University of Maryland Global Campus Mathematics Problems & Solutions

Part

1

Y

ou are planning to purchase a house that will require a mortgage of $

4

00

,000.

You find 2 mortgage offers both at the same rate of 2.7

5

%.One is a

3

0-year mortgage and the other is a 20-year mortgage.

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.

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.

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 $

6

00

0.00 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.

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

G

roup A

mean walking time?

B

y what percent did

YOU

exceed or fall below the group

A

mean?

E

xpress your answer rounded to the nearest hundredth.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.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.One other way to look at the data is by percentiles.What was your percentile rank in each group?

R

ound the percentiles to the nearest whole number.

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

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.

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

H

ow much interest would be earned after

3

years? Be sure to show all of your work.

Part2

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

Group A

Person

YOU

650

B 400

C

500

D

650

E

350

F

700

G 500H

550

I

8

00

900

Minutes Walking in May 2020

K

Group

B Person

YOU 400

X

250

Y 500

Z

450

Q

650

600

Minutes Walking in May 2020

R

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

The Needs Improvement category is for the percentageof 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.

Part 3.

Here is data for a math class:

Final Grade

A

5

B 4 8C

3

D

1

1

Women	Men
6
3
1
F	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?

Part 1
YOUR ANSWER
(do NOT show work here)
1
Difference in monthly payment
2
Difference in total interest
3
Number of months until pay back
4
Amt. of compound interest earned
Part 2
1
Group A mean and percent YOU fell behind or
exceeded group A mean
2
Group B median and percent YOU fell behind or
exceeded group B median
3
Group with larger NI percentage & percent amt
4
Your percentile in each group
Part 3
1
Probability of a B student
2
Probability of not a

D

student
3
Number of ways 5 students can be chosen
4
Probability 3 women for the 5-person group