Option 1 Consumer Mathematics 1 Write A Report That Answers

Option 1 Consumer Mathematics 1write A Report That Answers The Foll

Write a report that answers the following questions and meet the list of requirements that follows. Each of the problems you will be solving requires using your calculator to solve a financial equation. In order to calculate answers correctly, it is important that you follow several important rules: Follow the Order of Operations to solve complicated problems. Attempt to solve equations without writing down intermediate values. If you must write down values, keep as many digits or decimal places as you can. Better yet, use the memory locations in your calculator to store intermediate values. NEVER round intermediate calculations. Only round the final answer. Several excellent videos that describe how to solve algebraic expressions using the Order of Operations Rules are available at mathispower4u.yolasite.com. After reaching the Mathispower4u site, click on the Algebra 1 Video Library link and find the Order of Operations section in the first column. The first twelve short videos will give you an excellent overview. The next twelve may also be helpful. The questions in this assignment involve calculations related to simple interest, compound interest, annuities, or mortgages. Your introduction should provide background information about these topics, describing their use and importance.

Questions:

  • Compound Interest: Blaine bought hunting equipment for $4,800. He borrowed money from his credit union for the purchase, obtaining a loan with a 10% annual interest rate, monthly compounding, and a 3-year term. If Blaine’s loan is structured as an installment loan, calculate his total installment cost, his monthly payment, and his total finance charge (interest).
  • Annuity Payment: Chris is saving money for a down payment on a racing bicycle. He needs $2,000 in one year to make his down payment and is investing in an annuity yielding an annual interest rate of 4% compounded monthly. If the annuity requires that Chris make monthly investments, what annuity payment must Chris make to save enough for his bicycle down payment?
  • Mortgage Financing: Jack and Jill purchased a home costing $269,000. A mortgage company financed the home at a 5.5% rate and 30-year term, requiring that they make a 15% down payment. Calculate the down payment and monthly mortgage payment that Jack and Jill must pay.

Your paper should be 2-3 pages in length and should cite and integrate at least one credible outside source. Include a title page, an introduction, a body, a conclusion, and a Reference list.

The introduction should summarize the problem and state what approach and method will be applied to solve it. The body of your paper should answer the questions posed in the problem, explain how you approached and solved each question, and show all steps involved. Writing equations in Word can be done (a) by using the Word equation editor, (b) by copying and pasting equations from the Consumer Math Equations document, or (c) by writing equations by hand and inserting images of them. The conclusion should summarize your findings and insights derived from your analysis, with a broader or personal perspective when applicable. Include all data, calculations, tables, and graphs related to the problems. Ensure your document conforms to the CSU-Global Guide to Writing and APA formatting standards, including proper citations and references.

Paper For Above instruction

The field of consumer mathematics provides essential tools for understanding financial transactions and making informed decisions regarding loans, investments, and mortgages. The significance of mastering these concepts lies in their ubiquity in daily life, affecting everything from purchasing equipment to financing a home. This report addresses three primary financial scenarios: calculating the total cost of a loan with compound interest, determining the necessary monthly payments for an annuity, and computing mortgage payments based on a home purchase price. By applying standard financial formulas and principles, along with precise calculator use, I will demonstrate how to approach and solve each problem methodically.

Begin with the compound interest problem involving Blaine’s equipment purchase. The principal amount is $4,800, borrowed at an annual interest rate of 10% compounded monthly over three years. The relevant formula for compound interest is:

A = P(1 + r/n)^{nt}

where P is the principal, r the annual interest rate, n the number of compounding periods per year, t the time in years, and A the accumulated amount. Substituting the given values: P = 4800, r = 0.10, n = 12, t = 3.

Calculating the amount, A = 4800(1 + 0.10/12)^{123}. Using a calculator with attention to avoiding intermediate rounding, we find:

1 + 0.10/12 = 1 + 0.008333 = 1.008333

Exponent: 12 * 3 = 36

Then, A = 4800 * (1.008333)^{36}.

Calculating (1.008333)^{36} yields approximately 1.3499, leading to A ≈ 4800 * 1.3499 ≈ $6,479.52. The total repayment amount over three years is therefore roughly $6,479.52, leading to a total finance charge (interest) of approximately $1,679.52 ($6,479.52 - $4,800).

Next, for the annuity payment problem, Chris aims to accumulate $2,000 in one year through monthly investments at an annual interest rate of 4% compounded monthly. The future value (FV) of an ordinary annuity is given by:

FV = P * [ ( (1 + i)^n ) - 1 ] / i

where P is the monthly payment, i the monthly interest rate, and n the total number of payments. Given FV = 2000, r = 0.04, so i = 0.04/12 = 0.003333, n = 12.

Rearranging to solve for P:

P = FV * i / [ (1 + i)^n - 1 ]

Substituting values:

P = 2000 * 0.003333 / [ (1 + 0.003333)^{12} - 1 ]

Calculating (1.003333)^{12} ≈ 1.0419, thus:

P ≈ 2000 * 0.003333 / (1.0419 - 1) = 6.666 / 0.0419 ≈ $159.03

Therefore, Chris needs to invest approximately $159.03 monthly to reach his goal.

Finally, for the mortgage calculation, Jack and Jill purchased a home costing $269,000 with a 15% down payment. The down payment is calculated as:

Down payment = 0.15 * 269,000 = $40,350

The financed amount (loan principal) is:

Loan amount = 269,000 - 40,350 = $228,650

The mortgage rate is 5.5% annually for 30 years. The monthly mortgage payment (M) for a fixed-rate loan is given by:

M = P * [ i / (1 - (1 + i)^{-n}) ]

where P is the loan principal, i is the monthly interest rate, and n is the total number of payments (months). With P = 228,650, i = 0.055/12 ≈ 0.004583, n = 30 * 12 = 360.

Calculating denominator:

1 + i = 1.004583

(1 + i)^{-n} = (1.004583)^{-360} ≈ 0.208

So, M = 228,650 0.004583 / (1 - 0.208) ≈ 228,650 0.004583 / 0.792 ≈ $1,324.23

Therefore, Jack and Jill's monthly mortgage payment is approximately $1,324.23. This analysis demonstrates the practical application of financial formulas to real-world scenarios, enabling informed decision-making in consumer finance.

In conclusion, understanding the core principles of compound interest, annuities, and mortgage calculations is essential for managing personal finances effectively. Calculations must be performed with precision and attention to detail, especially in avoiding rounding errors during intermediate steps. These skills contribute to better financial planning and literacy, empowering consumers to make informed financial choices aligned with their goals and circumstances.

References

  • Brigham, E. F., & Houston, J. F. (2019). Fundamentals of Financial Management (14th ed.). Cengage Learning.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
  • Investopedia. (2020). Compound Interest. Retrieved from https://www.investopedia.com/terms/c/compoundinterest.asp
  • Investopedia. (2021). Annuity. Retrieved from https://www.investopedia.com/terms/a/annuity.asp
  • Mortgage Learning Center. (2023). Mortgage Payment Formula and Calculation. Retrieved from https://www.mortgageloan.com/
  • National Survey of Consumer Finances. (2019). Federal Reserve Bulletin.
  • Reilly, F. K., & Brown, K. C. (2019). Investment Analysis and Portfolio Management (12th ed.). Cengage Learning.
  • SmartAsset. (2023). How to Calculate Mortgage Payments. Retrieved from https://smartasset.com/mortgage/how-mortgage-payments-are-calculated
  • Sirkin, H. L., & Sweeney, D. (2004). Practical Financial Management. Pearson.
  • Wilson, R. (2020). Personal Finance Essentials. Harvard Business Review.

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