Worksheet for March 31
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.
Wednesday, March 22, 2017
Week 8 - Reminders for Friday
I appreciate your patience this week with my missing class Monday and Wednesday. If you did not turn in your worksheet in class today, I will accept it at the start of class on Friday. If you would like to make corrections to a worksheet that you turned in, I will accept that on Friday as well.
Be sure that you watch the video from Monday’s class if you haven’t already.
Your midterm grades include all the homework submitted up to this point, 2 exams, participation, and 2 comments on the blog. If you have not commented on the blog yet, please make sure that you start doing so.
Below are some links to articles that describe the power of compound interest and why it's better than simple interest. Click on the links and comment with your thoughts.
I will be having additional office hours this week on Thursday from 12:15 pm - 2:00pm. If you have questions over the material covered on Monday or Wednesday or questions about your midterms, please come see me.
Friday's office hour at 9:00am will be moved to Agenstein 126.
I will be handing your exams back on Friday or you may pick them up in my office on Thursday.
Sunday, March 19, 2017
Week 8 - Simple and Compound Interest - Class Makeup Video
This week, we will begin a new unit on Financial Math. Please make sure you print out the notes and bring them with you to class. We will start this week with a discussion of interest - simple interest and compound interest. There will be a lot of formulas in this unit, and you will need to practice with them to get comfortable using them. I will provide you with the formulas (unlabeled) for the exam, so you need to focus on identifying what formulas apply to what problems. In addition, it will be very important to remember your calculator for class every day in this unit - you don't want to have to do these calculations by hand!Those of you in MAT099 should have been reviewing logarithms and exponentials in that class recently. We will be using logarithms to help solve problems in this unit; if you need additional review of logarithms, please see me. The webpage below is also a good source of review for problems involving logs and exponents.
Exponential and Logarithmic Equations
We will be starting with simple and compound interest on Monday. Unfortunately, due to a nasty stomach bug that's been taking down my family one-by-one this weekend, I need to cancel class on Monday. To make up for this, I have recorded a video lecture over simple and compound interest. Please watch the video below and then complete the worksheet linked below. I will be collecting the worksheet in class on Wednesday, March 22.
Challenge Problem (Due Monday, March 27): A PayDay loan company charges $25 in (simple) interest for every $100 borrowed for a 14 day loan. The total borrowed, plus interest must be paid back at the end of 14 days. Suppose you want to borrow $400 to pay for your Spring Break trip. How much will you be required to pay back at the end of 14 days? What is the interest rate on this loan?
Exponential and Logarithmic Equations
We will be starting with simple and compound interest on Monday. Unfortunately, due to a nasty stomach bug that's been taking down my family one-by-one this weekend, I need to cancel class on Monday. To make up for this, I have recorded a video lecture over simple and compound interest. Please watch the video below and then complete the worksheet linked below. I will be collecting the worksheet in class on Wednesday, March 22.
Challenge Problem (Due Monday, March 27): A PayDay loan company charges $25 in (simple) interest for every $100 borrowed for a 14 day loan. The total borrowed, plus interest must be paid back at the end of 14 days. Suppose you want to borrow $400 to pay for your Spring Break trip. How much will you be required to pay back at the end of 14 days? What is the interest rate on this loan?
Friday, March 3, 2017
Lecture Video
I made a video last semester over the most recent material covered in MAT110(E). I have linked the video below if you would like to use this to review this material.
Remember that our Probability and Statistics exam will be in class on Friday, March 10. An exam review is posted on the right side of the blog.
Remember that our Probability and Statistics exam will be in class on Friday, March 10. An exam review is posted on the right side of the blog.
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