Mathematical Thinking Exam 1 09 October 2017

Transcription

1 Mathematical Thinking Exam 1 09 October 2017 Name: Instructions: Be sure to read each problem s directions. Write clearly during the exam and fully erase or mark out anything you do not want graded. You may use a scientific or graphing calculator for any calculation or derivation unless otherwise stated so long as you show your work leading up to that point and then state that that is what you are doing. You must show all your work to receive full credit unless otherwise stated. Don t cheat. See below. Prohibited: Class Notes Class Handouts Study Guides and Materials Previous exams or exam solutions The Book Any Electronics (excluding approved calculators) This includes, but is not limited to, all: computers, phones, tablets, ebook readers, headphones, audio players, dictionaries, and translators. Other People s Exams Page: Total Points: Score:

2 MATH 101 Exam 1, Page 2 of October 2017 (Some) Financial Formulas A = P (1 + rt) A = P (1 + i) n A = [ (1 + i) n ] 1 d i d = [ ] i A (1 + i) n 1 g = r a 1 + a $1 = $1 $a 1 + a 1 + a A = [ (1 + i) n ] 1 d i d = [ ] i P 1 (1 + i) n d = P 12t(1 rt) d = P (1 + rt) 12t out of a possible 0 points

3 MATH 101 Exam 1, Page 3 of October 2017 Multiple Choice For this section, you must write the letter corresponding to the correct answer in the blank space provided on the right side of the exam. Markings on the question itself will not be given any credit. 1. (3 points) The voting system which does not always produce at least one winner when there are an odd number of voters is A. Plurality. B. Condorcet. C. Dictatorship. D. Sequential Pairwise. 2. (3 points) What is the name of the theorem that states there can never by a voting system of 3 + candidates that always produces a winner, satisfies Pareto s condition and IIA, and is not a dictatorship? A. May s B. Arrow s C. LaGrange s D. Bexley s 3. (3 points) In a two option election, which of the following fairness criteria does Imposed Rule fail? A. Never Ties B. Fair to Voters C. Fair to Options D. Monotone 4. (3 points) You have $5, 000 to invest at 6% simple interest. How much money will you have after 3 years? A. $5, 300 B. $5, 900 C. $6, 800 D. $15, (3 points) What is the APY for 6% compounded weekly? A. 6.00% B. 6.09% C. 6.18% D. 7.25% 6. (3 points) Suppose your fourth grade teacher bought a house in 1990 for $125, 000 and sold it in Knowing that that the CPI for 1990 was and the CPI for 2016 was , how much was the house worth when it was sold? A. $68, B. $127, C. $229, D. $245, 342, (3 points) A 15% loan rate is most favorable (from the borrower s perspective) if compounded A. continuously. B. daily. C. monthly. D. annually. 8. (3 points) What is the APR of a credit card loan with a 1.660% monthly interest rate? A % B % C % D % out of a possible 24 points

4 MATH 101 Exam 1, Page 4 of October 2017 Computation and Techniques 9. Use the following election for the below parts. Rank (10) (14) (13) (8) First A C B D Second B D A A Third C A D C Fourth D B C B (a) (6 points) Which candidate would win if the Hare system is used? (b) (6 points) Which candidate is the plurality runnoff winner? out of a possible 12 points

5 MATH 101 Exam 1, Page 5 of October Jason wants to buy a house for $205, 000 and can pay out of his savings, a 20% down payment on it. (a) (3 points) How much money does Jason need to take out as a loan to afford the house? (b) (7 points) If Jason can secure a 30-year, fixed rate loan at 5.125% and makes no additional payments on the loan, what will he end up paying for his house after 30 years? Assume that he must make monthly payments (most mortgages require this schedule). out of a possible 10 points

6 MATH 101 Exam 1, Page 6 of October 2017 (c) (7 points) In this scenario, what would be his monthly payments? (d) (7 points) Assume that Jason decides he can actually afford to take out a 15-year, fixed rate loan at 6.875%. How much would he save by taking the 15-year loan compared to the 30-year loan from the previous part or would he actually pay more in total? (Again assume monthly payments.) out of a possible 14 points

7 MATH 101 Exam 1, Page 7 of October 2017 Concepts 11. (10 points) Produce a preference list ballot of 13 voters showing that the plurality voting system can elect as a winner, the option that appears last on the majority of ballots (7 of the 13). Be sure to justify your ballot with complete sentences and do actually calculate the winner. out of a possible 10 points

8 MATH 101 Exam 1, Page 8 of October (10 points) Suppose you decide you want to have two million dollars saved by the time you retire in 40 years to be able to live comfortably. If you can get a 10% return in the stock market (big assumption), how much do you have to save (invest in the stock market) each month to reach this goal? 13. (3 points (bonus)) How much money in 40-years would you need if in fact you wanted 2 million dollars in today s money? out of a possible 10 points

9 MATH 101 Exam 1, Page 9 of October 2017 Short Response 14. A voting system is said to satisfy the Majority Criterion if an option ranked first by a majority of voters is always among the winners. For each of the following voting systems, explain in a few sentences why the voting system satisfies or doesn t satisfy the Majority Criterion. (a) (5 points) The Plurality System (b) (5 points) The Borda Count System out of a possible 10 points

10 MATH 101 Exam 1, Page 10 of October (10 points) Explain what the real (effective) growth rate tells a person. Complete the following problem and reference it in your explanation when describing each of the factors. Nyki wants to make an investment that will have real growth rate of 12%. If inflation is current at 2.7%, what annual interest rate much she earn to get on her investment to accomplish this goal? out of a possible 10 points