Finance algebra
With the following variables the periodic (annual) repayment is given by The recurrence equation for the balance b at the end of month x is derived from b[x + 1] = b[x] (1 + r) - d where b[0] = s giving The interest portion of the final payment is b[n - 1] r and the total principal repaid at the end of period n - 1 is s - b[n - 1] Solving simultaneously n = 8.9998 and s = 7240 The principal repaid at the end of the first period is s - b[1] or d - r s = 479.74
"I guess it depends on what you think ""tough math"" is.   A lot of finance folks have only a passing familiarity with algebra in day-to-day use.  At the portfolio-building level, it depends on the style of management. Pretty much every PM will be somewhat familiar with statistics into the concepts of linear regression. The quants, however, start going into all sorts of things. Multiple regression models to start with, but ARCH/GARCH stuff, vector autoregression, et cetera on the econometrics side. Other folks bring in things like martingale theory and some other things I don't know about.  Derivatives and arbitrage are where you'll probably find the most ""fun"" math. They use of binomial pricing models, various types of calculus, and whatever else they dream up these days. I don't work in this area, so I'm not as clued in here.  If you'd like to do something a little bit more guided than self-learning, check out the curricula for MS programs in Financial Engineering; they'll give some leads, too." Mortgage interest is a different story. That's a consumer financing consumption. A business is financing a profit making enterprise.  Not sure what the implications would be once this settles down -- probably less long term debt and a greater dependency on equity financing. "&gt; Not all Bachelor's are the same, DeVry...  Of course! A degree in ""gender studies"" is worthless, while a degree in ""computer science"" worth more. But, with so many ""computer science"" degrees, even that degree does not give you much headway... without experience.  It's very simple what happens today, compared to the past.  Today, the idea is to keep kids in schools, for as long as possible (because BAs are worthless and you need Masters), charge them tons of money, pass them so they continue to pay, get them into debt and then pay them less, because so many people have the degrees. Even require BA degree for jobs that don't need it.  In the past, if you finished high school, it was an accomplishment. If you got accepted to college, it was an accomplishment. If you survived the first year in college or got your bachelor degree, it was a major accomplishment.  **If you did not know, those accomplishments in the past gave you substantial(!!!) benefits compared to others.**  It was much cheaper in the past and much better education. They did not care about money, and will kick you out of college for any fail.  So, in the past to be a teller in the bank, you did not need to finish high school, but just be good with basic algebra.  **Today, you need a BA degree and get a lousy salary to be teller in a bank. Do you understand what happened here?**  Also, in the past, a person with lower socioeconomic background, if they finish high school or got a BA, it would (for sure) really change their lives and they become middle or high class.  Today, a person with poor socioeconomic background, even if they got their [worthless] BA degree, they are worst off because they do not have any competitive advantage over other people as all of them have degrees too... you are worst off, because you are in debt to get the degree and the ""education"" you got is bad." FYI: David Knopf is a graduate of Princeton with a BA in Econ. His parents are rich. Like totally fucking rich. You might do better. If your parents make less than $140k, tuition at Princeton is zero. Of course your chance of getting into Princeton, unless you are a legacy admission, or ace the SAT, is about zero. Better bone up on Algebra if you want to ace the SAT. And yes, you ARE a math person. Everyone is. It's just that nobody ever taught you right.  Forget about the CCNA or CCNP, that stuff will be obsolete before you would finish learning it. And even if you did, some H-1 visa immigrant will do the job for a quarter of what it would cost you to make a living.  I completely sympathize with your situation. I'm not going to pour out my life story, but I always thought I'd be a multimillionaire by the time I was 30. Instead, I have made choices that took a troublesome path, including depression and poverty. Even today I am suffering from choices I made (or avoided making) decades ago. BUT I am suffering only by OTHER people's standards. I don't regret the choices I made. I turned down fast money I could have made by exploiting people, it would have only cost me my soul. I have been exploited by other people, and it taught me the value of dealing with people who have ethics like my own. So ultimately, you have to admit to yourself, you are exactly where you need to be. You are struggling because what you want to do is hard. I am an artist too, and that is just about the hardest thing to do on this earth. If it was easy, anyone could do it. So don't despair, get busy. I remember when I lived in a slum, barely subsisting, but I had a sunny window and a table, I spent $2 on a cheap brush and a tube of black watercolor, and a $2 tablet of cheap watercolor paper. And I sat at that sunny table and made art that made me happy. Nobody but me has ever seen it. And for all the changes I have gone through in decades since, I would give almost anything to be living in abject poverty, sitting at that sunny window with that cheap paintbrush in hand again. [So I'll just leave you with this odd comic by Carol Lay, it's one of my all time favorites.](http://i.imgur.com/4XsDbnE.gif) I was wondering if someone could recommend a textbook  I'm taking a course right now in foundations of finance and we're dealing with subjects such as utility functions, risk aversion, prudence, temperance, Arrow-Debreau securities, portfolio theory, and more  I'm finding the textbook we're using (Intermediate Finance, Danthine &amp; Donaldson) a bit hard to understand Assuming you were immersed in math with your CS degree, the book **'A Non-Random Walk Down Wall Street' by Andrew Lo** is a very interesting book about the random walk hypothesis and it's application to financial markets and how efficient markets might not necessarily imply complete randomness.    Lots of higher level concepts in the book but it's an interesting topic if you are trying to branch out into the quant world.  The book isn't very specific towards algorithmic trading but it's good for concept and ideas.  Especially for general finance, that will give you a good run down about markets and the way we tackle modern finance.    **A Random Walk Down Wall Street** (which the book above is named after) by **Burton Malkiel** is also supposed to be a good read and many have suggested reading it before the one I listed above, but there really isn't a need to do so.    For investing specifically, many mention **'The Intelligent Investor' by Benjamin Graham** who is the role model for the infamous Warren Buffet.  It's an older book and really dry and I think kind of out dated but mostly still relevant.  It's more specifically about individual trading rather than markets as a whole or general markets.  It sounds like you want to learn more about markets and finance rather than simply trading or buying stocks.  So I'd stick to the Andrew Lo book first.    ---  Also, since you might not know, it would be a good idea to understand the capital asset pricing model, free cash flow models, and maybe some dividend discount models, the last of which isn't so much relevant but good foundations for your finance knowledge.  They are models using various financial concepts (TVM is almost used in every case) and utilizing them in various ways to model certain concepts.  You'd most likely be immersed in many of these topics by reading a math-oriented Finance book.  Try to stay away from those penny stock trading books, I don't think I need to tell a math major (who is probably much smarter than I am) that you don't need to be engaging in penny stocks, but do your DD and come to a conclusion yourself if you'd like.  I'm not sure what career path you're trying to go down (personal trading, quant firm analyst, regular analyst, etc etc) but it sounds like you have the credentials to be doing quant trading.    ---  Check out www.quantopian.com.  It's a website with a python engine that has all the necessary libraries installed into the website which means you don't have to go through the trouble yourself (and yes, it is fucking trouble--you need a very outdated OS to run one of the libraries).  It has a lot of resources to get into algorithmic trading and you can begin coding immediately.  You'd need to learn a little bit of python to get into this but most of it will be using matplotlib, pandas, or some other library and its own personal syntax. Learning about alpha factors and the Pipeline API is also moderately difficult to get down but entirely possible within a short amount of dedicated time.     Also, if you want to get into algorithmic trading, check out Sentdex on youtube.  He's a python programmer who does a lot of videos on this very topic and has his own tool on quantopian called 'Sentiment Analyzer' (or something like that) which basically quantifies sentiment around any given security using web scrapers to scrape various news and media outlets.  Crazy cool stuff being developed over there and if you're good, you can even be partnered with investors at quantopian and share in profits.    You can also deploy your algorithms through the website onto various trading platforms such as Robinhood and another broker and run your algorithms yourself.    Lots of cool stuff being developed in the finance sector right now.  Modern corporate finance and investment knowledge is built on quite old theorems and insights so expect a lot of things to change in today's world.  ---  With a math degree, finance should be like algebra I back in the day.  You just gotta get familiar with all of the different rules and ideas and concepts.  There isn't that much difficult math until you begin getting into higher level finance and theory, which mostly deals with statistics anyways like covariance and regression and other statistic-related concepts.  Any other math is simple arithmetic. "For 3X, it's about 114, and for 4X, 144, which naturally, is twice 72.  These are close, back of napkin, results. With smart phone apps offering scientific calculators, you should get comfortable just taking the nth root of a number for a more precise answer.  Update in response to Brick's comment. The rule of 72 says that (n)(y)=72 to double your money. It answers both questions, how much time do I need, given a rate, and how much return do I need, given a time?  Logic tells me that if 72 is the number to double, 144 is the 4X. But I'm a math guy, and my logic might not be logical to OP. So -  Let's take the 20th root of 4.   This is the key to use. 4, (hit key) 20, equals. The result is 1.07177 or 7.177%. And this is the precise rate you'd need to quadruple your money in 20 years) Now (n)(y)= 20* 7.177 = 143.55 which rounds to 144. ""Rule of 144"" to quadruple your money.  This now answers OP's question, ""How to derive a Rule of X"" for a return other than doubling.  One more example? I want 10X my money. Of course I need the initial guess to enter one calculation. People like 8%, in general. It's a bit below the 10% long term S&P return, and a good round number. The Rule of 72 says 9 years to double, so, 18 years is 4X, and 36 years is 8X. For my initial calculation, I'll use 40 years. The 40th root of 10. I get 5.925% (Again the precise rate that gives 10 fold over 40 years) and multiplying this by 40, I get a ""Rule of 237"" which I'm tempted to round to 240.  At 6%, 237/6= 39.5 yrs,  1.06^39.5 = 9.99 At 6%, 240/6= 40.0 yrs,  1.06^40.0 = 10.29 You can see that you lose some accuracy for the sake of a number that's easier to remember, and manipulate. 72 to double is pretty darn accurate, so I'll stick with ""Rule of 237"" to get 10X my money.   To close, the purpose of these rules is to create the tool that lets you perform some otherwise tough calculations away from any electronic device. Of course I know how to use logs, and in real life I'm paid to explain them to students who are typically glad when that chapter is over. I've shown above how the ""Rule of X"" can be formulated with a power/root key, which, for most people, is simpler. Ironically, log calculations as @jkuz offered, force a continuous compounding which may not be desired at all. It would give a result of 230 for my 10X return example, and the following (using the first equation he offered) - At 6%, 230/6= 38.3 yrs,  1.06^38.3 = 9.31 which is further away from the desired 10X than my 237 or rounded 240." Here's a very good series of classroom lectures by Robert Schiller, one of America's top economists and a prof at Yale:  http://www.youtube.com/user/YaleCourses#g/c/8F7E2591EE283A2E  This should give you some general insight into basic principles of finance and give you a framework to learn more later.