Number Sense, Estimation, And Financial Computations

Number Sense Estimation And Financial Computationsbe Sure To Show Al

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 0.24 3. 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 Compounding period, n 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 assignment provided two main topics: consumer credit management and retirement savings planning. Each involves financial computations, estimation, and understanding interest mechanisms. The first topic emphasizes understanding the implications of deferred billing options, simple and compound interest, and comparing their effects on the total amount owed. The second topic focuses on planning for retirement by calculating future value, periodic contributions, and the significance of compound interest in building long-term wealth.

Consumer Credit and Interest Computations

When considering purchasing appliances using deferred billing, understanding the impact of interest is crucial. Suppose a consumer purchases appliances valued at a certain amount P, determined by the first letter of their last name. For example, if a person’s last name starts with S, their appliance cost might be between $8,000 and $8,999. The store offers an interest-free period if paid within two years; otherwise, interest accrues if payment is late, even by a day. The annual interest rate, which varies between 22% and 26%, affects the total interest paid upon late payment.

For simple interest, the interest calculation over two years is straightforward and based solely on the principal P. Using the formula I = P × r × t, where P is the principal ($8,500, for illustration), r is the annual interest rate (say, 24%, or 0.24), and t is 2 years, the total interest amounts to $4,080. When considering daily compounded interest, the formula becomes more complex, involving the daily interest rate and compounding periods. Using the compound interest formula A = P(1 + i)^nt, interest accumulates faster, and the total interest paid is higher than with simple interest.

Comparison between simple and compound interest reveals that compound interest grows exponentially over time, especially when compounded frequently (daily). This demonstrates that the method of interest calculation can significantly influence the total amount owed if a payment is late. In practical terms, understanding this difference helps shoppers make informed decisions about deferred billing plans.

Retirement Savings Planning

Retirement planning entails estimating future expenses and determining how much needs to be saved regularly to reach a desired lump sum, F. Research indicates that retirees face costs such as healthcare, housing, and daily living expenses, which often increase with inflation. Therefore, a substantial lump sum is necessary for financial security in later years.

Assuming a target future value F, a time horizon t in years, and an annual interest rate r, the periodic contribution C can be calculated using the future value of an ordinary annuity formula:

F = C × [( (1 + i)^n t - 1 ) / i ]

where i is the interest rate per period, obtained by dividing the annual rate by the number of periods n per year. By rearranging, one can compute the required contribution C. The total contributions over time, TC, are then given by C × n × t.

Understanding the difference between total contributions and the future value F provides insight into how interest accumulates over time, emphasizing the importance of starting to save early. The term "interest earned" refers to the growth of invested money over time due to compound interest, highlighting its crucial role in retirement planning.

Early preparation for retirement allows an individual to leverage the power of compound interest, leading to a much larger fund than the total contributed. In conclusion, consistent contributions and understanding interest mechanisms enable better planning and ensure financial security post-retirement.

References

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• National Institute on Aging. (2022). Planning for Retirement Expenses. Retrieved from https://www.nia.nih.gov
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