Test 2 Study Guide: Finance

The purpose of this test experience is to help you understand the material and make connections. Research has shown that the effort you expend in studying for tests and clearly explaining your work solidifies your learning.

At the Exam

  • One 8.5*11 sheet with writing on both sides allowed. You can put anything you like on your sheet.
  • One scientific calculator or graphing calculator mandatory (but no cell phone nor other calculators bundled in combination with additional technologies)
  • You may have out food, hydration, ear plugs, or similar if they will help you

    On the test, your grade will be based on the quality and depth of your responses in the timed environment (the test must be turned in when time is called). Questions will mainly consist of computations and short answer or essay types. There is NO need to write in full sentences - bullet points, etc will be fine.

    The test will be a mixture of computational questions as well as critical reasoning and reflection involving the "big picture." You will be expected to answer questions about activities from class or lab and the homework readings. For instance, review the following:

    Computational Questions

    You will be given targeted finance questions with various parts, like on homework and in class, and this will form the majority of the test:
  • ASULearn Jane and Joan,
  • the Benjamin Franklin lab
  • the ASULearn Car loan practice
  • the Condo and Car Purchases: Decisions, Decisions (Part 1)
  • Car Purchases: Decisions, Decisions (Part 2)
  • How Do You Know Exercise Set 1.2 #9, 14, 21, and 24 and Exercise Set 1.3 # 8, 10
  • Clicker questions from classes (but not in multiple choice format)
  • and the recent ASULearn Material Review Questions for Test 2 (but not in multiple choice format)

    For instance, in part a) you might be asked for a monthly loan payment, in part b) the total paid, in part c) the first month's interest... So review the lump sum, periodic payment and loan payment scenarios as well as the total paid/put in, the total interest, the first months interest, "simple" interest...

    You can expect to have scenarios that are similar to what we have seen.

  • Be sure that you could explain information given on a student loan statement or an Excel amortization table (see class notes, condo lab chart and Paying extra each month on option 2, ASULearn car loan practice problem, and the student loan work as a review of this), and that you could relate that information to by-hand formulas that we have used and answer questions on it. You will NOT be tested on Excel formulas such as =B3*$c$2, but you might be asked how to write down how you would get a number in an excel box using by-hand formulas, or you might be asked to use a portion of an Excel table (and your knowledge of how it works) in order to answer questions like how much interest you save when you pay extra money each month (the condo lab is a good review of this):
    For table 2, when paying extra, the 2nd row is
    325     538.51     0.79     537.71     -385.27
    which is also the first row of the amortization table with a negative balance. To calculate the total interest in this case,
    325*538.51 - 385.27 - 84212,
    ie the number of months times the monthly payment minus the overpayment that last month minus the original loan amount.

  • Make sure that you understand the what we have gone over in class and the "calc keys" that will work with the calculator you will have that day (no cell phone allowed nor anything bundled in combination with additional technologies).

    For the test, you might need to

  • write down the setup of the formula with numbers,
  • explain why (in words) the formula you chose applied to this problem,
  • solve the problem on your calculator, and
  • write down "math common sense" - did your answer make sense or not and WHY?: For example, "we have seen that it is possible to double your money in about 20 years because it is sitting there a long time", or "it makes sense that the interest on the loan is more than the loan itself since the bank is loaning us a large lump sum up front, and we are taking a long time - 30 years - to pay it back. The bank could have deposited their money in a lump sum account instead of loaning it to us, and the money would have more than doubled in this account. Hence, we must pay back more than double the interest."

    Other Directed Questions and Short Essay Questions

    You should review the philosophy of how we derived
    lump sum philosophy,
    periodic payment philosophy
    loan payment philosophy - a good review is the ASULearn Review Questions. You should be able to answer questions like where the 1 comes from in the lump sum formula, where the -1 comes from in periodic payment, where the negative power comes from in the loan formula by philosophically expaining what these stand for/represent in the context of how we obtained the formulas.

    You will also be asked to look at examples from the finance segment and discuss the similarities with the following themes:

  • Impossibility of checking all the cases, but finding a solution by shifting our viewpoint (Jeff Weeks' research) A similar example from the finance segment occurred in the derivation of the periodic payment formula - we looked at the future value of each payment. Even though we found a pattern, it was impossible to use for long time periods since there were as many terms as compounding periods. So next we stepped back, shifted our view of it by transforming it by a common piece and then we combined the shifted equation with the original. The overlap cancelled to give us a general formula that was easy to use and only had a couple of terms. Specifically, breaking it up into manageable parts and combining the shifted equation with the original was similar to Jeff Weeks' research research on higher dimensional spaces, since each involved looking at a change in view and organization that eventually simplified an impossible problem and made it possible to solve.

  • Impossibility of constructing a solution but finding a non-constructivist approach. (Jeff Weeks' research) Thrifty Saver's account from The Simpsons
    Lisa: I got their new Thrifty Savers savings account, with 2.3% annual interest instead of the normal 2.25%, so a year from now, *I'll* have an extra nickel.
    .05= 100 (1+ .023/n)n - 100(1+.0225/n)n
    It was impossible to construct a solution since the unknown compounding period appeared both in the power and what was being raised to the power. So algebraic techniques cannot construct a solution [even logs aren't powerful enough for this problem]. Goal Seek in Excel also was not powerful enough to solve this for us, and gave us an answer that did not make sense, so we used the Equation Solver in Excel along with common sense and a "guess and check" perspective - this is not a constructivist proof, as it does not show us how or why it works. Instead the computer (or we) guesses and checks until it finds an answer [and then we use common sense to evaluate whether that answer suffices].

  • How the number of stars in the universe can connect to finance. Recall the Richard Feynman quotation: There are 1011 stars in the galaxy. That used to be a huge number. But it's only a hundred billion. It's less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers.

  • Also think about
    local to global connections
    ethical connections
    what is mathematics theme
    diverse ways that people succeed in and impact finance theme
    truth and consequences (When are we convinced? What are the consequences of certain truths? What is the role of chance and probability?) theme
    For instance, a question could be phrased like: Name an instance where we discussed the theme of truth and consequence and the role of chance and probability, or a more directed question like, discuss how that theme arose during our investigation of our discussion of the lottery. Similar types of open ended and/or directed questions would ask about the other themes.

    Additional Resources

  • Here is a partial sample test so that you can see examples of question formatting. The actual test will be about 5 pages long.
  • The main web page and class highlights page contain links to homework readings and class activities and clickers, which also serve as a good review.
  • Also see the glossary/wiki on ASULearn
  • and the ASULearn Review Questions for Test 2.

    I want you to succeed and I am happy to help you understand by answering questions in class or online, or going over material with you in office hours. Here are a few words of encouragement that are adapted from Heart of Mathematics:
  • To really learn something new, you must experience it yourself via hands-on hard work and practice. We don't learn deeply by watching someone else. You could watch many movies about baseball, but in order to really learn how to play well, you must actually pick up a bat yourself.
  • The only stupid question is the unasked question.
  • Make mistakes and fail but never give up. Instead, learn from your mistakes and use them to grow.
  • Life is a journey - not a destination. Someone could give you all THEIR answers, but it is your experiences and what you've learned during the process that really matters.