Number 1
Would you rather start with one penny ($0.01) and double your wealth every day or start with one dime ($0.10) and double your wealth every 5 days (assuming you want to get rich)? Explain your answer in detail and show all your math calculations that helped you reach your conclusion.
Number 2
Scientists estimate that the ocean pH was about 8.25 before the beginning of the industrial era, around 1750. Today it is about 8.05, and if current trends continue, it may fall to 7.9 by 2050.
• Use this data to calculate the percent change in the hydrogen ion concentration of the ocean from 1750 to today, and from 1750 to 2050. Show your math calculations.
• Using credible sources, research ocean acidification and its impact on both marine ecosystems and human society. Based on your research, write a short report that summarizes the issues and that discusses recommendations about how we should work to address it. The Scholarly, Peer Reviewed, and Other Credible Sources table offers additional guidance on appropriate source types.
Number 3
Assume that you have a relatively simple health insurance plan with the following provisions:
• The annual deductible is $500. The insurance company pays 100% of all costs after deductible and co-payments
• Office visits require a co-payment of $25.
• Emergency room visits have a $200 co-payment.
• Surgical operations have a $1000 co-payment.
• You pay a monthly premium of $350.
During a one-year period, your family has the following expenses:
• February 18: Office visit — $100 (total cost before insurance)
• March 26: Emergency room — $580 (total cost before insurance)
• April 23: Office visit — $100 (total cost before insurance)
• May 14: Surgery — $6500 (total cost before insurance)
• July 1: Office visit — $100 (total cost before insurance)
• September: 23 Emergency room — $840 (total cost before insurance)
Based on the above information, complete the following. Show your math calculations.
• Determine your health care expenses for the year with the insurance policy.
• Determine your health care expenses for the year if you did not have the insurance policy.
• What is the current status of federal law in the U.S.A. regarding health insurance?
• Has the law changed since the Affordable Care Act was passed in 2010? If so, explain.
• Compare the U.S.A. health insurance coverage and health care federal laws to other developed, first-world countries like Canada, Australia, Japan, or Western Europe.
• How do the U.S.A.’s health insurance coverage and federal laws affect the various strata (upper or higher income, middle-income, low-income) of the society?
Number 4
Find data on the increase in consumer credit card debt in the U.S.A. Based on your findings, do you think the extent of the consumer debt is (a) a crisis, (b) a significant occurrence but nothing to worry about or (c) a good thing? Justify your conclusion.
Number 5
When it comes to saving disposable income, Americans have a remarkably low savings rate. Find sources that compare the savings rates of Asian and European countries to that of the U.S.A. Discuss your observations and put the savings habits of someone you know on the scale.
Number 6
Jose invests $1500 in an account that earns a 5.6% compounded annually. Marta invests $1500 in a different account that earns 5.7% compounded annually. Based on this information complete the following:
• Compute the balances in both the accounts after 10 and 30 years.
• Discuss the differences between your 10 year and 30-year balances.
• Find a website that compares interest rates available for ordinary savings accounts at different banks and identify the range of rates currently being offered. Specify the best rate available.
Number 7
Consider an account with an APR of 5%.
• Calculate the APY with quarterly compounding, monthly compounding, and daily compounding.
• Describe how changing the compounding period affects the annual yield.
• Explain why APR and APY are the same with annual compounding.
• Explain why APR and APY are different with daily compounding.
• Does APY depend on the starting principal? Why or why not?
• How does APY depend on the number of compounding during a year? Explain.
Number 8
Suppose you want to accumulate $120,000 for your retirement in 30 years. Consider the following two
plans:
• Plan A. Make a single deposit into an account with annual compounding and an APR of 5%.
• Plan B. Make a single deposit into an account with continuous compounding and an APR of
4.8%.
MAT202: Quantitative Explorations in Everyday Life
Complete the following based on the above information.
• How much do you need to deposit in each account in order to reach the goal?
• Calculate the current APR, the compounding period, and the claimed APY for your personal savings account (or pick a rate from a nearby bank).
• Calculate the APY on your account (or someone you know).
• Does your calculation agree with the APY claimed by the bank? Explain.
Number 9
Suppose you are 25 years old and would like to retire at age 65 with an accumulated retirement fund from which you could draw an income of $200,000 per year — forever! Complete the following:
• How much would you need to deposit each month to accomplish this goal? Assume a constant APR of 6%.
• Locate an advertisement for an investment plan and describe some of the cited benefits of the plan.
• Apply what you learned in Section 4C (Savings Plans and Investments) in your course textbook to identify at least one possible drawback of the plan.
Number 10
Choose three stocks, three bonds, and three mutual funds that you think would make good investments.
Imagine that you invest $1,000 in each of these nine investments. Use an internet resource to track the value of your investment portfolio over the next five weeks. Based on the portfolio value at the end, find your return for the five-week period. Which investments did better, and which did worse?
Number 11
Choose one of the 30 companies in the Down Jones Industrial Average (DJIA), and using credible sources, research that company as if you were a prospective investor. The Scholarly, Peer Reviewed, and Other Credible Sources table offers additional guidance on appropriate source types. Answer the following questions.
• How has the company performed over the last year, last five years, and last 10 years?
• Does the company offer dividends?
• How do you interpret its P/E ratio?
• Overall do you think the company stock is a good investment? Why or why not?
• Visit one of the many financial news and advice websites and describe the service offered by the website.
• Did you find the website useful as a prospective investor?
• Visit the website of at least two online brokers and compare the commissions charged by the
brokers.
MAT202: Quantitative Explorations in Everyday Life
Number 12
Imagine you work for an accounting firm and a client has told you he needs a loan of $120,000 to purchase a house. His monthly income is $4000, and he is single with no children. He has $14,000 in savings that can be used for a down payment. Based on this information, complete the following.
• Find the current rates available from local banks for both fixed rate mortgages and adjustable rate mortgages (ARMs).
• Analyze the offerings and summarize in writing the best options for your client, along with the pros and cons of each option.
Number 13
Suppose the federal debt increases at an annual rate of 2% per year. Based on this assumption, complete the following.
• Use the compound interest formula (Unit 4B) to determine the size of the debt in 10 years.
Assume the current size of the debt (the principal for the compound interest formula) is $20 trillion.
• How serious a problem is the gross debt? Locate arguments for both sides of the question.
• Using credible source, research various proposals for solving the budgetary problems of Social Security and Medicare and state your own opinion of what should be done. The Scholarly, Peer Reviewed, and Other Credible Sources table offers additional guidance on appropriate source types.
Number 14
When it comes to income taxes, one of the key political debates concerns whether the overall system is
fair. Pews research center collected the following data from the IRS in 2014:
Adjusted Gross Income (in
dollars)
Percentage of federal income tax
returns filed
Percentage of total federal
income tax paid
Less than 15,000 24.3% 0.1%
15,000 — 29,999 20.4% 1.4%
30,000 — 49,999 17.6% 4.1%
50,000 — 99,999 21.7% 14.9%
100,000 — 199,999 11.8% 21.9%
200,000 — 249,999 1.5% 5.9%
MAT202: Quantitative Explorations in Everyday Life
250,000 and above 2.7% 51.6%
Based on the above data, complete the following.
• Consider people with an adjusted gross income of less than $100,000. What percentage of federal tax returns were filled by this income group, and what percentage of total federal income taxes did this income group pay?
• Consider people with an adjusted gross income of more than $100,000. What percentage of federal tax returns were filled by this income group, and what percentage of total federal income taxes did this income group pay?
• Does the U.S. have a fair income tax system? Research various arguments about the fairness of the U.S. income tax system and state your own opinion. If the system is not fair and there are problems with it, then what do you propose to fix the system?
Number 15
Suppose you want to borrow $100,00 for your education. You find a bank offering a 20-year term with an APR of 6%. Based on this information, complete the following.
• What are your monthly payments?
• Do you save money if you pay off the loan earlier (that is before the 20-year term)? If yes, how much? Show all your calculations.
• Discuss the advantages/disadvantages of financing a student loan online (as there are many websites that offer student loans) rather than through a bank or through your school.
