A few interesting things

In class the other day, I decided to further test the idea that compounding interest annually, monthly, daily, and continuously will continue to yield large differences in the amount of interest earned. In short, I found that for a significant interest rate, there is a significant difference in the final amount in the account after 50 years. I define a significant interest rate as above 3%, as this is the point at which the difference between compounding continuously and compounding monthly is above $100. At rates below this, after 50 years the difference is less that $100.

My findings show that unless you have an interest rate about 5%, and you keep your money in the bank for over 50 years, the difference between the different final amounts is not very significant. You might make an extra $10 in 50 years if you compound continuously instead of monthly, but lets be honest, you aren't likely to make a savings account for much more than 50 years.

If you want to see my process for finding this, I will post the process below, including screen shots.

I did this by using Microsof Excel as a calculator, inserting the correct equations, and auto filling own to 50 years.

I will walk you through how to do this, and then you can try it too!

First I made two columns. The first, column A, was titled "Number of Years" and the second, column B, "Interest Rate." I auto filled

the numbers 1-100 in column A, and entered the number .02 in column

B to represent a 2% interest rate.

*Note: To make this easier to fit in a blog post, i skipped over the numbers 6-50 and 51-100.

I then made four more columns with the headings Continuous, Daily, Monthly, and Yearly. This is only to show which compounding period is being used.

Then I entered the compound interest formula in column C, compounded continuously. To do this, I entered this equation into cell C2: =5000*exp(B$2*A2) In the equation, exp() tells the computer to use the constant e and raise it to an exponent. I then used auto fill to fill in the rest of the cells with this formula.

I then entered the equation =5000*(1+(b$2/365))^(365*a2) in cell D2, under the heading Daily. This formula is the compound interest formula. I did the same thing in the next two. columns, but used the formula for monthly and yearly.

I used 4 decimal places as in some of the examples it is not possible to see a difference with just 2 decimal places.

Because of how these equations are set up, if you change the number in cell b2, you change all of the equation. If you instruct excel to use a specific cell, in this case B2, adding a dollar sign to the cell name in the equation will make that cell a constant. That way, auto fill will always use the same cell in the equation.

There is another, simpler way to calculate this. It is called the rule of 72. If you take you interest rate and divide it out of 72, you will get the number of years that it should take any amount of money under that rate to double. It is not exact, but it works. This is generally used for non continuous compounding, and is used as a rough estimate.

In this case, it should take 36 years for any amount of money deposited to double at a rate of 2%.

I hope you find this interesting.

Marc

Notes for Wednesday 8/31: 21.7 A Model for Accumulation

For a uniform deposit of d per compounding period and an interest rate i per period, the amount A accumulated after n periods is given by the SAVINGS FORMULA:

A= d[(1+i)^n - 1/i]

For more information, refer to pages 772-776

Simple Interest vs. Compound Interest

Notes for Monday 8/29: 21.5

COMPOUND INTEREST VS. SIMPLE INTEREST 

According to Thomas Malthus, human populations increase geometrically but food supplies increase arithmetically - so that the increase in food supplies will eventually be unable to math increases in population but there are/will be natural restrictions on the human population like war, famine, and disease....


More frequent compounding yields more interest. But as the frequency of compounding increases, the interest tends to a limiting amount, shown in the far right column.
- this is because the extra interest from compounding often is interest on interest.

Page 769 of the textbook does a good job of walking you through the steps to determining the limiting amount. ( look at the blue boxes).

As “n” is made larger and larger, the limiting amount is e^r, and the interest method is called continuous compounding. Continuous compounding in greater detail (with examples can be found on page 770 in the book)

Next scribe is Luna

7 Billion

Today in class, after talking about Thomas Malthus and exponential growth (relating to human populations) we watched a video made by National Geographic about how the world's population will reach 7 billion by October. It's pretty interesting, and the video uses numbers to really put 7 billion in perspective for us. Not to mention there IS a graph on human population growth.

It's pretty cool. Check it.

http://www.youtube.com/watch?v=sc4HxPxNrZ0

Take an Interest in Interest

Check Out the link for more info on CDs and Money Markets

Helpful Video On Compound vs. Simple Interest

While studying I decide to look at youtube because I remembered when I had Jojo my Sophomore year of high school we found really good explanatory math videos on youtube.

http://www.youtube.com/watch?v=B3IdfBcXrLA

Maybe if you're having trouble hearing it from another person will help... Helped me.

Good luck!

-Luke

Bonds or Loans?

Over the summer, I read a fair number of college texts on different subjects. One of the texts was a brief look at economics. You might wonder when a college text on economics would come in handy to anyone other than a broker--I wondered the same. Well, it turns out that I was able to apply my newly gained knowledge of good investing in this math class before I could apply it in economics.
Anyway, here's my article discussing which is a better choice: Bonds or loans?
(But don't go buying bonds or loans based on the coupons I used as examples in the article.)

Bonds or Loans? - Google Docs

"By suspending judgment, by confining oneself to phenomena or objects as they appear, and by asserting nothing definite as to how they really are, one can escape the perplexities of life and attain an imperturbable peace of mind."
-Pyrrho

What is Discrete Math...?

So, I found myself still confused about just what discrete math was. So, I thought it'd probably be in the first few pages of our book.

Then I realized that the book is ALL the way over there on my desk, and I'm lying on my bed.

That book is approximately four feet away from me.

So, I lazily thought, "I'll just google it."

Found a pretty interesting and useful link:

http://www.cs.tufts.edu/research/dmw/what_is_dm.html

Greek Debt Crisis

Eurozone members and the IMF have agreed a 110bn-euro (£95bn; $146.2bn) three-year bail-out package to rescue Greece's embattled economy.

In return for the loans, Greece will make major austerity cuts which Prime Minister George Papandreou said involved "great sacrifices".

The EU will provide 80bn euros in funding and the rest will come from the International Monetary Fund (IMF).

The deal is designed to prevent Greece from defaulting on its massive debt.

However, it must first be approved by some parliaments in the 15 other eurozone countries.

Luxembourg's Prime Minister, Jean-Claude Juncker, said up to 30bn euros would be disbursed to Greece in the first year. The first loan tranche will be released before 19 May - the date of Greece's next debt repayment, he said.

The leaders of the 16-nation Eurogroup will hold a summit in Brussels on Friday to "draw initial conclusions from the Greek crisis", he added.

CLASS EXPECTATIONS

The main goal of this class is to help you acquire a deep understanding of and appreciation for  discrete mathematical structures. You will learn to think about these structures in a more confident and focused manner.


A secondary goal of this class is to help you become adept at mathematical communication. Opportunities to improve your communication skills on several levels will arise throughout the class (see below for details): speaking precisely about mathematical ideas in class; writing informally about mathematical ideas on this Discrete Math Blog; and writing careful mathematical conclusions on homework assignments.


GRADING SETUP

Tests 30%
Quizzes 20% (drop the lowest)

Homework/Notes 20%
Final Exam 20% (can replace lowest test grade)
Projects/Other 10%



Homework

All homework will be submitted through Google docs for grading. You should include your name, lesson number, and the assigned problems.

Here is an example of how you should title your work (top left corner of document):
Michael: How to Title My Homework, Pg. 1 1 - 20 all 
 

Homework will be graded as follows out of 5 points:

1 did something

2 did half

3 did most

4 did all

4.5 did all and checked

5 did all, checked, and formatted correctly


Notes

For notes, you should include your name, the pages, and the lesson title.  Notes must also be submitted to Googledocs.

Here is an example of how you should title your work (top left corner of document):


Isabella: How to Title My Notes, 22.1

Notes will be graded as follows out of 5 points:

1 did something

2.5 half information is covered

4 most of material covered

4.5 All material Covered

5 Neat, Images included, organized

Attendance
You must come to class if you are at school. If you are not here when I take attendance you will be marked absent. If you arrive late I will change the mark to tardy. If you have a note your tardiness will be excused. (Note: excessive absences can prohibit you from passing the class) For every unexcused absence you will lose a whole point from your final average. For every three unexcused tardies you will lose a whole percentage point to your final average.


If you miss class you are still responsible for the homework. The best way to prepare for a trip is to get your assignment in advance.


BEHAVIOR
Disruptive or offensive behavior will not be tolerated. Offensive language is not used in my room.


NO CHEATING! Do not roam your eyes around the room. Please keep your eyes on your own paper to avoid even the appearance of looking at the answers of classmates it may be mistaken as cheating.


CELL PHONES
Cell phones must be turned off and put away at all times during class. A violation of this policy will result in the removal of the phone and it will be given to Paul Hayward.


EXTRA HELP
We all need a little extra help every now and then. While every effort will be made to answers questions during class, there may be times when you need further clarification. I will be regularly available to help students with math during:


Wednesday @ Lunch


Please contact me as soon as you become uncomfortable and we will find a time even outside of these times to get you help. I’m more than willing to work with you, but I also expect you to make the effort and show me you are invested in learning. If you are having trouble with any part of my class, let me know and I will help you. I am a big helper, that’s my job.

The Path to Success!!

You can succeed in math and in this course if you:

1. Respect everyone in the class at all times. We all work at different paces and use different methods. Please respect those differences.
2. Always be on time and prepared for class.
3. Have read the lesson and done the homework.
4. Show all your work
5. Check your work carefully so that you know what’s hard for you and mark the items on your homework that you want to discuss in class.
6. Review your class notes every night before going to bed.
7. Always get extra help from the teacher when you feel you are falling behind.
8. Find one or two people to be your study partners and form a study group.
9. Make the class work for you by making sure you get your questions answered, and listening to what other students have to say. Your classmates have great ideas, sometimes better than my ideas, so, be attentive. They may also ask questions you want to ask. Listen to your classmates.
10. Participate regularly on the class blog

Tools We Will Use In This Class

Twitter -hashtag: #pidm12

Flickr -you will need a yahoo account
Test Aftermath -required unless you score higher than a 91 on the test

Tutorials 

Blogging  -BOB, Scribing (be sure to tag your name on each entry, as well as the assignment)

Challenges -varying point totals

Web Page Answers 

DEAR SUMMER

Dear Summer,

It was a great summer! Mixed into my ongoing work with the Paideia basketball program, I got married.  Most of July was spent traveling to great places to celebrate our marriage.

The first stop was one of my favorite places to visit, the North Georgia Mountains in Blue Ridge, GA.  My wife and I spent time tubing, shopping, eating, and relaxing with our family members.


We then made our way to to Jamaica, where we stayed two weeks at Sandals Montego Bay and The Rockhouse in Negril! We finally returned to Atlanta after having tons of fun in Jamaica just in time to start preparing for teaching Discrete Math and putting together this blog! :-)
Twitter details about the summer, etc.

Now it is time to leave the summer and enjoy the beginning of the school year. Use this blog as a window of opportunity and keys for access to the world around you! Become a global learner!

Posting Guideline

Blogging is a very public activity. Anything that gets posted on the internet stays there. Forever. Deleting a post simply removes it from the blog it was posted to. Copies of the post may exist scattered all over the internet. That is why we are being so careful to respect your privacy and using first names only. We do not use pictures of ourselves. If you really want a graphic image associated with your posting use an avatar -- a picture of something that represents you but IS NOT of you.

Two teachers in the U.S.A. worked with their classes to come up with a list of guidelines for student bloggers.

One of them, Bud Hunt, has these suggestions, among others:

1. Students using blogs are expected to treat blogspaces as classroom spaces. Speech that is inappropriate for class is not appropriate for our blog. While we encourage you to engage in debate and conversation with other bloggers, we also expect that you will conduct yourself in a manner reflective of a representative of this school.


2. Never EVER EVER give out or record personal information on our blog. Our blog exists as a public space on the Internet. Don’t share anything that you don’t want the world to know. For your safety, be careful what you say, too. Don’t give out your phone number or home address. This is particularly important to remember if you have a personal online journal or blog elsewhere.


3. Again, your blog is a public space. And if you put it on the Internet, odds are really good that it will stay on the Internet. Always. That means ten years from now when you are looking for a job, it might be possible for an employer to discover some really hateful and immature things you said when you were younger and more prone to foolish things. Be sure that anything you write you are proud of. It can come back to haunt you if you don’t.


4. Never link to something you haven’t read. While it isn’t your job to police the Internet, when you link to something, you should make sure it is something that you really want to be associated with. If a link contains material that might be creepy or make some people uncomfortable, you should probably try a different source.

Look over the guidelines and add the ones you like in the comments section below this post. I think Bud's suggestions are excellent. We'll be using the one's I highlighted above as a basis for how we will use our blog.

Scribe Guidelines

Scribe Guidelines
The kind of post I'd like you to make should have one or more of these characteristics:

• * A reflection on a particular class (like the first paragraph above).

• * A reflective comment on your progress in the course.

• * A remark on something that you've learned that you thought was "cool".

• * A remark about something that you found very hard to understand but now you get it! Describe what sparked that "moment of clarity" and what it felt like.

• * Have you come across something we discussed in class out there in the "real world" or another class? Describe the connection you made.

One might describe the role of writing a scribe like this.

A scribe post is basically like you are teaching the class again, but this time in your words in a way that other people can understand it. You can also recap other important things that we talk about in class, so that if someone was away in our class, they would know what they missed. Also don't forget that when you scribe, you get the power to choose the next scribe.

Be sure to Title your scribe post properly ("First Name", "Unit Title"). Be sure to Label (Tag) your post as Scribe Post.

When you are done as the class scribe, visit the scribe list page to name a scribe for the following day!