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.
I find the topic Finance interesting and useful. I know many people who were affected by the financial crisis in 2008 especially regarding their home mortgages. I also hope that we go into student loans a bit during this section.
ReplyDeleteWe will spend most of next week on amortized loans, which is what your student loans would be.
DeleteI was very nervous for this section of Math, but so far it seems very understandable. I was most nervous for learning to do logs because it was something not taught at my high school, but the way you and the sub talked about it made it very easy to understand. As for the annuity I am still a little confused about the algorithm we use, but hopefully it will make more sense on Wednesday.
ReplyDeleteI hope Wednesday helped solidify the methods for solving questions about annuities!
DeleteI find the Finance portion much easier than the last two. I understand this section a lot better. The only thing im not sure about is what ammune means?
ReplyDelete-Jessica Nagel
I'm not sure what ammune means either - is that a typo?
DeleteI think the simple interest pretty simple but, when I got into compound interest I think the problems get harder to set up.
ReplyDeleteThey do have an extra variable and take a little more effort to solve for r or t.
DeleteIn finance set 2, question 12, there were a few questions dealing with annuities. I have been stumped on this one because it does not have the amount of times the account is compounded yearly. If it doesn't say the account is compounded monthly, quarterly, semiannually etc. what are we supposed to put in for m? Is it assumed that its 12 because we add money to the account every month or is this some kind of error?
ReplyDelete-Caleb Klingseis
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ReplyDeleteSimple Interest,Compound Interest, and Compound Interest, compounded continuously are the only three I really understand everything is confusing, and I feel like we are rushing to get everything done and its not helping at all.
ReplyDeleteSo far, this has to be my favorite section we have started. It seems to be one of the easier sections, because it's all about plugging into formulas. The hardest part is probably figuring out how to use basic mathematical properties in the right way so as to get a correct answer. For example, bringing down unknown exponents by using natural log. Once you get the hold of these properties and how to use them properly, the answers seem to fall into place. I also enjoy this section because it's so easily applied to real life situations. I can actually see myself using these formulas in the near future!
ReplyDeleteI was a little afraid of financial math, but have found it to already be quite insightful. I figured this unit would be much harder than it has been thus far. The material we are dealing with is very easy to figure in to one's everyday life and financial decisions. I'm happy we are learning about this.
ReplyDeleteI understand the simple interest and compound interest and find that to be easier than the annuities and sinking funds. I think the annuities and sinking funds are hard when you have to solve for the rate.
ReplyDeleteThank you for the extra videos to substitute for lecture. It helps me take it in when I can watch a problem being broken down step by step over and over again rather than trying to sort it out in my notes.
ReplyDeleteI was nervous at first when we started financial math because I did not think I would understand it. After classes this week I really understood what I was doing wrong and how this math is very simple if you follow step-by-step. I am very glad we are learning financial math and how to calculate the annuity and sinking funds because we will need it now and in the future.
ReplyDeleteI have found the PowerPoints and the videos very informational and helpful. The formulas are a lot to remember, but they aren't hard to get comfortable with. You just have to know what you are looking for in the problem. I have found the ways in which you have explained how to use these formulas very helpful and informational. I appreciate the fact that these formulas are everywhere in order to remind us and keep us comfortable with them; they are posted on the blog, in the video, and in the PowerPoints also.
ReplyDeleteI was very nervous coming into this new section about financial math. But now that we have been going over it this week, I was wrong because it's actually very simple if you follow the steps and memorize the equations and which one to use for the right problem. The confusing part is on webwork, like when you need to put your answer into a decimal, its not specific on how many numbers you need after the decimal point.
ReplyDelete-McKenzie Rhodes
For the most part I understand that the problems should give some hint about which way to set the problems up but I still get confused. After watching the videos they have cleared them up part of the way, so I am not as confused.
ReplyDeleteI love financial math, it makes me better understand how money works, but I am having trouble understanding annuity formulas and why they are useful for people.
ReplyDeleteI like the finance math it has help me learn how to calculate how much my interest i am saving when i pay extra on my car.
ReplyDeleteAlthough I did worse on this topic than any other topic I liked that the math was pretty straight forward about what you had to do. you just had to know what formula to use in certain situations. For me the tricky part was knowing what to do when you had to use log and ln.
ReplyDelete- Tiana Butler