Math125 Unit 2 Individual Project: Number Sense Estimation

Math125 Unit 2 Individual Projectnumber Sense Estimation And Financ

Math125: Unit 2 Individual Project Number Sense, Estimation, and Financial Computations Be sure to show ALL of your work details. Submit your answers in a Word document in the Unit 2 IP Submissions area. Question 1: CONSUMER CREDIT For big purchases, many stores offer a deferred billing option (buy now, pay later) that allows shoppers to buy things now without paying the bill at checkout. 1. Assume you bought new appliances for your newly renovated home. Based on the first letter of your last name, choose the total value of the appliances that you have purchased. This will be denoted by P. It does not necessarily have to be a whole number. First letter of your last name Possible values for P A–F $5,000–$5,999 G–L $6,000–$6,999 M–R $7,000–$7,999 S–Z $8,000–$8,999 Total value of the appliances, P $ 8,. The store where you bought these appliances offered you a provision that if you pay the bill within 2 years, you will not be charged any interest for your purchases. However, if you are even a day late in paying the bill, the store will charge you interest for the 2 years. Although the annual interest rate is based on your credit worthiness, disregard this on this assignment and instead, choose an interest rate between 22% and 26%. This will be denoted by r. Annual Interest rate in decimal form, r 0.. Suppose you forget about the bill and pay it 1 day late. How much interest do you pay if the store charges you simple interest? Because this is a dollar value, round your answer to the nearest cent. (Assume t = 2 years.) Interest will be $2,040 annually, adding up to $4,080 over the 2-year period 4. How much is your total bill —the total value of the appliances plus the interest? Round your answer to the nearest cent. The total bill will sum up to the amount of $12,580. 5. How much is your total bill if, instead, the store charges you interest that is compounded daily? Use 6 digits on your intermediate calculations, and round your final answer to the nearest cent. (Assume t = 2 years.) P = $8,500 (the principal) r = 0.24 (% rate per half-year) t = 2 (years) I = $8,500(0.24) (2) = $40.80. You will earn $40.80 interest total over the two years. 6. How much interest do you pay if it is compounded daily? Round your answer to the nearest cent. 7. Based on the result of your calculations, write a summary about the difference between simple and compound interest. Simple interest is computed based on the principal only or original amount of the borrowed money. Compound interest on the other hand is computed periodically. The computations include the earned interest from the principal plus the compounded interest earned over a period of time. 8. Do you think a deferred billing option is helpful for shoppers? Explain your answer. Question 2: Saving for Your Retirement Suppose your goal is to have a lump sum that you can withdraw when you retire. To accomplish this, you decided to contribute a portion of your paycheck in an annuity. 1. Using the AIU Library or the Internet, read about what kind of expenses you will be faced with when you retire. Write a brief summary of your research. 2. Based on your research, state the lump sum, in U.S. dollars, that you want to have when you retire. This is the future value of your investment; denote it by F. Future Value, F $ 3. State the time, in years, that you plan to contribute to your retirement account. Denote this by t. Time, t 4. Based on the first letter of your last name, choose the annual interest rate for your retirement account. Denote this by r, and you will convert this to its decimal form. It does not necessarily have to be a whole number. First letter of your last name Possible values for r A–F 6.00%–7.99% G–L 8.00%–9.99% M–R 10.00%–11.99% S–Z 12.00%–13.99% Annual interest rate in decimal form, r 5. From the table below, choose how many times per year you want to contribute to your retirement. Denote this by n, and this will also be your compounding period. Compounding Period n Yearly 1 Semi-Annually 2 Quarterly 4 Monthly 12. 6. Calculate the interest rate per compounding period, which you will denote by i, by dividing the annual interest rate from #4 by the compounding period from #5, i.e., . Round your answer to 6 decimal places. Interest rate per compounding period, i 7. Your contribution per period, which you will denote by C, to this retirement account is calculated using the following formula: Using the values that you have chosen for F, i, n, and t, calculate your contribution per period. Use six decimal places for your intermediate calculations, and round your final answer to the nearest cent. NOTE: Make sure to review exponents and the order of operations from College Math Chapter 1. 8. Calculate your total contribution to this retirement account, which you will denote by TC, by using the formula TC = C x n x t. 9. What can you say about the difference in value between your total contribution (TC) and the lump sum (F) that you will receive? Based on what you have learned in this unit, is there a term that is used for this difference? 10. Summarize the results of your calculations, and explain why it is important to prepare for your retirement.

Paper For Above instruction

The following comprehensive analysis addresses the key aspects of consumer credit and retirement savings, illustrating the practical applications of financial mathematics through real-world scenarios. The first part explores consumer credit options, focusing on deferred billing, interest calculations, and the comparison between simple and compound interest. The second part discusses retirement planning, emphasizing the importance of early savings, interest rate strategies, and the significance of understanding investment growth over time.

Analysis of Consumer Credit and Interest Calculations

In the context of purchasing household appliances, understanding the financial implications of deferred billing is crucial. Suppose an individual named with a last name starting with “R” invests in appliances valued at between $7,000 and $7,999, specifically choosing a $7,500 purchase for simplicity. The store offers a no-interest promotion if paid within two years, but a late payment triggers interest charges based on a chosen rate. If this rate is set at 24% annually, the simple interest calculation becomes pertinent.

The simple interest formula is I = P r t, where P is the principal, r is the annual interest rate, and t is the time in years. Given P = $7,500, r = 0.24, and t = 2, interest calculation yields I = 7,500 × 0.24 × 2 = $3,600. However, since the individual pays one day late, the interest accrues for only 2 years, but interest is compounded differently if using compound interest methods.

When interest is compounded daily, the calculation is more involved. The formula for compound interest is A = P(1 + i)^n, where i is the interest per period and n is the total number of periods. If r is 24% annually, the daily interest rate is r/365 ≈ 0.0006575. The total number of days over two years is 730, making the calculation A = 7,500 × (1 + 0.0006575)^730. This results in a larger total due to compounding, emphasizing how compound interest can significantly increase the amount owed when payments are late.

Comparison of Simple and Compound Interest

The comparison reveals that simple interest is straightforward, calculated only on the original principal, leading to a smaller total interest over time. Conversely, compound interest incorporates accumulated interest, leading to a higher total payable. For example, with a principal of $7,500 and a 24% annual rate compounded daily, the total repayment after two years would be approximately $7,500 × (1 + 0.0006575)^730 ≈ $9,846. This demonstrates how compound interest can substantially increase costs when payments are delayed.

Implications for Consumers and Shoppers

The analysis underscores the importance of timely payments and understanding interest calculations. Deferred billing can be advantageous if paid within the promotional period, avoiding interest altogether. However, late payments can lead to significant interest charges, especially when compounded. Consumers should evaluate whether the convenience outweighs the potential cost and consider paying early whenever possible to minimize interest expenses.

Retirement Savings and Investment Growth

Retirement planning involves estimating future expenses and setting tangible savings goals. Suppose an individual plans to retire in 30 years with an aim to accumulate a future value F of $500,000. Based on research, retirees often face expenses including healthcare, housing, and daily living costs, which can significantly vary but typically increase over time. Regular contributions into an annuity account can help reach this goal, provided they are invested wisely with compounded interest.

Assuming the individual’s last name begins with 'L', an appropriate interest rate could be 8% annually. If contributions are made quarterly (n=4), the interest rate per period is i = 0.08 / 4 = 0.02. Using the future value of an ordinary annuity formula, the contribution per period C can be calculated by rearranging:

F = C × [(1 + i)^nt - 1] / i

Solving for C ensures the desired future value considering the total number of periods (nt). For example, with F = $500,000, n=4, t=30, and i=0.02, the calculation of C involves exponential functions, emphasizing the significance of consistent contributions and compound interest in wealth accumulation.

Conclusion and Significance of Retirement Preparation

The juxtaposition of the debt accumulation due to late payments and the benefits of systematic retirement savings demonstrates the importance of financial literacy. Understanding interest calculations helps consumers avoid costly mistakes, like accruing excessive debt through late payments or misinterpreting the power of compound interest in investments. Early and consistent saving, informed by these principles, can lead to a secure and comfortable retirement, highlighting the critical need for proactive financial planning.

References

• Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice (15th ed.). Cengage Learning.
• Gitman, L. J., & Zutter, C. J. (2015). Principles of Managerial Finance (14th ed.). Pearson.
• Investopedia. (2023). Simple Interest vs. Compound Interest. https://www.investopedia.com
• Ross, S. A., Westerfield, R. W., & Jaffe, J. (2016). Corporate Finance (11th ed.). McGraw-Hill Education.
• Financial Industry Regulatory Authority (FINRA). (2021). Basics of Investing. https://www.finra.org/investors
• U.S. Securities and Exchange Commission. (2023). Retirement Planning. https://www.sec.gov/investor
• Moore, D. (2020). Personal Finance: An Encyclopedia of Modern Money Management. ABC-CLIO.
• Higgins, R. C. (2018). Analysis for Financial Management. McGraw-Hill Education.
• Clark, M. (2017). Asset Management and Financial Planning. Wiley.
• SMART Financial Planning. (2022). The Power of Compound Interest. https://smartfinancialplanning.com