Mathematics Education

how about the left and right bank of a river?

The famed Bohemian Left Bank of the Seine would be the Right Bank of the American River.

But are units needed? The billowing white scarf served as the pilot's oil pressure gauge and did so without units.

Australians are happy using Stones to weigh men and horses, they don't seem to weigh their women at all but they use Bowsers and buy capcicums.

Don`t be surprised about the general public.have you ever seen the tonight show segment called Jaywalking,where they ask
Basic questions to random people on the street. Last week they asked which is the largest U.S state only 1 out of 5 people got it right. The wrong answers were Texas,Florida,and Illinois.As for the smallest state no one answered correctly.

Here's a typical math problem lots of people fall for:

Suppose three people have lunch together and the check comes to $25. they each pay $10. The waiter brings back five $1 bills as change. They each take one bill and leave a grand total of $2 as a tip. Ok so far? good. Now, since each apid ten, then took back one, then each paid $9 total. That and $2 in tip makes a net of $29. Where's the missing dollar?

Of course, the reason people flal for it is the problem is stated badly. Change the wording and all is perfectly clear.

Spreadsheet available for Markov Chain which calculates the probability of reaching a certain number of throws in craps.

Although this problem has been done several times on the Wizard's site, I was trying to make the spreadsheet as intuitive as possible. That way you can clearly see the nature of the calculation, and furthermore that the initial conditions are also very specific.There are only two basic equations not counting sums and simple inversions and basic arithmetic. I would appreciate any comments.

The purpose is for teaching.

Quote: Face

Near as I can figure, we stubborn Americans are the last hurdle to a world of common sense measurements. As an economic superpower, our adoption of the metric would be the nail in the coffin to feet, rods, stone, miles, pounds, ounces, quarts, gallons, pints, and all other convoluted types of measure.

Ladies, the number which represents your weight would instantly halve. No pills, no diet, no exercise. Poof! 150 goes to, like, 70.

Men, who wants to drive a 350ci? BAM! 5,000cc’s of tire ripping fury! Raaahrr!!

No longer will cakes be ruined by double or half recipe conversions! No longer will our Imperial sockets round off the bolts of foreign goods! The time has come! The future is now!

METRIC OR DIE!

Face in 2016.

You got my vote!

Reposted from Wizard of Vegas

The Wizard mentioned one time, how a salesman tried to persuade him that he would be paying more in interest if he purchases a car then if he leases it, but the interest rate was higher on the lease than on the purchase. He commented that it took him a while to figure out what the salesman did to fool him.

The blogger does something similar in this post where he shows that leasing is clearly better than purchasing a BMW.

Leasing vs Buying a BMW: When is it right for you? By Manny Antunes.May 17th, 2011

In this blog the writer goes on and on generically about the pros and cons of leasing vs puchasing vs. buying. He then does a hypothetical comparison.
(1) Purchasing has a higher down payment
(2) Purchasing has a higher monthly payment
(3) Finally he concludes that the time value of money slightly favors the lease. His concluding statement is:
{For 5 year finance option} the total of payments with interest and down payment; $62,860. Pretty close to leasing the car at a total of $62,048. The car in discussion is a (BMW 525i) and costs $59,125.

Having all three of these conclusions at once should seem impossible to an astute reader. You can't have everything. If you have lower payments and lower downpayment, you reasonably must pay for it somewhere.

Would anyone like to try and explain what the blogger did?

Witchcraft, of course.

I can say without a shadow of a doubt that I am the most ignorant person when it comes to finances. The only way I even know there’s an issue in what you posted is because you said so =p

When I go car shopping, I make a plan, set a goal, and don’t let the dealer talk at all, lest he cast a spell on me. I certainly don’t get the math wiz special and likely pay more than I should, but I think I at least prevent myself getting screwed.

Last purchase I made, I walked in entirely cold. Didn’t make an appointment, they had no idea I was coming. 150 minutes later I was already home with my new-to-me truck.

And they still got me. I’m now $5k underwater on my rig >< Witchcraft, I tell ya.

At least I stuck them with a pile on my trade in =p

Quote: Face

Witchcraft, of course.
I can say without a shadow of a doubt that I am the most ignorant person when it comes to finances. The only way I even know there’s an issue in what you posted is because you said so =p

The BMW purchaser and the truck purchase may be concerned with the same bottom line. To quote the figures in the blog
(Option A) You must put down $10,000 plus first month's payment, plus state taxes, local taxes or motor vehicle documentation . Your payment will be $881 /month
(Option B) You must put down $2,6250 plus first month's payment, plus state taxes, local taxes or motor vehicle documentation . Your payment will be $771 /month

The articles says 80% of people choose to lease a BMW. Then the article asks "So what do they know that the rest of us don’t ?".

Now the prospective BMW owner will almost always go with option B because it is easier. Unlike the truck owner, he probably doesn't care about turning the car in again in 3 years, and paying state taxes, local taxes or motor vehicle documentation all over again, and buying what will probably be a more expensive vehicle.

But the BMW purchaser has a nagging doubt in the back of his head. What would his parents say about these kind of purchases? Is he paying through the nose in financing.

So the salesman (or blogger) does a quick calculation and comes up with the following statement:

Total of payments with interest and down payment; $62,860. Pretty close to leasing the car at a total of $62,048.

The salesman does this simple calculation to back up the numbers
(60 months)*($881 per month)=$52,860+$10,000 down payment = $62,860 adjusted basis for car for 5 year financing
(36 months)*($771 per month)=$27,756+$34,292 residual value = $62,048 adjusted basis for car for 36 month lease

So now the BMW buyer feels much better about his financial savvy. Not only does he get the lower down payment, and the lower monthly payment, but he saves $812 on the time value of the money. He may not have gone with Option A anyway, but now he feels much smarter.

Of course the BMW buyer has been hoodwinked. But it takes some effort to figure out how.

The purchaser of the truck is more likely to say that he doesn't want to pay those state taxes, local taxes or motor vehicle documentation all over again. He was hoping to pay the truck off, and then try to get a couple of years with just maintenance costs out of the vehicle. He doesn't care about $812 in "adjusted basis".

Next time you are buying a car, see if you get the exact same song and dance. The salesman knows that it will be much easier to sell a car as a lease than as finance simply because the buyer doesn't have to produce as much money. It is a very important part of their sales technique. It is a standard part of the sales pitch for high end cars in particular.

Sort of off topic, but I wonder if the brain damage I have received somehow completely stymies my ability to deal with math. I just don’t see how I can pick up complicated sciences with little more than a cursory glance, yet can’t understand basic math even when it is spoon fed to me ???

After your explanation, all I see is that someone is going for saving ~$800 all the while ignoring all the licensing and tax fees that going for the $800 will bring.

Is that the “scam”? Making the lease seem palatable enough so that the customer returns every 3 years and nick him with all the fees?

Quote: Face

Is that the “scam”? Making the lease seem palatable enough so that the customer returns every 3 years and nick him with all the fees?

Leasing is very profitable for a car dealership in many ways (in particular a loyalty buy like BMW). You guarantee that the customer must return to the dealership in 36 months even if he is not in a particular financial position to purchase a new car. Most of the time he has exceeded the mileage limit on his lease so he must pay a hefty fee. He almost always had some dings which he is required to pay to fix. Since he is without a vehicle he almost always leases another car from the same dealership. This behavior is reinforced with loyalty payments. If in fact the driver has driven the car way below his mileage, he gets no credit at all.

As an alternative, consider a long term loan (usually 7 years). You will usually find that the monthly payments, and the loan balance after 3 years is almost identical to the monthly payments and the residual value of the lease terms. Now look at all the advantages of the long term loan:
(1) You don't have to make a decision right at 36 months. If that is inconvenient you can make a decision at 32 months or 42 months
(2) If you have taken exceptional care of your care, or driven it very little, you will reap the benefits in higher value
(3) If you go over by 1000 miles you will not be stuck with an overinflated penalty fee
(4) The "easy peasy" aspect of turning back the car in a lease after 36 months is largely over-exaggerated. If you actually take care of a car within the parameters specified by the lease, the dealership will gladly give you a trade in value at least equal to your loan balance. In many cases you can get more than the loan balance.
(5) You can more easily work with another dealer or another manufacturer.
(6) Minor dings can be negotiated. The dealer may deduct some value for them, but as he is anxious to make a sale, he is likely to let them go. He can fix them for just a little labor of one of his employees. You have to pay the retail shop rate to fix them.

But psychologically it is much harder to sell a 7 year loan to many people. If they are old enough, they remember when a standard car loan was only 4 years. They may likely determine that they can't really afford this car, and purchase a cheaper model.

In order to persuade people that a lease is not such a bad deal, they resort to some mathematical shenanigans. The bad calculations are mostly designed to make you "feel better" about the decision to go with a lease, and most policing organizations can't be bothered with what they consider to be minor manipulation.

In reality, I think most salespeople are told how to do the calculation, and are not even aware that they are manipulating numbers.
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In general if you had a 5 year note with a $1000 monthly payment and an $20K downpayment compared to a 36 month lease with $44K residual value, a salesman will tell you that both loans cost you the same amount of money. The supporting calculation is: 60*$1K+$20K=$80K vs 36*$1K+$44K=$80K. THEY ARE NOT THE SAME.

This is the point, the Wizard was making. It is more difficult to borrow $44K at the end of three years, then it is to borrow $20K at the beginning of the loan. All money comes at a cost. You are either removing it from a profitable investment or you must borrow it. You can't just ignore the time value of money.