Compound Interest

22.) You borrow 1,000,000 for one year from a friend at an interest rate of 1% per month instead of taking a loan from a bank at a rate of 13% per year. Compare how much money you will save or lose on the transaction.

24.) John expects to receive Php 20,000 in 10 years. How much is the money worth now considering interest at 6% compounded quarterly?

25.) A man who won P 500,000 in a lottery decided to place 50% of his winning in a trust fund for the college education of his son. If the money will earn 14% per year compounded quarterly, how much will the man have at the end of 10 years when his son will be starting his college education?

26.) Rex borrowed a certain amount on October 1990 from Jason. Two years later, Rex borrowed again from Jason an amount of P500. Rex paid P200 on October 1993and discharged his balance by paying P700 on October 1995 What was the amount borrowed by Rex on October 1990 if the interest rate is 8% compounded annually?

The table below contains real data for the first two decades of AIDS reporting.

Graph "year" versus "# AIDS cases diagnosed" (plot the scatter plot). Do not include pre-1981 data. Perform linear regression. Write the equations. (Round your answers to the nearest whole number. Round r to four decimal places.)

(a)    Linear Equation: ŷ =  +  x

(b)    a =

(c)    b =

(d)    r =

(e)    n =

For the dataset describing year, US Return, and Overseas Return

1. Find the least-squares regression equation of overseas returns on U.S. returns.

2. In 1997, the return on U.S. stocks was 33.4%. Use the regression line to predict the return on overseas stocks. (You may either calculate this by hand or use SAS output.) The actual overseas return was 2.1%. Are you confident that predictions using the regression line will be quite accurate? Why?

DATA

1971  29.6  14.6
1972  36.3  18.9
1973 -14.9 -14.8
1974 -23.2 -26.4
1975  35.4  37.2
1976   2.5  23.6
1977  18.1  -7.4
1978  32.6   6.4
1979   4.8  18.2
1980  22.6  32.3
1981  -2.3  -5.0
1982  -1.9  21.5
1983  23.7  22.4
1984   7.4   6.1
1985  56.2  31.6
1986  69.4  18.6
1987  24.6   5.1
1988  28.5  16.8
1989  10.6  31.5
1990 -23.0  -3.1
1991  12.8  30.4
1992 -12.1   7.6
1993  32.9  10.1
1994   6.2   1.3
1995  11.2  37.6
1996   6.4  23.0
1997   2.1  33.4

1. Listed below is the selling price for a share of PepsiCO Inc. at the close of each year.

Year             Price                            Year                Price

1990             12.9135                       2000                49.5625

1991             16.8250                       2001                48.6803

1992             20.6125                       2002                42.2211

1993             20.3024                       2003                46.6215

1994             18.3160                       2004                52.2019

1995             27.7538                       2005                59.8534

1996             29.0581                       2006                62.0002

1997             36.0155                       2007                77.5108

1998             40.6111                       2008                54.7719

1999             35.0230                       2009                60.8025

a. Plot the data.

b. Use EXCEL’s Data Analysis add-in to determine the least squares trend equation.

c. Discuss the regression equation and include both the coefficient of determination and the          

   correlation coefficient in the discussion. Make sure to test the coefficient to determine if  

   it is statistically significant at the .01 significance level.

d. Calculate the points for the years 1992 and 2004.

e. (i) Estimate the selling price in 2014.                                                                                                                       

(ii) Does this seem like a reasonable estimate based on historical data? Why or why not?

f. By how much has the stock price increased or decreased (per year) on average during the period?

Show ALL of your work and show it in a neat and orderly fashion.

Year/Number of Years Since 1971/Number of stores

• Identify the initial value and the growth rate of your exponential model and explain what they mean in the context of Starbucks Stores. Put your explanations in a text box.

• Use your exponential model to predict the number of Starbucks locations in the following years:

1980, 1990, 2000, 2010, 2020, 2030, 2040, 2050

Pregnant women were recruited during their first trimester to study the relationship between chocolate consumption during pregnancy and risk of preeclampsia (pregnancy-induced hypertension). They were interviewed about chocolate consumption, age, race, education, smoking, body mass index, and previous pregnancy history. Participants were re-interviewed after delivery to obtain information on chocolate consumption during the third trimester of pregnancy. In addition, umbilical cord blood was collected at the time of delivery and measured for concentration of theobromine (the major metabolite of chocolate). Obstetrics records were obtained to determine if preeclampsia developed during the pregnancy. Of 1995 eligible women, 348 were excluded due to preexisting hypertension or preeclampsia at the first study visit, leaving a sample size of 1647 women

(h) Only women who delivered a live birth were included in the analysis. A concern is that exclusion of women who miscarried could cause bias in the study findings.

(h-i) Would this be a type of information bias or selection bias? Explain.

(h-ii) 8% of women enrolled in the study miscarried. Is it likely that the associations observed above are due to bias from excluding these women? Explain.

Chapel Hill has decided to see if there is less drunk driving during the quarantine along a checkpoint on 15-501. It is known that before the quarantine the number of impaired drivers in an evening on 15-501 is normally distributed with mean of 73.5.

A) If the police department checks the data after quarantine for 7 evenings and gets the following results: 71, 66, 63, 72, 74, 70, 67.
What is the variance of this sample? _____
What is the value of our test statistic? _____
What is our p-value for the test? _____

B) Let's say we still don't know if drunk driving behavior has changed, but the Chapel Hill police department has been accused of "juking the stats" (inflating arrest numbers for nefarious reasons) so they've bought a new brand of breathalyzers so they can test every individual twice to make sure their drunk driving convictions stick. The police department wants to check if the blood alcohol content measurements for the new tests are different from the old tests. The first 12 measurements from breathalyzer 1 (multiplied by 10,000) are as follows:
4.4
2.1
3.6
9.2
7.3
7.9
8.4
1.2
0
11.4
5.5
3.6


The first 12 measurements from breathalyzer 2 (multiplied by 10,000) are as follows:
4.2
2.1
3
8.6
7.2
8.1
8.2
0.6
0.2
11.1
5.5
3.8

What is the value of the test statistic? (Give a positive value):______
What is the p-value for the test?:______

Question 2:

After the same cruise ship accident, Ron and Don are deserted on a separate island.

Unfortunately for them, they did not manage to bring anything with them. On the island, there

are only two edible items: Bananas (B) and Coconuts (C). Each day, Ron and Don go and collect

fruit. Ron is twice as good at collecting bananas as he is at collecting coconuts and the maximum

number of bananas he could collect in a day is 24. Don is the opposite: he is twice as good at

collecting coconuts as he is at collecting Bananas and could collect a maximum of 24 coconuts in a day.

(a) Suppose Ron and Don are not getting along (Don accused Ron of stealing his binoculars)

and refuse to trade. Draw a diagram showing the production possibilities frontier for Don,

and a separate diagram for Ron.

(b) For Ron, what is the “price” of collecting a coconut? What about for Don?

(c) Suppose Ron and Don both have the same utility function:

U=B^0.5C^0.5. How many bananas and coconuts will Ron and Don each produce (and then consume)?

(d) After some time, Ron and Don reconcile and discuss the possibility of trading with one

another. By cooperating, how much of each fruit will Ron and Don produce? Will they be

better off?

(e) Suppose they play the same market game as Annie and Bert to escape boredom, and the

prices are pB=pD=1. How much fruit will each person collect? At these prices, how

many bananas are demanded by Don and how many bananas is Ron willing to supply?

Introduction

The Healthy People 2020 initiative of addressing social determinants of health is a high priority for improving physical fitness and healthy lifestyle choices. Factors such as lifestyle, demographics, and heredity ultimately help to determine quality of life and health for both individuals and communities (HealthyPeople.gov, 2014).

Case Study

Promoting individual and community participation in making positive lifestyle changes will require a multitiered approach. For example, empowering people to exercise and increase physical activity by walking more often is a positive behavioral intervention endorsed by Healthy People 2020. Renewed emphases on transformation of health care delivery and support of public health promotion programs by addressing lifestyle choices and healthier decision-making are fundamental drivers of social determinants. For example, the national healthcare environment is primed to support health promotion programs through recent legislative efforts that emphasize disease prevention and care coordination. This approach helps public health interventionists to design strategies and programs by promoting change and enhancing decision-making. Ideally, the call-to-action message will be reinforced with robust health education efforts on social media.

Discussion

The future of health care delivery systems will require novel approaches to meet or exceed the Healthy People 2020 initiatives. For example, Healthy People 2020 establishes a set of standards for health systems to strive toward quality outcomes grounded in evidence-based medicine (EPM). Small- to medium-sized health systems often struggle to implement new care delivery models and evidence-based practices for many reasons, including a lack of external guidelines and monitoring. As a result, clinical care delivery is fragmented at worse and health outcome are inconsistent at best. Thus, clinical care is neither evidence based nor adherent to national quality-based standards.

Conclusion

Health systems with novel models in clinical care delivery are champions of best practices. “An organizational culture that supports and encourages clinical inquiry and welcoming change will lead to improved clinical outcomes” (Hall & Roussel, 2014). The pursuit of the Healthy People 2020 is a worthy goal that can assist future health care delivery systems to develop a modern clinical and administrative infrastructure. Finally, a gap often exists between the skills and knowledge needed for implementation of these types of cutting-edge care delivery models. This type of strategic planning and focus will help reinforce EBM and best-clinical practices for the adoption of quality initiatives such as Healthy People 2020.

Question

1. How can external initiatives such as Healthy People 2020 assist health care delivery systems to implement quality-based measures to improve clinical outcomes? Provide an example with support from the text or a peer-reviewed reference.
2. Research previous Health People initiatives from 2000 and 2010. Track one of the initiatives and monitor its progress over the 10-year period. Prepare a SWOT analysis and discuss your findings in the context of measuring a quality outcome.