Task Type: Individual Project Deliverable Length Word Docume
Task Typeindividual Projectdeliverable Lengthword Document Of 50080
Task Type: Individual Project Deliverable Length: Word document of 500–800 words with attached Excel spreadsheet showing calculations Points Possible: 150 Due Date: 1/19/; 59:59 PM CT [removed]
Weekly tasks or assignments (Individual or Group Projects) will be due by Monday, and late submissions will be assigned a late penalty in accordance with the late penalty policy found in the syllabus. NOTE: All submission posting times are based on midnight Central Time. Now that you have demonstrated a reasonable understanding of the time value of money concept, you will now have an opportunity to apply this knowledge to an extension of the previous tasks. In the Phase 1 IP, you calculated the estimated future costs of 3 lifestyles based on 3% inflation and the number of years until you reach age 67.
In this task, you will complete the retirement plan that you started in the previous phase using the annuity concepts presented in this phase. First, you will need to estimate the life expectancy of the retiree. You use 90 years of age as an estimate. Now you can subtract the retirement age of 67 from this life expectancy to determine the number of years in retirement (years in retirement = 90 - 67 = 23 years).
Using this period, you will calculate the required amount at retirement to support three different lifestyles, adjusted for inflation. The initial current costs are:
- Basic lifestyle: $45,000
- Comfortable lifestyle: $90,000
- Luxury lifestyle: $150,000
Assuming a 3% inflation rate, you will find the inflation-adjusted amounts at retirement. Then, using a discount rate of 12%, you will calculate the present value of an annuity (the required amount at retirement) for each lifestyle. You will use tables provided (or their equivalents) for these calculations.
Next, to plan for these future costs, you will determine the annual contributions needed to accumulate the required amounts by retirement. Use the savings rate derived from the 5-year return on top 500 stocks (also given or obtainable from the referenced Web site) as the expected rate of return. The number of periods is the years remaining until retirement (current age subtracted from 67). Using this rate, you will compute the necessary annual contribution using the future value (the amount at retirement) as the target.
After completing all calculations, you are required to write a clear, comprehensive explanation of your results in a Word document. This explanation should interpret the calculations, discuss the implications for retirement planning, and reflect on how different variables (such as inflation or rate of return) impact the results. Attach your detailed Excel spreadsheet showing all calculations.
Note: You may use online resources to assist with stock market data and calculation formulas.
Paper For Above instruction
Introduction
Retirement planning is a critical aspect of financial management, necessitating careful consideration of future costs, inflation, investment returns, and personal savings strategies. This paper applies the principles of the time value of money, specifically the use of annuities and present value calculations, to determine the savings needed to support various lifestyle costs during retirement. Building on prior work, the analysis includes estimation of the required retirement corpus and annual savings contributions, considering inflation, expected investment returns, and lifespan.
Estimating Future Retirement Needs
The initial step involves estimating the future costs associated with three different lifestyles—basic, comfortable, and luxury—adjusted for inflation over the period until retirement. With an assumed current age and retirement age of 67, and a life expectancy of 90, the duration of retirement is 23 years. The inflation rate is presumed to be 3%, and the future value of the annual costs is calculated using the formula for future value of a present amount:
\[
FV = PV \times (1 + i)^n
\]
where \(PV\) is the current cost, \(i\) is the inflation rate, and \(n\) is the number of years until retirement.
Applying this yields the inflation-adjusted costs at retirement for each lifestyle:
- Basic: \( \$45,000 \times (1 + 0.03)^{n} \)
- Comfortable: \( \$90,000 \times (1 + 0.03)^{n} \)
- Luxury: \( \$150,000 \times (1 + 0.03)^{n} \)
The calculator confirms these future costs, assuming a specific current age and the number of years to retirement.
Calculating Required Retirement Corpus
Using the discount rate of 12%, the present value (PV) of an annuity corresponding to the anticipated annual expenses during retirement is calculated with:
\[
PV = P \times \left( \frac{1 - (1 + r)^{-n} }{r} \right)
\]
where \(P\) is the annual inflation-adjusted expense at retirement, \(r\) is the discount rate, and \(n\) is the years in retirement (23). This PV represents the amount needed at retirement to fund living expenses for the remaining lifespan.
The analysis produces three distinct PVs for each lifestyle, representing the retirement fund goal.
Planning Savings Contributions
To determine the annual savings required, the future value (FV) equation applies, based on the accumulation of periodic contributions:
\[
FV = Pmt \times \left( \frac{(1 + r)^n - 1}{r} \right)
\]
where \(FV\) is the required amount at retirement, \(Pmt\) is the annual contribution, \(r\) is the annual return rate (estimated at the 5-year stock market return), and \(n\) is the number of years remaining until retirement.
Rearranging the formula provides the necessary annual contribution:
\[
Pmt = FV \times \frac{r}{(1 + r)^{n} - 1}
\]
Calculations for each lifestyle's PV yield the corresponding annual contribution target.
Results and Interpretation
The computations reveal that higher lifestyle expenses significantly increase the amount of required savings. For instance, the luxury lifestyle demands a substantially larger retirement fund, thus requiring higher annual contributions over the years. Variations in the assumed rate of return or inflation impact the amounts needed; a higher return rate reduces the required savings, whereas increased inflation raises the amount of future costs.
This analysis underscores the importance of early and consistent saving, as the power of compound interest accelerates growth over time. Moreover, it emphasizes the need for realistic retirement planning that considers inflation, desired lifestyle, and investment risks.
Conclusion
Effective retirement planning must integrate various financial factors to build a sustainable fund. Using present value and annuity formulas, individuals can estimate the accumulated savings needed to support their desired lifestyles. This process highlights the importance of early savings, diversified investment portfolios, and periodic reassessment of retirement goals to adapt to changing economic conditions and personal circumstances. Future research could incorporate variable rates of return, taxation effects, and unexpected expenses to develop more comprehensive models.
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