Reviews for the Final Exam have been posted on the right side of the blog. We will review Graphing and Finance on Wednesday and Probability and Statistics on Friday. We will be reviewing Voting on Monday - you should bring both the Voting Review from the Final Exam Review folder and the worksheet title Voting - More Problems from the voting theory worksheet folder for class Monday.
The CAS is offering reviews this week (April 24-27) in Remington 117 from 4pm-6pm.
Monday - Graphing
Tuesday - Probability
Wednesday - Statistics
Thursday - Finance
I have my regularly scheduled office hours this week and students may also join me in Agenstein 123 MW 9-9:50am to review for the final.
Next week (May 1-5) my office hours will be as follows:
Monday, May 1: 10:30am - 12:30pm
Wednesday, May 3: 9:00am - 11:00am
or by appointment
Saturday, April 22, 2017
Wednesday, April 19, 2017
Week 13 - Voting
This week, we've discussed some fairness criteria on Monday, and started looking at how we might compare plurality versus plurality with elimination on Wednesday. You will receive full participation credit for this project by simply being in class on Wednesday and Friday and participating. I have posted the project and the Voting Methods summary on the right side of the blog.
Recall that the state of Maine voted in November to switch to plurality with elimination (called ranked choice voting) for many of their elections. Here are some interesting articles about this switch and about plurality vs plurality with elimination
Maine's Ranked Choice Voting: It's not Plurality (has a couple interesting videos)
Top 5 Ways Plurality Voting Fails
Maine Ranked Choice Voting Initiative, Question 5(2016) - Ballotpedia
Portland Press Herald
Podcast Meeting with Supporters on Both sides of Question 5 (scroll down to find this)
The Reasons for Maine to Adopt Ranked Choice Voting are Unconvincing
Yes on '5': No More Lesser of Two Evils in Maine
Maine became the first state in the country . . . to pass ranked choice voting
Can you find any interesting articles about Question 5 on Maine's ballot? How would you have voted on Question 5?
Recall that the state of Maine voted in November to switch to plurality with elimination (called ranked choice voting) for many of their elections. Here are some interesting articles about this switch and about plurality vs plurality with elimination
Maine's Ranked Choice Voting: It's not Plurality (has a couple interesting videos)
Top 5 Ways Plurality Voting Fails
Maine Ranked Choice Voting Initiative, Question 5(2016) - Ballotpedia
Portland Press Herald
Podcast Meeting with Supporters on Both sides of Question 5 (scroll down to find this)
The Reasons for Maine to Adopt Ranked Choice Voting are Unconvincing
Yes on '5': No More Lesser of Two Evils in Maine
Maine became the first state in the country . . . to pass ranked choice voting
Can you find any interesting articles about Question 5 on Maine's ballot? How would you have voted on Question 5?
Friday, April 14, 2017
Voting Theory Homework
There will be no Webwork assignments for the Voting Theory unit. Instead, there will be only paper homework assignments, which will be collected in class. The first assignment is posted on the link on the right side of the blog under Voting Worksheets, and will be collected in class on Wednesday, April 19. A selection of solutions will be available for you to check your answers in the CAS or my office before Wednesday.
Tuesday, April 11, 2017
Week 12 - Exam 3
Remember that our third exam is scheduled during class on Wednesday, April 12. Your Finance Worksheets 1-4 will also be due in class on April 12. There are two review sheets with answers linked on the right side of the blog. Make sure that you bring your calculator with you to class for the exam!
On Friday, we will begin our final unit with a discussion of voting theory. We will be discussing four ways of determining the winner of an election on Friday: Plurality, Plurality with Elimination, Pairwise Comparison, and Borda Count. Next week, we will discuss how we might compare these methods and determine one is "better" than another.
Challenge Problem: (Due Monday, April 17) In preparation for next week, research "fairness criteria for voting". In particular, describe the following criteria and give an example of an election and a voting method that fails to satisfy each criteria. (i.e., Give the results of a sample election under one of the voting methods and describe why this election violates the criterion. Do not use the examples in the notes.) Be sure to cite your sources.
1. Majority Criterion
2. Condorcet's Criterion
3. Monotonicity Criterion
4. Independence of Irrelevant Alternatives Criterion
On Friday, we will begin our final unit with a discussion of voting theory. We will be discussing four ways of determining the winner of an election on Friday: Plurality, Plurality with Elimination, Pairwise Comparison, and Borda Count. Next week, we will discuss how we might compare these methods and determine one is "better" than another.
Challenge Problem: (Due Monday, April 17) In preparation for next week, research "fairness criteria for voting". In particular, describe the following criteria and give an example of an election and a voting method that fails to satisfy each criteria. (i.e., Give the results of a sample election under one of the voting methods and describe why this election violates the criterion. Do not use the examples in the notes.) Be sure to cite your sources.
1. Majority Criterion
2. Condorcet's Criterion
3. Monotonicity Criterion
4. Independence of Irrelevant Alternatives Criterion
Tuesday, April 4, 2017
Week 11 - Amortized Loans
This week, our focus will be on amortized loans. Most loans that you take out will be amortized loans - mortgages, student loans, car loans, furniture loans, etc. Last week we learned how to determine the payment on an amortized loan. This week, we'll be focusing on answering several questions.
1. If you know how much you can afford to pay each month and you know the rate and term of the loan, how much can you afford to borrow?
2. Suppose you are several years into a given loan and you are offered to refinance to another loan at a different rate. What does it mean to refinance? Will this particular offer save you money?
3. Suppose you pay extra each month on your amortized loan. How much will you save in interest by paying ahead? How soon will you pay off the loan?
These are all very interesting questions to ask when you are looking at a loan. Question 1 simply requires you to solve for P in the formula below. Questions 2 and 3 will require a little more thought before we can solve them.
\[ P = R\left[\dfrac{1-\left(1+\frac{r}{m}\right)^{-mt}}{\frac{r}{m}}\right] \]
We will be learning how to use the formula to answer the questions above by hand. However, there are many calculators online to help answer these questions and more about taking out a loan. Below are links to some calculators that you may find useful when you want to consider taking out a loan in the future.
Bankrate.com
Amortization Schedule Calculator
Mortgage Payoff Calculator
Cost of Living Calculator
Is it Better to Rent or Buy?
We will only be considering fixed rate loans in all of our examples. But lenders may also offer you an adjustable rate mortgage (ARM). As the name suggests, with an adjustable rate mortgage, your rate can change, depending on market rates. These loans can be risky - if rates go up, so does your monthly payment.
Challenge Problem: (Due Wednesday, April 12) Determine what kind of job you want to have after you graduate. Research salaries for this job in your dream town. Using a home affordability calculator, determine how expensive a house you could afford based on this salary. Then, go to zillow.com, and choose a home to purchase (in your budget) in your dream town. Looking at current interest rates, choose a loan. Given this loan, calculate the following by hand. (You may use the online calculator to check your answers, but you must also work out the answers by hand.)
1. Your monthly payments.
2. The amount of interest you would pay by just making the minimal monthly payments.
3. The amount of interest you would pay by paying an extra $100 each month and how soon you would be able to pay off the loan.
4. The amount of interest you would pay by paying an extra $250 each month and how soon you would be able to pay off the loan.
Include the resources you used to determine your future salary, home affordability, loan terms, and the zillow page for the home you chose.
1. If you know how much you can afford to pay each month and you know the rate and term of the loan, how much can you afford to borrow?
2. Suppose you are several years into a given loan and you are offered to refinance to another loan at a different rate. What does it mean to refinance? Will this particular offer save you money?
3. Suppose you pay extra each month on your amortized loan. How much will you save in interest by paying ahead? How soon will you pay off the loan?
These are all very interesting questions to ask when you are looking at a loan. Question 1 simply requires you to solve for P in the formula below. Questions 2 and 3 will require a little more thought before we can solve them.
\[ P = R\left[\dfrac{1-\left(1+\frac{r}{m}\right)^{-mt}}{\frac{r}{m}}\right] \]
We will be learning how to use the formula to answer the questions above by hand. However, there are many calculators online to help answer these questions and more about taking out a loan. Below are links to some calculators that you may find useful when you want to consider taking out a loan in the future.
Bankrate.com
Amortization Schedule Calculator
Mortgage Payoff Calculator
Cost of Living Calculator
Is it Better to Rent or Buy?
We will only be considering fixed rate loans in all of our examples. But lenders may also offer you an adjustable rate mortgage (ARM). As the name suggests, with an adjustable rate mortgage, your rate can change, depending on market rates. These loans can be risky - if rates go up, so does your monthly payment.
Challenge Problem: (Due Wednesday, April 12) Determine what kind of job you want to have after you graduate. Research salaries for this job in your dream town. Using a home affordability calculator, determine how expensive a house you could afford based on this salary. Then, go to zillow.com, and choose a home to purchase (in your budget) in your dream town. Looking at current interest rates, choose a loan. Given this loan, calculate the following by hand. (You may use the online calculator to check your answers, but you must also work out the answers by hand.)
1. Your monthly payments.
2. The amount of interest you would pay by just making the minimal monthly payments.
3. The amount of interest you would pay by paying an extra $100 each month and how soon you would be able to pay off the loan.
4. The amount of interest you would pay by paying an extra $250 each month and how soon you would be able to pay off the loan.
Include the resources you used to determine your future salary, home affordability, loan terms, and the zillow page for the home you chose.
Thursday, March 30, 2017
Make-up Assignment for Friday March 31
We will not have class on Friday, March 31. Instead, you should complete the worksheet below. You may work in groups of 3-4 people. I will collect the completed worksheets in class on Monday, April 3. The videos below may also be useful.
Worksheet for March 31
Worksheet for March 31
Tuesday, March 28, 2017
Week 10 - Annuities and Amortized Loans
Last week, we looked at what happens when you take a fixed amount of principal, P, and invest it in an interest-bearing account for a set amount of time, t. We looked at simple interest and compound interest. You will need to be very comfortable with those formulas when it comes time for the exam. So far, the formulas you've seen have been
Simple Interest \[ A=P(1+rt)\]
Compound Interest, compounded m times per year \[A=P(1+\frac{r}{m})^{mt}\]
Compound Interest, compounded continuously \[A=Pe^{rt}\]
This week, we'll be looking at what happens when, instead of depositing once into your account, you make regular deposits of equal amounts for a set amount of time. This is called an annuity. The formula for the amount, A, in the annuity after t years, if you make m regular payments of R dollars per year is given by
\[A=R\left[\dfrac{(1+\frac{r}{m})^{mt}-1}{\frac{r}{m}}\right] \]
When we know A and want to solve for R, we sometimes call the account a sinking fund. On Wednesday, we'll start looking at amortized loans. Your school loans, car loans, and mortgages are all usually amortized loans. The formula we'll be using for this will be
\[PV = R\left[\dfrac{1-(1+\frac{r}{m})^{-mt}}{\frac{r}{m}}\right]\]
where PV (sometimes left as just P) is the present value of the loan (i.e., the amount you are borrowing).
We are taking a very simplistic look at these accounts. Other factors such as inflation, tax rates, and cost of living also will have a big impact on your investments and loans. The financial crisis in 2008 was precipitated by many factors. Your parents' or grandparents' retirement accounts may have been quite affected by the events surrounding 2008.
Challenge Problem: (Due Monday, April 3) Research the events leading up to the financial crisis in 2007-2008 and/or the subprime mortgage crisis that occurred during this same period. Some questions you might consider are: What caused so many banks to close in 2008? What is a subprime mortgage? What was the investment bank Lehman Brothers and how did its collapse occur? What impact did the collapse of Lehman Brothers have on global markets? What is Fannie Mae and Freddie Mac? What role did they play in the subprime mortgage crisis?
Write at least one page (typed) on your findings, being sure to appropriately cite your sources.
Simple Interest \[ A=P(1+rt)\]
Compound Interest, compounded m times per year \[A=P(1+\frac{r}{m})^{mt}\]
Compound Interest, compounded continuously \[A=Pe^{rt}\]
This week, we'll be looking at what happens when, instead of depositing once into your account, you make regular deposits of equal amounts for a set amount of time. This is called an annuity. The formula for the amount, A, in the annuity after t years, if you make m regular payments of R dollars per year is given by
\[A=R\left[\dfrac{(1+\frac{r}{m})^{mt}-1}{\frac{r}{m}}\right] \]
When we know A and want to solve for R, we sometimes call the account a sinking fund. On Wednesday, we'll start looking at amortized loans. Your school loans, car loans, and mortgages are all usually amortized loans. The formula we'll be using for this will be
\[PV = R\left[\dfrac{1-(1+\frac{r}{m})^{-mt}}{\frac{r}{m}}\right]\]
where PV (sometimes left as just P) is the present value of the loan (i.e., the amount you are borrowing).
We are taking a very simplistic look at these accounts. Other factors such as inflation, tax rates, and cost of living also will have a big impact on your investments and loans. The financial crisis in 2008 was precipitated by many factors. Your parents' or grandparents' retirement accounts may have been quite affected by the events surrounding 2008.
Challenge Problem: (Due Monday, April 3) Research the events leading up to the financial crisis in 2007-2008 and/or the subprime mortgage crisis that occurred during this same period. Some questions you might consider are: What caused so many banks to close in 2008? What is a subprime mortgage? What was the investment bank Lehman Brothers and how did its collapse occur? What impact did the collapse of Lehman Brothers have on global markets? What is Fannie Mae and Freddie Mac? What role did they play in the subprime mortgage crisis?
Write at least one page (typed) on your findings, being sure to appropriately cite your sources.
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