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Expectations for Project Work
Form a group of about 3 students and together select one of the approved topics for your project. Please note the due date carefully - late projects will not receive full credit. Projects must be typewritten on 81/2 x 11 paper - but math formulas, equations, diagrams can be written in by hand only if done neatly. In your project you should pay particular attention to the following guidelines:
- The project is a report on an investigation or question. This means your report should begin with an introductory paragraph in which you discuss the question or problem that you are examining and introduce briefly how you approached your work, perhaps give a brief statement of something that you discovered or a conclusion you will examine in more detail later in the report. The next part of your report will be the main body in which you discuss your work, give your analysis, and demonstrate your results. The last part of your report should be a nice summary of your findings and conclusions backed up by the evidence you presented in the middle part of your report.
- As with any report or project for a university course, you should edit your report at least once before submitting it for grading. Things to look for in the editing process include typographical errors, grammar and spelling errors, and awkward writing. All members of the group should read the final draft of the project, approve it before it is submitted, and sign their name on the title page. If there is group member who has made no contribution to the project, the instructor should be informed and that student's name not included in the report.
- Equations and calculations should be accompanied by explanations given in complete sentences of what these calculations mean.
- If tables or graphs are attached at the back, then the main body of the report should include correct references to page numbers and figures.
- Sources used for information or data should be described and adequate references for these sources given. Material taken from references must be summarized in one's own words. Students should be aware of issues of plagiarism in "copying and pasting" information.
The analysis of the problem, organization of work, grammar, and spelling will all be considered in the project grade. Specifically, in evaluating the projects we will consider the following.
Mechanics: (5 points) Spelling/grammar; neatly typed on 81/2 by 11 paper; title page with project title and names of group members; references cited correctly.
Mathematics & Analysis: (15 points) Correct use of mathematical concepts; math concepts accurately described and explained; calculations correct; appropriate use of models/reasoning; logical reasoning in presenting arguments or making conclusions.
Group Work/ Presentation: (5 points) Thoughtful approach to the topic; depth of research; organization of ideas; clarity of discussion; unusual aspects of project; appropriate group effort.
Individual Work : (5 points) After you have submitted your projects, you will be asked to evaluate the contribution of the members of your group. These evaluations will be taken into consideration for each member's individual grade.
2. Planning for Retirement (Ch 4: compound interest; investment plans; percents) Many practical questions arise in dealing with one's finances. Pick a newspaper or magazine article published during the past year that discusses the savings patterns of Americans (provide the name of the newspaper/magazine and the date of the article). Examine the article in your group, summarizing the points made, and then do the following problem.
Suppose that Julia, age 30, opens a bank account paying 2.5% annual interest compounded monthly. She plans to deposit $250 each month in the account. Assuming the interest is the same for the next 35 years, how much will Julia's account be worth when she retires at age 65? Compare her accumulation to her total investment both in absolute and relative terms. Then do the same analysis for Bob who is 20 and for Beth who is 40. Now, summarize and compare the investment results of these three people and discuss the implications for saving for retirement. Certainly saving from a younger age will accumulate more funds, but are there any other noteworthy results from your data? How would you compare the return on the investments made? Were there any connections between your calculations and the article you've read? ( In doing your calculations you will find the formulas in Ch 4 very helpful.)
Now, determine how much you think you can afford to save per month and determine what kind of interest rate you could get at your bank. Depending on how old you are and when you want to retire, determine how much savings you could accumulate. Would it be possible to live on the interest from your accumulation when you retire? Estimating a 2.5% APY at that time, what would your annual interest, or your yearly income from your savings, amount to when you retire? Determine how much this yearly income would be in terms of today's dollar if you assume 2% annual inflation over the years till you retire. Suppose you merely wanted your interest from the account to supplement your retirement income (the more likely scenario) and to correspond to $20,000 today, how much should you plan to have in your savings account when you retire and what would you need to deposit each month to reach that goal? Most likely the interest from your savings will be only one of the sources of income you will have when you retire. What other methods of saving or sources of income are generally used to plan for retirement? Discuss some of these briefly and present their benefits and drawbacks. Check out the web site on retirement issues, http://www.fool.com/retirement.htm?ref=G02A04, and read one of the relevant columns. Finally summarize your findings and any conclusion(s) your group has made.
3. Home Mortgage (Ch 4: compound interest, savings and loan formulas) In this project assume that you have a regular job, that you are planning to buy a house and that you want to investigate some of the financial aspects of buying a house and obtaining a mortgage. First, determine what criteria you desire in your house and then either contact a realtor or use the internet to find out the approximate cost of such a house. Then decide how much you can afford as a down payment and what you will need to borrow.
Now, shop around for a mortgage, contacting at least two mortgage companies or banks, and find out: a) The APR for a 15 year loan, 30 year loan, and for an adjustable rate mortgage; b) The total closing cost - you may want to get a truth and lending statement c) Determine the cost of mortgage insurance - can you afford a large enough down payment to eliminate mortgage insurance.
With the above information, choose a mortgage company and calculate the following: a) The monthly payment on each of the 15 year loan and the 30 year loan. Be sure to show your calculations. Does this agree with what the lender quoted? b) Next calculate the total cost of the 15 year loan and the 30 year loan as well as how much you will pay in interest for each loan. c) If you could afford to pay an extra $180 a month toward your principle, estimate by trial and error (or see your instructor for an easier method) how long would it take you to pay off your mortgage. How much would you save in interest over the length of the loan? Would you be better off in the long run if you invested this $180 a month in a mutual fund? Explain.
Now investigate the adjustable rate mortgage. What will your starting monthly payments be? What is the upper limit of the APR? How fast can it move to the upper limit and what would your monthly payments be if you did have to pay the upper limit on the APR? Check out the following web site and report any useful information you find here: http://www.fool.com/homecenter/finance/finance.htm.Finally, summarize your findings as you examine the circumstances under each option might be the most reasonable choice.
4. Financial Aspects of Buying a Car (Ch 4: compound interest, loans, amortization tables) You want to buy the "car of your dreams". Determine the price of the "car of your dreams" by going to a new car dealership or looking in the newspaper. Find out the tax and the license fees for the car. Let's assume that you cannot buy the car outright and will need a car loan. Contact at least two of the following: a bank, credit union, or other financial institution. Find out the rates for 3-year, 4-year, 5-year auto loans. Also find out what percentage down payment is required. State which financial institution you have chosen to use and why.
Now, calculate the amount of the loan you will need (selling price of the car minus the down payment) and use one of the formulas in Ch 4 of your text to calculate your monthly payment on the loan. Calculate the payments for: i) 3-year loan, ii) 4-year loan, iii) 5-year loan. Also, calculate the amount of money that you will need before you can take possession of the car (down payment, tax, license fees). Now write an amortization schedule for the first year of payments on the 3, 4, and 5 year loans. You should include the following: Payment No., Payment Amount, Interest Paid, Principal Repaid, and Balance. Then, calculate the total amount that you will pay for each of those auto loans over the three, four, or five year period.
expenses, when both children will be attending college, and so on. You will have six savings accounts in all.
From your chart, you will know how much you will want in savings account #1 after 16 years. Compute the monthly payment required to reach this goal. Also from your chart, you know how much you will want in savings account #2 after 17 years. Compute the monthly payment required to reach this goal. Do this for each of the six savings accounts, then add the six different monthly payments together to find your total monthly payment. Discuss whether this will be a reasonable amount for you to invest each month. Finally, compute the total amount you will have invested and compare this to the total cost of your children's educations. Discuss the benefits and drawbacks of this investment plan. Can you think of a better plan?
6. Population Projections : (Ch.3, 8, 9: absolute and relative change, linear models, exponential model) First, describe and compare linear and exponential growth in your own words. Then, give 3 examples of each type of growth explaining why it would be linear/exponential growth. i) Do you think that the population in Utah has grown linearly or exponentially over the last 100 years? Please see the data bellow and make sure to use a graph and appropriate calculations of the absolute and relative changes over time to justify your answer. Year: Population of Utah: Year: Population of Utah: 1900 276,749 1960 890, 1910 373,351 1970 1,059, 1920 449,396 1980 1,461, 1930 507,847 1990 1,722, 1940 550,310 2000 2,233, 1950 688,862 2003 2,351,
ii) From the latest census data available, select the m-th largest city in USA, where
m =
x 4
- 7, x represents the last two digits of you student identification number. (Please
round m to the nearest whole number.) This is your city. For example, if your student ID number ends in 37, you should find the data for the 16th^ largest city in the United States. Using internet site(s), find and record the populations (using a table) for your city in 1910, 1920, 1930, 1940, 1950, 1960, 1970, 1980, 1990, 2000. Find the absolute and relative change in population during this period (decade to decade and overall). Can you see any big gap in your data? Can you explain any big changes (if that is the case)? Plot you data on a graph. Develop (derive) linear equations that model the data. It could be based on two actual points (that fit the line the well), or you should come up with the line that visually fits the data well. Draw your line on your graph and discuss the meaning of the slope of the model. Use the linear model (that you developed) to predict the population for 2003, 2010, and 2050? Next, develop an exponential equation to model your population data, and sketch it on your graph. What does this model predict for the year 2003, 2010, and 2050? How do these values compare to the values you found using a linear model?
Find the estimated population for 2003 using U.S. Census web site and compare it to the value that your models predicted. Do the same for the year 2010 and 2050 (compare U.S. Census projection for those years with the prediction that you got using your model). In your opinion, which graph/model would better represent the population of your city?
Note: Some useful sites: www.nationsonline.org/oneworld , www.census.gov.
7. Periodic Drug Doses : (Ch 8, 9: exponential models, half-life, working with logarithms) First, describe and compare linear and exponential growth in your own words. Then give examples of each type of growth that are drawn from the fields of study of the students in your group. Be sure to describe your examples clearly and state the area of study from which each example is drawn.
Now consider the following situation. It is common to take a drug (such as aspirin, ibuprofen, antibiotic) repeatedly at a fixed time interval. Suppose that an antibiotic has a half-life of 12 hours and that an initial dose of 200 milligrams is given followed by a 100 milligram dose taken every 8 hours. First describe the amount of antibiotic left in the bloodstream that remains from the initial dose t hours after the initial dose is taken as a function of t. Eight hours after the initial dose, a second dose is taken. How much of the drug is in the bloodstream now when you combine both the remains of the initial dose and the second dose? Sixteen hours after the initial dose is given a third dose will be taken. Combining the remains of first two doses with this third dose, how much of the drug is now in the bloodstream? Continuing in the same way, determine the amount of antibiotic in the bloodstream just after the follow-up dose is taken at 24 hours, 32 hours, 40 hours, 48 hours,.. ., 80 hours and display your results in a table. Then illustrate your results with a graph of the amount of antibiotic in the bloodstream for the first 80 hours after the initial dose is taken. Looking at your table and your graph, and assuming the dose continues as above, determine whether the amount of the drug in the bloodstream tends to increase, decrease, or does not change over time. If you decide that it increases or decreases, does it approach a limiting value over time and if so, can you estimate what that might be? Justify your answers to these questions in a quantitative way. If possible (ask your instructor for some help), write down an equation that will describe the amount of drug in the bloodstream 8n hours after the first dose in terms of n. Your equation will involve expressions of the form (1/2)(8/12)n. Now, carry out the same investigation assuming that the initial dose is 400 milligrams. Do you notice anything interesting when you compare the graphs for your two initial doses? Next, suppose that instead of having the dose continue indefinitely, the last dose takes place 120 hours (5 days) after the first dose. How long will it take for the amount of drug remaining in the bloodstream to be less than 10 milligrams?
Consult a pharmacist (or read the fine print on the information sheet enclosed with many medicines) to find the half-live of a common drug other than ibuprofen. Create a model for the metabolism of that drug using the above procedure with the initial dose equal to the recommended dose and the time interval for each dose equal to that recommended on the package. Make a table and a graph that shows the amount of the drug in the
The data reported above has not been adjusted for inflation. Since $1 in 2003 does not have the same purchasing power as $1 in 1990, a real comparison of income should take the purchasing power of the dollar in a given year into consideration. The Consumer Price Index is often used to adjust for effects of inflation. Use the inflation calculator on the Bureau of Labor Statistics web site, http://www.bls.gov/cpihome.htm, to determine the purchasing power of $1.00 in 1990 in terms of 2003 dollars. Do this for each year from 1990 through 2003 and report your results. Then, using these factors rewrite the above table in "inflation adjusted income" or, more precisely, in 2003 dollars. Now do the same analysis on the inflation adjusted data that you did on the data above. Explain the effect of adjusting for inflation on your conclusions above. Finally, relate your own analyses and calculations to the information in the articles you have read and summarize your group's conclusions about an income gap in the United States.
