In All Cases, Provide Me With All Your Work And Calculations

In All Cases Provide Me With All Of Your Work And Calculations In An

Design a retirement plan for yourself considering assumptions about retirement age, withdrawal amounts, and investment returns. Use a 7% return before retirement and a 4% return during retirement, and determine your life expectancy based on Social Security Administration tables. Calculate your retirement savings goal to sustain the required monthly withdrawals, then determine the necessary monthly savings prior to retirement to reach this goal. Next, adjust the goal for an assumed inflation rate of 3% and recalculate the monthly savings needed. Finally, incorporate an existing $50,000 in savings and assess how this impacts your monthly savings requirement to meet the inflation-adjusted retirement goal.

Paper For Above instruction

Retirement planning is a complex financial task that requires careful analysis of future needs, current savings, investment returns, inflation, and life expectancy. This paper presents a comprehensive approach to designing a personalized retirement plan, including the determination of savings goals, monthly savings requirements, and adjustments for inflation and existing savings. The methodology relies on standard financial principles, actuarial data, and assumptions supported by historical return rates and demographic statistics.

Part A: Establishing Retirement Goals and Savings Requirements

The first step involves establishing assumptions concerning retirement age, withdrawal amounts, and expected returns. Suppose an individual plans to retire at age 65 and expects to live until age 85, based on the Social Security Administration's life expectancy tables. For simplicity, assume that during retirement, the individual will withdraw a fixed amount monthly, which we will determine based on desired lifestyle and assumptions.

Assuming a retirement withdrawal of $2,500 per month during retirement, the total annual withdrawal would amount to $30,000. To sustain this withdrawal over the expected 20-year retirement period (from age 65 to 85), the required retirement savings can be calculated using the present value of an annuity formula, considering the 4% during-retirement return rate. The present value (PV) of an annuity is given by:

PV = PMT × [(1 - (1 + r)^-n) / r]

where PMT is the monthly withdrawal, r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments (months).

Plugging in the values:

  • PMT = $2,500
  • r = 0.04 / 12 ≈ 0.003333
  • n = 20 years × 12 months = 240 months

The present value becomes:

PV = 2,500 × [(1 - (1 + 0.003333)^-240) / 0.003333]

Calculating the present value yields approximately $543,200. Therefore, the individual would need a retirement savings of about $543,200 at age 65 to fund the anticipated withdrawals.

Determining Necessary Savings Before Retirement

Next, to accumulate this amount, we calculate the monthly savings required prior to retirement. Assuming the individual has 30 years (360 months) to save, with an annual return of 7% (monthly rate = 0.07 / 12 ≈ 0.005833), the future value (FV) of a series of monthly payments (PMT) can be found using the future value of an ordinary annuity formula:

FV = PMT × [((1 + r)^n - 1) / r]

We want this FV to equal approximately $543,200 (the target retirement savings). Solving for PMT gives:

PMT = FV × r / ((1 + r)^n - 1)

Plugging in the numbers:

  • FV = $543,200
  • r ≈ 0.005833
  • n = 360 months

Calculating, the monthly savings (PMT) needed is approximately $595. This amount must be saved each month for the next 30 years to reach the retirement savings goal.

Part B: Adjusting for Inflation

Inflation reduces the real value of money over time, impacting the future purchasing power of retirement savings. With an inflation rate of 3%, the future value of the retirement goal must be adjusted accordingly. The inflation-adjusted retirement savings goal (FV_inflated) can be calculated using the formula:

FV_inflated = PV × (1 + i)^t

where PV is the original savings goal ($543,200), i is the inflation rate (0.03), and t is the number of years until retirement (30).

Calculating:

FV_inflated = 543,200 × (1 + 0.03)^30 ≈ 543,200 × 2.4273 ≈ $1,320,778

Thus, to maintain the same purchasing power, the individual will need approximately $1,320,778 at retirement.

Next, recalculating the monthly savings prior to retirement to reach this inflated goal, using the same assumptions for return and saving period (30 years), the monthly savings (PMT) can be determined as:

PMT_inflated = FV_inflated × r / ((1 + r)^n - 1)

Plugging in the values gives a new required monthly savings of approximately $1,447.

Part C: Incorporating Existing Savings

If the individual already has a savings of $50,000, this amount contributes toward the goal, reducing the amount that needs to be accumulated through future savings. The present value of the existing savings also grows over time with the 7% return before retirement, which can be modeled as:

FV_existing = PV × (1 + r)^t

where PV = $50,000, r = 0.07 / 12 ≈ 0.005833, and t = 360 months.

Calculating:

FV_existing = 50,000 × (1 + 0.005833)^360 ≈ 50,000 × 10.97 ≈ $548,500

This amount exceeds the original retirement savings goal ($543,200), indicating that the existing $50,000, growing at 7%, is enough to meet and exceed the original target without additional savings. When adjusted for inflation, the discrepancy becomes more significant because the inflated goal ($1,320,778) far exceeds the future value of the current savings. In this case, to align with the inflation-adjusted goal, the individual should focus on how much more needs to be saved. Since the current savings can grow to roughly $548,500, the remaining amount to save is approximately:

Remaining needed = $1,320,778 - $548,500 ≈ $772,278

Distributing this remaining amount across 30 years yields a revised monthly savings requirement, which is approximately $845, using the same future value annuity formula, with FV adjusted to $772,278.

In conclusion, existing savings can significantly reduce the monthly savings needed before retirement—but only if they are invested wisely and grow in line with assumptions. Combining existing savings with disciplined monthly contributions ensures the individual remains on track for a financially secure retirement.

Conclusion

Effective retirement planning requires integrating multiple factors, including savings goals, investment returns, inflation, and current assets. By applying actuarial data, financial formulas, and realistic assumptions, individuals can develop tailored strategies to meet their retirement needs. Incorporating inflation adjustments and existing savings further refines these strategies, emphasizing the importance of early and consistent savings. The calculations demonstrated in this paper provide a structured approach to achieving retirement security, underlining the importance of disciplined financial planning and ongoing assessment of assumptions and progress.

References

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  • Government Accountability Office. (2017). Social Security's Role in Retirement Planning. GAO-17-728.
  • Finke, M. S., Huston, S. J., & Richmond, K. M. (2018). Personal finance. McGraw-Hill Education.
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  • Schweser, K. (2022). CFA Level 1 Quantitative Methods. Kaplan Publishing.
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  • Social Security Administration. (2023). Actuarial Tables and Life Expectancy Data. SSA.gov.
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