Project MAT: Mathematics Questions

Project MAT: Mathematics Questions

About the Cost and Advantages of Home Ownership

Question 1.1: Introduction

Owning a home and making regular amortized payments enables one to build equity in the home. Homeownership is essential because it helps to create strong and stable communities. The exercise aims to make calculations concerning homeownership finance.

Question 1.2:

The formula for computing the payment amount is as follows:

,

Where,

 A = payment amount per period

P = initial principal (loan amount)

r = interest rate per period

c = total number of payments or periods

P = $120,000

r = 8% per year / 12*100 months = 0.0067% per period

c = 25 years * 12 months = 300 total periods

Therefore,

= $936 monthly.

Question 1.3:

P = $350,000

r = 7% per year / 12*100 months = 0.0058% per period

c = 30 years * 12 months = 360 total periods

The payment amount:

= $2318.4 monthly.

The monthly payment is $2318.4.

Payment number 1:

The interest payment = rate (r) X previous balance of payment.

= $350,000 X 0.0058= $2,030.00.

The principal payment = amount – interest.

= $2,318.4 – $2,030.00 = $288.40.

The new balance = principal – previous balance.

= $350,000.00 – $288.40 = $349,711.60.

Payment number 2:

The interest payment = rate (r) X previous balance of payment.

= $349,711.60 X 0.0058 = $2,028.33

The principal payment = amount – interest

= $2,318.4 – $2,028.33 = $290.07

The new balance = principal – previous balance.

= $349,711.60 – $290.07 = $349,421.53.

Table 1: Results

Question 1.4:

Beginning balance = $ 100,000

Term = 25 years

Initial index rate = 6.5%

Margin = 2.5%

Adjustment period = 1 year

Adjusted balance after 1 year = $98,884.32

Adjustment index rate = 7%

First-year monthly payment:

,

Where,

A = monthly payment

P = loan amount

r = monthly interest rate.

t = number of months in the loan (years * 12)

Interest rate(r) = initial index rate + margin

= 6.5%+ 2.5%

= 9% or 0.09

Second-year monthly payment:

Interest rate(r) = adjustment index rate + margin

= 7%+ 2.5%

= 9.5% or 0.095

t = 25 years – 1 year =24 years

Adjusted amount = $871.6 -$840.5 = $31.1

There is an increase of $31.1.

Question 1.5:

Public housing initiatives in Miami are reserved to only a limited number of low-income families. The criteria for such admissions differ according to the housing system stated below.

• Public housing

At least 40% of new admissions must be of low income (equal or below 30% of the median income in the area). The remaining 60% of new intakes should be people with income worth up to 80% of the area’s median income.

• Section 8 Housing Choice Voucher (HCV) and project-based vouchers

At least 75% of new enrollment must be of low income (equal or below 30% of the median income in the area). The remaining 25% of new applicants must be people with income worth up to 50% of the median income in the area.

About Some Games

Question 2.1:

Florida lottery has 53 numbers. Players are only allowed to choose 6 numbers per ticket. Therefore, 22,957,480 possible selections are feasible in this lotto game. Buying 50 tickets provides odds of 50 in 22,957,480. Thus, with 50 tickets, the probability of winning the lotto will be 50/22,957,480) or rather 0.000002177.

Question 2.2

Several features characterize the Florida Lotto games. The minimum age for the purchase of a Florida Lotto ticket is 18. Florida Lotto draw is broadcast live at 11:15 p.m. ET every Wednesday and Saturday. A single ball machine is used with ball numbers ranging from 1 to 53. Whoever matches all six numbers in any order wins the jackpot.

About the Possibility of Voting

Question 3.1:

In plurality voting, the voter picks one candidate and the candidate with the most votes wins. The U.S.A. uses the plurality voting system in its elections. In the Borda count system, voters are made to rant candidates in order of preference. Candidate with the most points wins. Slovenia uses Borda count in certain political elections. Lastly, the pairwise comparison voting method enables voters to rank candidates and make a series of comparisons in which every candidate is compared to each of the other candidates. The preferred candidate receives one point. In the case of a tie, each receives a half a point. The winner is the candidate with the most points.

Question 3.2:

The presidential election could be improved by allowing voters to rank all candidates according to their preferences. In this case, voting would be rated based on the first choice of each ballot. If no candidate manages to win the first-round majority of the votes, the candidate with the minimum number of votes shall be eliminated and the next round of voting begins. The candidate with a majority (over 50%) would win the election.

Question 3.3:

While the law does not force citizens to vote, citizens have a moral and social responsibility to vote. Exercising this obligation enables citizens to elect a leader that represents the welfare of the majority.