Posted: November 25th, 2022

# Mathematics

Topic 1: Mathematical Relationships

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Q-1

In Chapter 1 of the text (1-13) you will look at calculating a monthly payment for a loan.  A simpler problem is to compute the amount a loan would cost you in one month.

Using information from an internet source, determine the current interest rate a credit card or loan. Suppose you borrow \$1,000 (or spend \$1,000) on a credit card. How much will you owe in one month? 6 months if you pay nothing for 6 months?

Compute the 6 month cost in two ways:

1. Make 6 monthly computations. Enter these as formulas in a spreadsheet. (The goal here is really getting you to use spreadsheets and formulas for computations.)

2. Use the formula, A= 1000*(1 + r)^(N) where N = the number of periods (6) and r = the periodic interest rate = APR/12, where APR is the annual percentage rate.

Here are a couple of options to research loans that do not require personal information. Top10PersonalLoans, Credit Karma.

A Microsoft Excel spreadsheet is required for this Question.

Q-2

Roll two dice and add the numbers. Roll the dice 40 times and record your results.  Find the eight descriptive statistics in the Chapter 1 for this data set.

A Microsoft Excel spreadsheet is required for this DQ.

Topic 2: Ratios

Q-1

Go to choose a country, and find the following rates:  Birth, Death, and Net Immigration for the most current year.  Use the rates and the current population to find the number of each category expected for that year – use ratio tables and be sure to attach them to your answer.

A Microsoft Excel spreadsheet is required for this DQ.

Q-2

According to the National Center for Health Statistics, the mean height of an American male is 69.3 inches and the mean height of an American female is 63.8 inches. The standard deviation for both genders is 2.7 inches.

Assuming that heights among a single gender are normally distributed. Find the z-score for your height in inches using the mean of your own gender and then find the percentile at which you fall among people of your own gender using the percentile table from problem 25 of the Topic 2 Homework.

A Microsoft Excel spreadsheet is required for this DQ.

Topic 3: Unit conversions

Q-1

Choose one country that you might like to visit. Select a duration for your trip between two and six weeks, and then choose a number of participants between 5 and 10 people. Suppose one goal of your group is to speak to every adult citizen in the country. How many citizens must each missionary need to talk to per day, per hour, and per second to speak to every adult citizen in that country? Is that goal reasonable?

A Microsoft Excel spreadsheet is required for this DQ.

Q-2

According to the National Center for Health Statistics, the mean height of an American male is 69.3 inches and the mean height of an American female is 63.8 inches. The standard deviation for both genders is 2.7 inches.

· According to Chebyshev’s Theorem 75% of the data for your gender lies between what two heights?

· If height is assumed to be normal, what percentage of the data lies between those same two heights?

A Microsoft Excel spreadsheet is required for this DQ.

Topic 4: Percentages in the Real World

DQ-1

Define what a percent is? Write your height in inches. Suppose it increases by 15%, what would your new height be?  Now suppose your increased height decreases by 15% after the 15% increase; what is your new height?

A Microsoft Excel spreadsheet is required for this DQ.

DQ-2

Many students take online courses because they are more convenient for their schedules. What are some of the tradeoffs for taking an online course in a subject such as math? What tools are you using to overcome these challenges?

Topic 5: Linear Models

DQ-1

Select one of the options below and create a linear equation to represent the monthly bill for each Plan A and Plan B, you will have two equations, one for each plan. Find the common number of minutes at which both Plan A and Plan B cost the same amount. This number of minutes is called the break-even point. Which plan costs more before the break-even point and which cost more after the break-even point.

Option 1: Plan A \$39.99 for 200 min and \$1.25 for each min after.  Plan B \$29.99 for 200 min and \$1.50 for each min after.

Option 2: Plan A \$25.75 plus \$.75 per min. Plan B \$20.99 plus \$1.00 per min

Option 3: Plan A \$39.99 plus \$1.25 per min. Plan B \$25.99 plus \$1.75 per min

Option 4: Plan A \$45.99 for 400 min and \$.50 for each min after. Plan B \$49.99 for 400 min and \$.40 for each min after

A Microsoft Excel spreadsheet is required for this DQ.

DQ-2

In Chapter 1 of the text we looked at calculating a monthly payment for a loan.  A related formula is to calculate the amount accruing when regular payments are made into an interest bearing account – often called the Savings Plan formula.

(A is the accrued amount after t years of making regular payments, PMT, into an account at interest rate, r%, compounded n times each year.)

A(t) =  PMT·((1 + r/N)N·t – 1)/(r/N)

= PMT*((1 + r/N)^(N*t) – 1)/(r/N)

The second version is essentially in the form used in Excel

Suppose you want to buy a car and have decided that you can save \$100 a month.  Using information from an internet source, determine the current interest rate on savings accounts and use the information to answer the following:

1. How much money will you have saved in two year’s time?

2. How much will be interest?

3. Why wouldn’t a linear model work here?

Here is one option to research accounts that does not require personal information: NerdWallet

A Microsoft Excel spreadsheet is required for this DQ.

Topic 6: Exponential Models

Q-1

Use the digits of your birthday as the amount of your initial investment (i.e., 6/25 is \$625), calculate the value of this investment after 10 years at 3.5% APR for interest compounded yearly, quarterly, monthly, and daily. What do you notice?

A Microsoft Excel spreadsheet is required for this DQ.

Q-2

Using the average inflation rates from: use the geometric mean to find the average percent change in inflation for the past 5 years.

A Microsoft Excel spreadsheet is required for this DQ.

Topic 7: Personal Finance

Q-1

What are the four major categories of securities?  How are they evaluated?

Q-2

What are your favorite and least favorite experiences in this class so far? When responding, please refrain from using names and sharing comments that are inappropriate for the discussion forum.

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