Initial Investment After Reading Chapters 3 And 4 Of Your Te

Initial Investmentafter Reading Chapters 3 And 4 Of Your Textbook Add

After reading Chapters 3 and 4 of your textbook, address each of the following questions: a) Think of something you want or need for which you currently do not have the funds. It could be a vehicle, boat, horse, jewelry, property, vacation, college fund, retirement money, etc. Select something which costs somewhere between $2,000 and $50,000. Use the “Present Value Formula”, which computes how much money you need to start with now to achieve the desired monetary goal. Assume you will find an investment that promises somewhere between 5% and 10% interest on your money (you choose the rate) and pretend you want to purchase your desired item in 12 years. (Remember that the higher the return, usually the riskier the investment, so think carefully before deciding on the interest rate.) How much do you need to invest today to reach that desired amount 12 years from now? b) You wish to leave an endowment for your heirs that goes into effect 50 years from today. You don’t want to be forgotten after you pass so you wish to leave an endowment that will pay for a grand soirée yearly and forever. What amount would you like spent yearly to fund this grand party? How much money do you have to leave to your heirs 50 years from now assuming that will compound at 6% interest? Assuming that you have not invested anything today, how much would you have to invest yearly to fully fund the annuity in 50 years, again assuming a 6% monthly compounding rate? Guided Response: Review several of your classmates’ postings. Examine calculations and reply to at least two of your classmates’ posts by adding recommendations to extend their thinking or posing questions to help them consider components they may have missed. Reference: Byrd, J., Hickman, K., & McPherson, M. (2013). Managerial Finance. San Diego, CA: Bridgepoint Education Inc. This text is a Constellation™ course digital materials (CDM) title.

Paper For Above instruction

The process of financial planning involves understanding the time value of money, which is essential in making informed investment decisions. When planning for a future purchase or estate, calculating the present value and future value of investments guides individuals in determining how much to invest today or periodically. This paper explores these concepts through two practical scenarios derived from the textbook chapters, illustrating how to strategically approach savings and investments to meet long-term financial goals.

Part A: Determining the Present Investment for a Future Purchase

Suppose an individual intends to purchase a vehicle costing $20,000 in twelve years but currently lacks the necessary funds. Using the present value formula, which is expressed as PV = FV / (1 + r)^t, where PV is the present value, FV is the future value, r is the annual interest rate, and t is the number of years, the individual can calculate the amount needed today.

Choosing an interest rate of 7% (a moderate rate between 5% and 10%), the calculation proceeds as follows:

PV = 20,000 / (1 + 0.07)^12 ≈ 20,000 / (1.07)^12 ≈ 20,000 / 2.274 ≈ $8,793.52

This computation indicates that investing approximately $8,793.52 today at a 7% annual return would accumulate to $20,000 in twelve years. The interest rate selection significantly influences the initial investment; higher rates reduce the present value required, but also entail higher risk, reinforcing the importance of balancing return and risk in investment decisions.

Part B: Planning for a Permanent Endowment

For the second scenario, an individual desires to fund a grand annual soirée indefinitely, with the goal of leaving an inheritance in fifty years that will support this regular expenditure. Suppose the desired annual expense is $10,000. To determine the amount needed at the end of fifty years, assuming a 6% annual interest rate compounded annually, the future value can be calculated as FV = PV * (1 + r)^t, or directly employing the present value of a perpetuity since the expenditure is perpetual.

If the annual spending amount ($A$) is known, the present value required at the start of the endowment is PV = A / r. Substituting the values: PV = 10,000 / 0.06 ≈ $166,666.67. This sum represents the amount that needs to be accumulated fifty years from now to generate $10,000 annually forever, assuming a 6% return.

To determine how much to invest annually over fifty years to reach this target, the future value of an ordinary annuity formula is used: FV = P [( (1 + r)^n - 1 ) / r], where P is the annual contribution, r is the annual interest rate divided by the number of periods per year, and n is the total number of contributions. Assuming monthly compounding at a 6% annual rate, the monthly interest rate is 0.06 / 12 = 0.005, and n = 50 12 = 600 months.

Rearranging the formula to solve for P (monthly contribution):

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

P = 166,666.67 * 0.005 / [ (1 + 0.005)^600 - 1 ]

Calculating the denominator: (1 + 0.005)^600 ≈ e^(600ln(1.005)) ≈ e^(6000.004987) ≈ e^2.992 ≈ 19.94 Thus, P ≈ 833.33 / (19.94 - 1) ≈ 833.33 / 18.94 ≈ $44.02

This indicates that investing approximately $44.02 monthly for fifty years, with compounding at 6% monthly, would accumulate the needed amount at the end to support the perpetual yearly expenditure of $10,000.

Discussion and Recommendations

The calculations demonstrate the importance of disciplined saving and understanding interest compounding’s impact on long-term wealth accumulation. For individuals planning significant future purchases or endowments, selecting appropriate interest rates, considering investment risk, and maintaining regular contributions are vital. Diversifying investments to match desired risk levels while ensuring sufficient growth to meet goals is recommended. For the scenario involving perpetual endowments, understanding the balance between contribution frequency and compounding effects can optimize savings strategies. Additionally, considering inflation’s effect over extended periods is crucial, as real purchasing power and value may diminish if not accounted for properly. Financial advisors should tailor strategies based on individual risk tolerance, time horizons, and inflation expectations to ensure that long-term objectives are achievable.

Conclusion

In conclusion, applying the present and future value formulas allows individuals to plan effectively for future financial needs, whether for a specific purchase or long-term endowments. Recognizing the interplay of interest rates, compounding frequency, and contribution timing helps in devising optimal saving strategies. As financial markets and products evolve, continuous learning and adjustment of these calculations are necessary to adapt to changing economic conditions, ensuring financial security and fulfilling long-term aspirations.

References

• Byrd, J., Hickman, K., & McPherson, M. (2013). Managerial Finance. San Diego, CA: Bridgepoint Education Inc.
• Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Boston, MA: Cengage Learning.
• Ross, S. A., Westerfield, R., & Jordan, B. D. (2019). Fundamentals of Corporate Finance. New York, NY: McGraw-Hill Education.
• Mishkin, F. S., & Eakins, S. G. (2018). Financial Markets and Institutions. Boston, MA: Pearson.
• Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
• Investopedia. (2023). Present Value (PV). https://www.investopedia.com/terms/p/presentvalue.asp
• Investopedia. (2023). Future Value (FV). https://www.investopedia.com/terms/f/futurevalue.asp
• Corporation for Public Broadcasting. (2020). The Power of Compounding. https://www.pbs.org/newshour/education/the-power-of-compounding
• The Wall Street Journal. (2022). How to Invest for Long-Term Goals. https://www.wsj.com/articles/how-to-invest-for-long-term-goals-11608556498
• U.S. Securities and Exchange Commission. (2021). Investment Risks and Returns. https://www.sec.gov/investor/alerts/ia_prudence.pdf