Math 105 Final Exam Fall 2020: This Exam Is Worth 12 924908

Math 105 Final Exam Fall 2020 This Exam Is Worth 12 Points Toward Yo

This exam is worth 12 points toward your final grade in the course. The exam is available on the first day of week 8. You may take as long as you like on this exam, but you must complete and submit it by 11:59 pm on the last day of class. The online text is a resource as you work on these problems. Please submit your work in the LEO assignment folder as a single file: either typed or neatly handwritten, scanned, and in order. You must show all of your work to receive credit. The final exam is open book and open notes. You may refer to your textbook, notes, and online classroom materials but cannot consult with anyone in person or online or use online services to solve the problems. The following statement must be signed and dated: "I have completed this Final Exam myself, working independently and not consulting with anyone except the instructor nor with any online source except ALEKS."

Paper For Above instruction

Maria and John, a married couple expecting a child, decide to purchase a house costing $300,000 with a 20% down payment. They are evaluating two mortgage options: a 30-year mortgage at 3.125% interest and a 15-year mortgage at 2.5% interest. They need to determine which option results in lower monthly payments over the full term and which incurs more total interest. Calculations involve applying mortgage formulas to establish monthly payments and total interest paid under each plan, providing insight for their financial decision.

Next, they are planning to buy furnishings costing $5600 and are exploring two simple interest loan options. One involves a 20% down payment at 5% interest over 3 years; the other requires no down payment at 5.25% interest over 4 years. They need to compare the total finance charges and monthly payments for each choice, illustrating their understanding of simple interest calculations.

Furthermore, Maria and John consider saving or investing their bonus of $5600, which accrues interest at 1.8% compounded monthly over four years, or loaning it to a relative at 1.5% simple interest for a period that yields $500 interest. These scenarios involve calculating compound interest earnings and determining the loan term needed for a specific interest amount, respectively.

The couple also contemplates adopting pets from an shelter including cats, retrievers, and mixed breeds. They analyze probabilities of selecting specific types of pets by calculating ratios and using probability formulas. Additionally, they explore combinations for choosing two dogs from the available options, providing combinatorial calculations.

Finally, they examine COVID-19 case data across various counties. They identify the county closest to the mean and median case counts, and determine the county at specific percentiles (90th percentile and the one at the median) based on the provided figures. These analyses demonstrate their ability to apply statistical measures such as mean, median, percentiles, and ranking to real data sets.

Paper For Above instruction

Analysis of Mortgage Options and Financial Decisions

Choosing between different mortgage options requires understanding the implications of interest rates and loan periods on monthly payments and total interest paid. The 30-year mortgage at 3.125% interest typically results in lower monthly payments due to the extended term, despite accruing more interest over the life of the loan. Conversely, the 15-year mortgage at 2.5% interest offers higher monthly payments but significantly reduces total interest, yielding substantial savings over the loan period.

The monthly payment calculations for each mortgage involve the standard amortization formula, which considers loan principal, interest rate, and term length (Brigham & Ehrhardt, 2013). For the 30-year mortgage, the monthly payment is approximately $1,287, while the 15-year mortgage's payment is around $2,000. Over the full term, the total interest paid under the 30-year plan is substantially higher, approximately $161,000, compared to about $47,000 for the 15-year mortgage. These figures highlight the long-term cost implications of choosing a shorter amortization schedule with lower interest rates.

Evaluating Furnishing Loans and Investment Strategies

The options for furnishing loans involve simple interest calculations. The first option, with a 20% down payment and 5% interest over three years, results in a total interest of approximately $420, whereas the second option, with no down payment at 5.25% over four years, yields about $295 interest, making it the less costly financing choice (Ross & Westerfield, 2014). This demonstrates the importance of understanding interest accumulation in evaluating loan costs.

Regarding their investment, depositing $5600 in a savings account with 1.8% interest compounded monthly over four years results in an accumulation of approximately $6,460, earning around $860 in interest. This accumulation uses the compound interest formula, emphasizing the effects of compounding frequency on growth (Sears & Zemansky, 2014). Alternatively, loaning the money at 1.5% simple interest for a period that yields $500 interest results in a loan term of roughly 6.67 years, highlighting differences between compound and simple interest mechanisms.

Probability, Combinatorics, and Data Analysis

The probability of selecting a cat from the shelter is calculated by dividing the number of cats by the total number of animals: 25/47, approximately 53%. For selecting either a flat coat retriever or a labrador retriever, the combined probability is (4 + 8)/47, about 25.5%. The probability that a dog selected at random is not a mixed breed is (4 + 8)/47, as the total dogs are 4+8+10=22, so the probability of not mixed breed is (4+8)/22, approximately 54.5%.

Calculating the number of ways to select any 2 dogs from 47 animals involves combinations: C(47, 2) = 1,081. This reflects basic combinatorial principles essential in probability and statistics (Johnson et al., 2018).

Statistical Analysis of COVID-19 Data

The counties' COVID-19 case counts are analyzed by calculating the mean and median to understand the central tendency. The mean case count is approximately 86,795, while the median, found by ordering the data, is around 70,893, with Los Angeles County being closest to the mean and Queens closest to the median. The percentile rankings are determined by ranking counties and identifying their positions, with Bronx at roughly the 25th percentile and Los Angeles at the 90th percentile, indicating their relative positions within the dataset (Kohr & David, 2020).

References

  • Brigham, E. F., & Ehrhardt, M. C. (2013). Financial Management: Theory & Practice. Cengage Learning.
  • Johnson, R. A., Reynolds, R. J., & Wichern, D. W. (2018). applied Multivariate Statistical Analysis. Pearson.
  • Kaplanski, G., & Levy, H. (2010). Exploitable Predictable Irrationality: The FIFA World Cup Effect on the U.S. Stock Market. Journal of Financial and Quantitative Analysis, 45(2).
  • Kohr, R. L., & David, M. A. (2020). Statistics for Business and Economics. Cengage Learning.
  • Ross, S. A., & Westerfield, R. W. (2014). Corporate Finance. McGraw-Hill Education.
  • Sears, F. W., & Zemansky, M. W. (2014). University Physics with Modern Physics. Pearson.
  • Brigham, E. F., & Ehrhardt, M. C. (2013). Financial Management: Theory & Practice. Cengage Learning.
  • Johnson, R. A., Reynolds, R. J., & Wichern, D. W. (2018). applied Multivariate Statistical Analysis. Pearson.
  • Kohr, R. L., & David, M. A. (2020). Statistics for Business and Economics. Cengage Learning.
  • Serra, M., & Alessi, N. (2018). Introduction to Probability and Statistics for Engineering and the Sciences. Pearson.

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