[Solution]Mortgages: Financing Options

Maria and John have been married for 2 years and just learned that they are pregnant.   They have been renting a small apartment but…

Maria and John have been married for 2 years and just learned that they are pregnant.
 

They have been renting a small apartment but decide to purchase a house. The selling price is $400,000. They will make a 20% down payment.

 
They are considering 2 financing options:
 
Option 1:         3.0% interest 30-year mortgage:  
 
Option 2:        2.75% interest 15-year mortgage:
 
Answer the following questions showing all your work to reach each answer.
 

Which option will result in a lower monthly payment if they take the full term of the mortgage? What will that monthly payment be?

 

Which option will result in the most total interest if they take the full term of the mortgage? What will that total interest be?

 
 

They decide to shop for furnishings for the new house. They choose items that amount to $3600.00.  The store has 2 fixed installment loan options for purchasing:

 
Option 1: 20% down payment and financing at 6% simple interest per year for 3 years.
 
Option 2:  no down payment and financing at 6.35% simple interest for 4 years.
 
Answer each of the following questions separately, showing all your work to reach each answer.
 

Which option will result in smaller total finance charge? What will that total finance charge be?

 

Which option will result in the smaller monthly payment? What will that monthly payment be?

 

They decide to defer any purchases and invest a $3600 bonus that Maria will be getting from work in a savings account. The interest rate is 1.6% compounded every month.  How much interest will they earn in 3 years?

 

They decide to defer any purchases and loan the $3600 bonus to a needy relative at 5% simple interest per year. How long will the term of the loan need to be if they want to earn $400 in interest (assuming the loan is not paid off early).

 
 
 

Maria and John have decided that once they live in a house, they want to have a pet. They go to an animal shelter and find several pets that they would love to take home. There are 30 cats, 4 German Shepherds, 10 Labrador Retrievers, and 22 mixed-breed dogs. Since they can’t decide, they place all the adoption cards in a container and draw one.

 
Answer each of the following questions separately, showing all your work to reach each answer.

What is the probability that they select a cat?
What is the probability that they select either a German Shepherd or a Labrador Retriever?
What is the probability that if they select a dog, that it is not a mixed breed?
If they decide to purposely choose 2 of the 36 available dogs rather than randomly choosing any 2, how many combinations of 2 dogs are possible?

 

Use the following information from June 17, 2020 to answer the questions below.

 

COVID-19 case data by county – Connecticut
 

County 
Total Cases 
 
 
 

New London
1,217
 
 
 

Fairfield
16,475
 
 
 

Windham
579
 
 
 

Hartford
11,405
 
 
 

Litchfield
1,467
 
 
 

Middlesex
1,259
 
 
 

New Haven
12,185
 
 
 

Tolland
895
 
 
 

 
 
 

Based on the data from 6/17/20, which county total is closest to the mean of these 8 data values?

 

Based on the data from 6/17/20, which county is closest to the median for these 8 data values

 

Which measure from the 6/17/20 data – mean or median – would be the most appropriate number to describe the total number of cases by county.

 

Suppose you decide to draw a pie chart to represent the data from 6/17/20. [Note: you do not actually have to draw a pie chart for this exam]

There will be 8 segments each one representing a county.  Each segment of your pie chart will represent the percentage of total cases on 6/17/20 in that county.   Name the percentage for each of the 8 counties.
 
 

Based on the data from 6/17/20, which county is at the 75th percentile for total number of cases by county.

 

Based on the data from 6/17/20, what is the percentile rank for New London?

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