### Test 2 Study Guide: Mathematicians and Finance

One 8.5*11 sheet with writing on both sides allowed. You can put anything you like on your sheet. Calculator is mandatory (but no cell phone nor other calculators bundled in combination with additional technologies).

### Targeted Problems

You will also be given targeted finance questions, like on homework and in class:
• ASULearn Jane and Joan,
• the Benjamin Franklin lab and project,
• the ASULearn Car loan practice
• the Condo and Car Purchases lab
• How Do You Know Exercise Set 1.2 #9, 14, 21, and 24 and Exercise Set 1.3 # 8, 10
• and the recent ASULearn Material Review Questions for Test 2

You can expect to have problems that are similar. For the ASULearn questions, be sure that you could explain WHY each answer is true or false.

• 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 - see table 2 and the related questions).

• Make sure that you understand the "math common sense" we have gone over in class and the "calc keys" that will work with your calculator.

For the test, you will 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."

### Big Picture Reflection

You should review how we derived each of the lump sum, periodic payment and loan payment formulas - a good review is the ASULearn Review Questions.

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

• Impossibility of checking all the cases, but finding a solution by shifting our viewpoint (Andrew Wiles' 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, combining the shifted equation with the original was similar to Andrew Wiles explaining what would go wrong if there was a solution, 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. (Andrew Wiles' research) Thrifty Saver's account from The Simpsons
.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].

• Also think about local to global connections and ethical connections in both the mathematician and finance segments.

### Success

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.