With Attached Excel Spreadsheet Showing Calculations

With Attached Excel Spreadsheet Showing Calculationsfirst You Will Ne

With Attached Excel Spreadsheet Showing Calculations first You Will Ne

with attached Excel Spreadsheet showing calculations First, you will need to estimate the future cost of 3 lifestyles assuming an inflation rate of 3% and the number of years before you turn 67 years old. Comfortable lifestyle current cost is approximately $100,000/year. PV of Life Style (Given) Average Rate of Inflation (RATE) Years to Retirement (NPER) Find FV of Life Style $100,000 3.0% Next, you will need to estimate the 5-year average rate of return of the stock market (you should use the top 500 stocks, which can be researched at finance Web sites). At this rate of return, how long would it take for an investment to double? Top 500 Stocks Value 5 yrs. ago (PV) Top 500 Stocks Value Now (FV) Number of Periods (NPER) 5-Year Return on Top 500 Stocks (RATE) 5 If an individual needed the following amounts to retire, how much would he or she have to invest today at the rate of return that you calculated in the previous step, assuming he or she will turn 67 in the same year you do? $3,000,000 FV of Account (Given) 5-Year Return on Top 500 Stocks (RATE) Years to Retirement (NPER) Find PV of Investment $ 3,000,000 Now, you will need to estimate the life expectancy of the retiree. Use 90 years of age as an estimate. Now, you can subtract the life expectancy of the retiree from 67 (the retirement age) and use the first of the 2 tables below to calculate the required amount at retirement to support the following lifestyles adjusted for inflation (hint: the inflation adjusted amounts will be the payment as you will be calculating the present value of this annuity using a rate of return of 12%) Now, using the second table, you can calculate the annual contribution that needs to be made to have each required amount at retirement. To determine the annual contribution, use the amount that you calculated above as the future value, the market rate of return from Phase 1 as interest rate, and number of periods as 67 minus your current age. FV of Life Style (PMT) Given Expected Rate of Return (RATE) Years in Retirement (NPER) Required Value at Retirement (Find PV of Annuity) 12.0% 23 FV of Account (Use PV of Annuity from above) 5-Year Return on Top 500 Stocks (Rate) Years to Retirement (NPER) Annual Contribution Required to meet goal (Find PMT) After completing the required calculations, explain your results in a Word Document and attach the spreadsheet showing your work. Be sure to explain the following: The difference between present and future values How the present value and future value calculations are calculated and related The difference between compounding and discounting.

Paper For Above instruction

This comprehensive financial planning analysis explores critical concepts such as future value calculation, present value assessment, compound interest, and discounted cash flow techniques, all within the context of retirement planning and investment strategies. The goal is to help individuals understand how to estimate future costs, assess investment growth, and determine the necessary savings and contributions to achieve retirement goals, especially considering inflation, market returns, and life expectancy.

Introduction

Retirement planning requires a detailed analysis of future financial needs, investment growth, and the timing of savings to ensure financial security during the later years of life. Key concepts include the calculation of future values (FV) and present values (PV), which are fundamental for estimating how much current savings need to grow to meet future expenses, or how much future benefits are worth today. These calculations underpin decisions related to investment strategies, inflation adjustments, and income planning for retirees.

Estimating Future Lifestyle Costs and Inflation Impact

The initial step involves projecting the future costs of three different lifestyles, starting with the comfortable lifestyle currently costing $100,000 annually. Assuming an inflation rate of 3%, the future value of this lifestyle cost is calculated over the period until age 67. Using the FV formula:

FV = PV × (1 + inflation rate)^number of years

For a lifestyle cost of $100,000, with 30 years to retirement, the future cost becomes approximately $243,700, considering inflation. This projection enables individuals to understand the increasing financial requirements and plan accordingly.

Assessing Market Returns and Time to Double Investment

Next, estimating the 5-year average rate of return for the stock market, particularly the top 500 stocks, provides insights into potential investment growth. Research indicates that the average annual return for these stocks has been around 8%, but for demonstration, assuming the calculated rate is 8.5%. Using the Rule of 72—a common heuristic—the time to double an investment at this rate is roughly 8.5 years (72 divided by 8.5). Alternatively, the exact calculation involves solving the compound interest formula for the period required for the initial investment to double.

The formula:

FV = PV × (1 + rate)^n

Rearranged to find n:

n = log(2) / log(1 + rate)

This calculation suggests that at an 8.5% annual return, investments double approximately every 8 years, which guides strategic savings and investment timing.

Calculating Present Value of Retirement Fund Needed

To determine how much needs to be invested today to reach a future goal, the present value formula is employed:

PV = FV / (1 + rate)^n

Suppose an individual needs $3,000,000 at retirement. If the average return rate is projected at 8.5%, and the time until retirement is 30 years, then:

PV = $3,000,000 / (1 + 0.085)^30 ≈ $393,500

This indicates the lump sum to be invested now to attain $3 million in 30 years with the assumed rate of return.

Estimating Retirement Needs Considering Life Expectancy

Assuming a life expectancy of 90 years, and retirement at age 67, the individual has approximately 23 years in retirement. The required amount at retirement to sustain the lifestyle adjusted for inflation is calculated using the present value of an annuity formula:

PV = PMT × [(1 - (1 + r)^-n) / r]

Where PMT is the annual expense adjusted for inflation, r is the rate of return (12%), and n is the years in retirement (23).

For example, if the annual lifestyle cost at retirement is estimated at $245,000, then:

PV ≈ $245,000 × [(1 - (1 + 0.12)^-23) / 0.12]

Calculations yield the present value needed at retirement, guiding the investment target.

Calculating Annual Contributions to Meet Retirement Goals

Using the future value of an ordinary annuity formula, the required annual contribution (PMT) can be calculated to ensure the target retirement fund is achieved:

PMT = FV × [r / ((1 + r)^n - 1)]

Here, FV is the amount needed at retirement, r is the annual return rate, and n is the number of years until retirement (current age subtracted from 67). If the required FV is $1,000,000, with a 12% rate and 30 years remaining, then:

PMT ≈ $1,000,000 × [0.12 / ((1 + 0.12)^30 - 1)]

This formula provides the annual savings needed to reach retirement goals considering assumed market returns and investment periods.

Discussion: Fundamental Financial Concepts and Their Application

The concepts of present value and future value are central in financial planning. Present value reflects the current worth of a future sum, discounted by a specific rate, typically the expected rate of return or inflation. Future value indicates what an investment made today will grow to over a specified period at a given interest rate. The two are interconnected through the time value of money principle, emphasizing that money has different values depending on when it is received or paid.

Compounding refers to the process of earning interest on both the initial principal and accumulated interest, leading to exponential growth over time. Discounting, on the other hand, involves calculating the current value of a future sum by reversing the compounding process. Both concepts are essential for evaluating investments, savings, and liabilities in financial planning.

Understanding these principles enables individuals to make informed decisions about saving, investing, and spending, thus optimizing their financial security in retirement.

Conclusion

Effective retirement planning hinges on a solid grasp of financial principles such as valuing future costs, estimating investment returns, and calculating necessary savings. By applying formulas for present and future values, and understanding how compounding and discounting influence these calculations, individuals can develop realistic strategies to meet their retirement objectives. Proper planning ensures sufficient resources to sustain desired lifestyles, maintain financial independence, and adapt to unforeseen expenses or longer life expectancies.

References

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  • Investopedia. (2023). Future Value (FV). Retrieved from https://www.investopedia.com/terms/f/futurevalue.asp
  • Morningstar. (2023). 5-Year Stock Market Return Data. Retrieved from https://www.morningstar.com
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