question archive Part 1 You are planning to purchase a house that will require a mortgage of $400,000

Part 1 You are planning to purchase a house that will require a mortgage of $400,000

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Part 1

You are planning to purchase a house that will require a mortgage of $400,000.

You find 2 mortgage offers both at the same rate of 2.75%. One is a 30-year mortgage and the other is a 20-year mortgage.

 

1. You know, without any computation, that the 30-year mortgage will have lower monthly payments than the 20-year mortgage since the rates are the same. A friend advised that before taking the 30-year mortgage offer, you do some mathematical calculations to see if your budget can handle the extra amount of monthly payment for the 20-year mortgage.

 

What is the difference in the monthly payment? Be sure to show all of your work.

 

2. You ask your friend what advantage there is to be paying more per month on the 20-year mortgage. Your friend replies that it is all about total interest.

 

What is the difference between the total interest paid over the term of the 30 year and 20-year mortgage? Be sure to show all of your work.

 

 

3. After you purchase the house, you decide to do some remodeling in the kitchen. You ask your parents if they would lend you money, but you insist on paying them interest. The agreement is that they will lend you $6000.00 at a simple interest rate of 3% per year. Once the interest amounts to $300, you agree to pay them back the $6000 plus the $300 interest.

 

After how many months will you have to pay them back? Be sure to show all of your work.

 

 

4. Suppose that the $6000.00 was invested in a savings account that paid 2.5% interest compounded quarterly.

 

How much interest would be earned after 3 years? Be sure to show all of your work.

 

 

 

 

 

Part 2

You belong to two different walking groups. Here is data about each group’s walking in May 2020.

 

Group A

Person

Minutes Walking in May 2020

YOU

650

B

400

C

500

D

650

E

350

F

700

G

500

H

550

I

800

K

900

 

Group B

Person

Minutes Walking in May 2020

YOU

400

X

250

Y

500

Z

450

Q

650

R

600

 

Answer the following questions based on this data. Be sure to show all of your work for each question.

 

1. What was the Group A mean walking time? By what percent did YOU exceed or fall below the group A mean? Express your answer rounded to the nearest hundredth.

 

2. What was the Group B median walking time? By what percent did YOU exceed or fall below the group B median? Express your answer rounded to the nearest hundredth.

 

3. Let’s suppose you want to draw a pie chart that shows information for the members of each group classified by a rating based on the amount of walking time. There will be 4 categories: excellent, very good, good, needs improvement.

 

The Needs Improvement category is for the percentage of group members who walked for less than 600 minutes.

 

Which group [A or B] has the larger percentage of members in the Needs Improvement category? What is that percentage? Express your answer to the nearest hundredth.

 

4. One other way to look at the data is by percentiles. What was your percentile rank in each group? Round the percentiles to the nearest whole number.

 

 

 

Part 3.

 

Here is data for a math class:

 

Final Grade

Women

Men

A

6

5

B

4

8

C

3

3

D

1

1

F

1

1

 

 

Answer the following questions based on the above data for the math class. Be sure to show all of your work.

 

 

1. If one person is randomly chosen to participate in a focus group, what is the probability that the person will be a student who earned a B in the class?

 

2. If one person is randomly chosen to participate in a focus group, what is the probability that the student chosen will NOT have earned a D?

 

3. A focus group of 5 students is going to be randomly chosen. In how many ways can the 5 students be chosen?

 

4. What is the probability that 3 women will be randomly chosen for this focus group of 5 students?

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