Part 1
1.) Bryan invests $500 in an account earning 4% interest that compounds annually. If he makes no additional deposits or withdraws, how much will be in the account:
a. After 10 years?
b. After 15 years?
c. After 20 years?
d. After 25 years?
e. About how long would it take to double his $500 investment?
2.) Lori gets an offer from a bank that is paying 6% on CD's, but is compounding interest daily. How much will the $1500 CD be worth in:
a. 5 years?
b. 10 years?
c. 18 months?
3.) The average population growth rate for whitetail deer is 0.35. Hunting laws are set to limit the time allowed for hunting deer with a goal of achieving about a 35% mortality rate on deer to keep the population in check. Years with a higher than 35% mortality will result in an overall decline in the deer population while years with a lower than 35% mortality rate will result in an increased population.
Part 2
1. With a beginning balance of $1200 and no additional charges during the next three months, you will just pay the minimum payment each month for the next three months. The APR is 24.99% and the minimum payment each month is 3% of the balance. Determine the finance charge, new balance, and minimum payment required for each of the next three months, and the starting balance for month 4 in the table below:
Month Starting balance Finance charge New balance Minimum payment
1. $1200
2.
3.
4.
a. What is the total of the minimum payments?
b. What is the total of the finance charges?
c. How much does the starting balance decrease after these three payments?
d. The total of your finance charges is what percent of your total payments?
e. Explain why making the minimum payment all the time is great for the credit card company, but not so great for the user.
f. Explain why having a credit card and using it wisely is beneficial to you.
2. Create an Excel spreadsheet that can do the calculations for the credit card in #3 above. Using formulas and the drag function of Excel, find the balance for month 12.
a. If there were no hunting of whitetail deer allowed, how long would it take the population of deer to double? to quadruple?
b. If the growth rate exceeds the mortality rate, and the net effect were a 10% growth rate, how long would it take the population to double?
Part 3
1. Your classmate tells you the details of the great deal he got on his mortgage: 30-year 3.5% fixed rate with a 10% down payment.
a. If his new home costs $136,000, what is his down payment?
b. How much is he going to borrow to buy the house (assuming he only has the money to make the down payment from part a)?
c. Use Excel's PMT function to determine how much his monthly payments would be.
d. How much will he pay in interest over the lifetime of this mortgage?
2. Suppose Calvin Cordozar Broadus, Jr. (aka Snoop Doggy Dogg) is considering moving his family to Manhattan. His real estate agent has managed to locate a penthouse apartment that overlooks Central Park for $2.4 million. He will have $2.1 million from the sale of his current home as a down payment. Snoop would like to finance the remainder of the cost and his banker has presented two options: a 30-year fixed-rate mortgage at 8% or a 20-year fixed-rate mortgage at 7.5%.
a. How much will Snoop have to finance?
b. Which loan is more economical in the long run? Use Excel to help determine your response.
c. How much is saved in interest by choosing the more economical mortgage?
Part 4
1. If a cell in an Excel spreadsheet uses the following formula to determine the future value of an investment: "=FV(0.06/12, 12*6, I00.00)"
a. How much money is being invested each month?
b. What is the APR?
c. For how many years will monthly payments be made?
d. How much money will have been deposited into the account?
2. John makes $2,800 per month and has an opportunity to save $150 per month at an APR of 4.5% in a 401K plan through work. He plans to retire in 30 years. If income taxes are at 20% for him:
a. How much will his investment be worth in 30 years? (Use Excel for this)
i. Write the Excel formula that gives its future value
ii. Write the future value the formula gives:
b. How much money will he deposit into the 40IK over the 30 years?
c. How much will his monthly take-home pay decrease?
d. How much less will he receive in take-home pay over the course of 30 years with the income tax savings?
e. How much tax savings is there over the 30 years?
f. How much total interest will he earn on his 401K over the 30 years?
Part 5
|
Year
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
Jun
|
Jul
|
Aug
|
Sep
|
Oct
|
Nov
|
Dec
|
|
2003
|
5.8
|
5.9
|
5.9
|
6.0
|
6.1
|
6.3
|
6.2
|
6.1
|
6.1
|
6.0
|
5.8
|
5.7
|
|
2004
|
5.7
|
5.6
|
5.8
|
5.6
|
5.6
|
5.6
|
5.5
|
5.4
|
5.4
|
5.5
|
5.4
|
5.4
|
|
2005
|
5.3
|
5.4
|
5.2
|
5.2
|
5.1
|
5.0
|
5.0
|
4.9
|
5.0
|
5.0
|
5.0
|
4.9
|
|
2006
|
4.7
|
4.8
|
4.7
|
4.7
|
4.6
|
4.6
|
4.7
|
4.7
|
4.5
|
4.4
|
4.5
|
4.4
|
|
2007
|
4.6
|
4.5
|
4.4
|
4.5
|
4.4
|
4.6
|
4.7
|
4.6
|
4.7
|
4.7
|
4.7
|
5.0
|
|
2008
|
5.0
|
4.9
|
5.1
|
5.0
|
5.4
|
5.6
|
5.8
|
6.1
|
6.1
|
6.5
|
6.8
|
7.3
|
|
2009
|
7.8
|
8.3
|
8.7
|
9.0
|
9.4
|
9.5
|
9.5
|
9.6
|
9.8
|
10.0
|
9.9
|
9.9
|
|
2010
|
9.7
|
9.8
|
9.9
|
9.9
|
9.6
|
9.4
|
9.5
|
9.5
|
9.5
|
9.5
|
9.8
|
9.4
|
|
2011
|
9.1
|
9.0
|
9.0
|
9.1
|
9.0
|
9.1
|
9.0
|
9.0
|
9.0
|
8.8
|
8.6
|
8.5
|
|
2012
|
8.2
|
8.3
|
8.2
|
8.2
|
8.2
|
8.2
|
8.2
|
8.1
|
7.8
|
7.8
|
7.8
|
7.9
|
|
2013
|
7.9
|
7.7
|
7.5
|
7.5
|
7.5
|
7.5
|
7.3
|
7.2
|
7.2
|
7.2
|
7.0
|
6.7
|
http:/ data.b1s.gov/timeseries/LNS14000000
1. The table above represents the monthly unemployment rates in the US from January of 2003 through December of 2013.
a. Find the relative change in unemployment from January 2003 to December of 2013.
b. Find the absolute change in the unemployment rate during 2013.
c. Find the relative change in the unemployment rate during 2013.
d. Write a few sentences reporting on the unemployment rate for 2013 using your values from parts a, b and c.
e. Find the absolute change in the unemployment rate during 2009.
f. Find the relative change in the unemployment rate during 2009.
g. Write a few sentences reporting on the unemployment rate for 2009 using your values from parts e and f.
2. The fair market rental rate for Bloomington is $747 and for Kokomo is $654.
a. Find the relative change from Bloomington to Kokomo and write a sentence describing the difference between the two cities rent.
b. Find the relative change from Kokomo to Bloomington and write a sentence describing the difference between the two cities rent.
3. Indiana's population has increased by 9.5% since 2000, when it was about 6 million people, what is Indiana's population now?
4. You got a great deal on a new computer for $800 that was marked down by 60% from the original price. What was the original price?
5. You plan to leave a 15% tip and your dinner bill is $45. How much tip money should you give?
6. If gas prices are now $3.75 and they were up 10% from 6 months ago, how much were gas prices 6 months ago?
7. You are charged $16.05 for a meal. Assume sales tax is 7%, what was the menu price for the meal?
8. Bloomington's enrollment is 24.3% of Indianapolis's enrollment. Stated another way Indianapolis's enrollment is % of the number of Bloomington's.
9. If the wholesale price of an item is 60% less than the retail price, the wholesale price is how many times the retail price?
Teen Smoking Rates Decline
Source: https://www.nytimes.com/2008/12/16/health/research/16smoking.htmlLr=0
Just 12.6 percent of high-school students this year said they'd had a cigarette in the last month, down from 13.6 percent last year, according to researchers at the University of Michigan, who conducted the survey.
Many teenagers have negative attitudes toward cigarette smoking. The vast majority said they'd rather not date someone who smoked and two-thirds said that "becoming a smoker reflects poor judgment," according to the survey.
"That's a very important message," said Lloyd Johnston, a research professor at the Institute for Social Research at the University of Michigan and the study's principal investigator. "For years and years, the industry pitch was that smoking makes you sexy and attractive to the opposite sex. It turns out the absolute opposite is true. It projects a negative image, for both girls and boys."
Each year, the institute surveys a nationally representative sample of more than 45,000 students in the eighth, tenth and twelfth grades at 400 schools. The survey assesses smoking prevalence by asking students whether they have smoked a cigarette in the previous 30 days.
This year's drop in smoking rates continues a sharp decline in teen smoking since 1996, about the time cigarette use peaked in that age group. The researchers found that only 7 percent of eighth-graders are smoking, down from 21 percent in 1996, while 12 percent of tenth-graders are smoking, down from 30.4 percent in 1996.
One in five high school seniors smoke now, down from more than a third in 1996.
These days fewer teens even try cigarettes: only 21 percent of eighth-graders said they had tried smoking, down from 49 percent in 1996, the study found. Many teens are critical of cigarette smoking, with over 80 percent of those surveyed saying they disapprove of smoking more than a pack a day and more than 70 percent saying it was a "dirty habit." Very few believe the harmful effects of smoking have been exaggerated, the survey found.
But it's still not difficult for youngsters to buy cigarettes, and some 57 percent of eighth-graders said they could obtain cigarettes easily, down from 77 percent in 1996.
10. This study was conducted in 2008. Using the data in the first paragraph, quantify the change in the percentage of teens that had smoked within the last month in both absolute and relative terms.
a. Absolute change
b. Relative change
c. This change was over what time period?
11. Quantify the change in eighth graders who smoke for the time period 1996 to 2008 in both absolute and relative terms.
12. Quantify the change in tenth graders who smoke for the time period 1996 to 2008 in both absolute and relative terms.
13. Calculate and comment on the change in the fraction of high school seniors who smoke over that same time period.
14. Has there been more of a change in the proportion of eighth graders, tenth graders, or high school seniors?
Part 6
1. Researchers find that there are 60 Raccoons on an island. When they return a year later, they find that there are 84. What is the annual population growth rate for the raccoons?
2. Consider the data in the table.
|
Time
|
Value
|
Absolute Change
|
Relative Change
|
|
0
|
13.6
|
|
|
|
1
|
17
|
|
|
|
2
|
21.25
|
|
|
|
3
|
26.56
|
|
|
|
4
|
33.2
|
|
|
|
5
|
41.5
|
|
|
a. Complete the table by computing the absolute and relative change.
b. Which model would better represent this data, linear or exponential? Write a meaningful sentence to explain your answer.
c. Find the model for this data.
d. What value does your model predict when time is 8?
3. Frogs -A species of frog's population grows 24% every year. Suppose 100 frogs are released into a pond.
a. Construct an exponential model for this population.
b. How many frogs will there be in 5 years?
c. How Enemy frogs will the; e be in 20 years?
d. About when will there be WOO frogs?
Part 7
1. The half tile of a radioactive substance is one day. meaning that every day halt of the substance has decayed Suppose you have 100 grams of this substance.
a. Construct an exponential model for the amount of the substance remaining, on a given day.
b. How much of the ubsterwe would be left aftet a week?
2. Suppose a tortoise is 2000 feet from the ocean. Each day the tortoise travels one-half of the ternaintrw, distance to the ocean. Use this information to:
a. Construct a model that represents the remaining distance that the tortoise must travel to reach the ocean.
b. Compute the remaining distance to the ocean ahet 4 days of travet
3. A certain vehicle loses 35% of its value each year.
a. If the vehicle has an initial value of 525,000, construct a mode\ that represents the value after x years.
b. Compute the value of the vehicle at the end of the 3rd Near.
Part 8
1. A tree increases in diameter each year by an average of 0.51cm. if the tree currently has a diameter of e inches, how old do you estimate the tree is?
2. Consider the variation of temperature with altitude depicted in the graph below.
a. What is the dependent variable?
b. What is the independent variable?
c. What is the "y-intercept"?
d. What is the slope?
e. Write a sentence to explain what the slope means.
f. Use your Jam-vet s to construct an equation for the linear model, y = mx + b, that describe the graph.
g. Use your model to predict what the temperature would be at 7000 feet above sea level.
3. The environment club 200 pounds of cans and promises to collect 20 pound of cans each week and will use the profits to buy additional recycling bins Construct a linear model lot their collection program.
a. What will the Independent variable, x, represent?
b. What wilt the dependent variable, y, represent
c. What is, the starting value, b, for this model?
d. What is the Slope, m, for this model?
e. Witte the model to y = mx + b form.
f. How many pounds of cans will the club have by week 12?
g. When will the dub have 320 pounds of cans?
4. The cost of a LCD TV dropped horn $265 in 2012 to $199 in 2014.
a. Find the average rate at which the cost has been decreasing.
b. Construct a linear model to estimate future cost of TV's.
c. Use your model to estimate what the cost will be in 2016.
5. In 1963, postage was 5 cent ounce. In 1983, postage was 18 cent per ounce
a. Establish a linear model which can be used to estimate the postage per ounce based upon the years.
b. If the trend continued through to today, what would the postage per ounce be?
Part 9
1. Vehicle Registrations
Use the above scatter plot to answer the following questions:
a. What is the independent variable and what does it represent?
b. What is the range of the independent variable?
c. What is the dependent variable and what does it represent?
d. State the trend line (regression line).
e. Write a sentence explaining the value of the slope for this regression line.
f. Use the R2 value to determine the r value. Is this a reasonable model for the data? Why or why not?
g. Consider the model/regression line.
i. How would you use the model to predict the registration for 2005? Note the rouge of the x-volue.
ii. What value does the model predict for the number of registrations in 2005?
iii. How does this compare to the actual value of 241 million?
h. What value does the model predict for the number of registrations in 2020?
i. Is it reasonable to use the model to make predictions for 2020! Explain your answer.