackpot creeps over $100 million. The odds are against me, but 1:175 million is still better than 0:175 million.

Compound Interest: The Silent Killer

I bought my first house about three years ago. It was my second major purchase (the first being a minivan, so I suppose this was an upgrade), so I was no stranger to the confusing and mind-numbing paperwork involved. But, while a car purchase usually requires a financing agreement, a vehicle inspection report, and proof of insurance, I believe that they had to chop down two or three trees in order to handle all of the paperwork involved in buying a house.

Somewhere in the midst of that avalanche of affidavits and agreements is your mortgage: a piece of paper from a bank that says "we'll loan you much more money than you make in a year, and you can pay us back a little bit at a time, with interest."

You don't need accounting classes to understand the basic concept of interest. Let's say you get a $1000 loan with 10% interest, that you pay back over 12 months. In it's simplest (and least profitable) form, that means you actually pay $1100 (10% of 1000 = 100) over those 12 months, or about $92 a month. Since this is a one year loan, you would say that the interest is "compounded" annually.

So what is "compounded" interest? The qualifier -- annually, monthly, daily -- tells you how often they put interest on the "principal": the remaining amount of money you owe on the loan.

Mortgages and credit cards generally have agreements to compound interest monthly. The generous lenders will compound quarterly. And now's the time to break out the calculator.

There's a mind-numbingly tedious way to determine total interest, and then there's the math way (which I like to call the "fun" way):

Let's say you got a 30 year mortgage for $150,000 and a 4.5% fixed rate interest (compounded monthly). First, how much would you pay over 30 years if the interest was zero?

$150,000/360 months = $416.67

Then, we need a magical formula for determining how to add the interest:

I = Fixed Rate (4.5%)
T = Term in Years (30)
A = I * T = 0.045 * 30 = 1.35
B = 1/2*Y = 0.675 (this is for simplification purposes)

The formula your lender uses to determine your monthly payment looks confusing, but we'll walk through it:

Monthly Payment = Zero Interest Payment * (1 + B + B²/3)

This is, actually, an approximate formula based off of what is actually a series:



where L is the principal, P is the payment, n is the number of months, and i is the annual interest rate compounded monthly. Between my formula and the "official" formula, which would you rather use?

I thought so.

So let's plug in our numbers on my formula:

Monthly Payment = $416.67*(1 + 0.675 + (0.675²)/3)
Monthly Payment = $416.67*(1.675 + 0.151875)
Monthly Payment = $416.67*(1.826875)
Monthly Payment = $761.20

Wowza. So for $150,000 house you actually give the lender nearly $275,000 over the life of the contract. Lenders know that people rarely have $100,000 saved up in their banks. They also know that people rarely stay in the same house for 30 years, either selling it, or foreclosing on it. With the compounded interest the banks mitigate their risk, taking a large chunk of the interest out early on.

So how does a homeowner fight back from this? Simple: pay as much as you can towards the principal each and every month. If you can afford an extra $100, then add $100. If you get a hefty tax return, then add that. Every single dollar you take off of the principal equates to almost $2 savings in interest. That can really add up over time.