You Are Now 30 Years Old, Married, And Your Significant Othe

You Are Now 30 Years Old Married And Your Significant Other Tells M

You are now 30 years old, married, and your significant other asks you to promise that you will work only until you are 60 years old. Your employer offers you a contract paying $150,000 annually for 30 years. You are given two retirement options:

  1. The employer will provide a pension equal to 2.5% per year of employment multiplied by your salary at retirement.
  2. Your employer will match your retirement contributions and invest them in a guaranteed stock fund at an annual interest rate of 6%, with your contribution set at 6.5% of your salary.

Calculate the total amount of your contributions to the retirement fund by age 60, the total value of your retirement savings at age 60 under each plan, and the annual withdrawal amount you can sustain for 25 years after retirement in each scenario. Finally, analyze which plan is more advantageous based on your calculations.

Paper For Above instruction

Introduction

Retirement planning is a critical aspect of financial management, especially for individuals who wish to secure their financial future. The decision between a fixed pension plan and a contribution-based savings plan hinges on various factors including the growth of investments, total contributions, and the payout structure. This paper aims to evaluate two retirement options provided by an employer, considering a hypothetical scenario where an employee is 30 years old, earning $150,000 annually, and plans to retire at age 60.

Scenario Overview and Assumptions

The employee’s annual salary is $150,000. They are promised either a pension based on their final salary and years of service or a matched contribution invested in a stock fund. They plan to work for exactly 30 years until age 60, fulfilling the promise not to work beyond age 60. For simplicity, we assume that salary remains constant over the years, and the annual contribution is fixed at 6.5% of the salary, regardless of salary changes. The calculations will ignore inflation and tax considerations for clarity.

Analysis of Plan 1: Fixed Pension

The first plan offers a pension calculated as 2.5% per year of employment times the salary at retirement. Since the employee works 30 years, the pension percentage is 2.5% multiplied by 30, equaling 75%. Therefore, at retirement, the annual pension benefit will be:

  • Annual pension = 75% of the salary at age 60
  • Annual pension = 0.75 × $150,000 = $112,500

To determine how much the pension fund is worth at retirement, we analyze the accumulated contributions over 30 years. The employee contributes 6.5% of their salary annually:

  • Annual contribution = 0.065 × $150,000 = $9,750

The total contributions over 30 years are:

  • Total contributions = $9,750 × 30 = $292,500

Since this is a defined benefit plan, it essentially converts accumulated contributions into the pension amount, which does not accrue interest. The pension is paid annually from age 60 onwards. However, if we consider the pension fund as a lump sum that, when annuitized, provides $112,500 annually, the present value at retirement depends on the assumed interest rate (or discount rate). Assuming the pension is paid as an annuity with a 25-year payout at a 6% interest rate, we can calculate the present value of this annuity at retirement to estimate how much the fund should have accumulated to support such a payout.

Calculating the Present Value of the Pension (Plan 1)

The present value (PV) of an annuity of $112,500 per year over 25 years at 6% interest is calculated using the annuity formula:

PV = P × [(1 - (1 + r)^-n) / r]

Where:

  • P = $112,500
  • r = 0.06
  • n = 25

Substituting the values:

PV = 112,500 × [(1 - (1 + 0.06)^-25) / 0.06]

Calculating the denominator:

(1 + 0.06)^-25 ≈ 1.06^-25 ≈ 0.232

Then:

PV ≈ 112,500 × [(1 - 0.232) / 0.06] = 112,500 × [0.768 / 0.06] ≈ 112,500 × 12.8 ≈ $1,440,000

Hence, approximately $1.44 million would be needed at retirement to fund a $112,500 yearly payout over 25 years at 6% interest.

Analysis of Plan 2: Contributions with Investment Growth

The second plan involves the employee making annual contributions of $9,750, which are matched by the employer and invested in a stock fund growing at 6% annually. The total amount invested over 30 years is:

  • Total employee contributions = $9,750 × 30 = $292,500

Since the employer matches these contributions and invests them, the total amount invested annually is effectively doubled, totaling $19,500 per year. The contributions grow over time at 6%, and the accumulated value at age 60 is calculated using the future value of an ordinary annuity formula:

FV = P × [((1 + r)^n - 1) / r]

Where:

  • P = $19,500
  • r = 0.06
  • n = 30

Substituting values:

FV = 19,500 × [((1 + 0.06)^30 - 1) / 0.06]

Calculating:

(1 + 0.06)^30 ≈ 1.06^30 ≈ 5.743

Then:

FV ≈ 19,500 × [(5.743 - 1) / 0.06] ≈ 19,500 × [4.743 / 0.06] ≈ 19,500 × 79.05 ≈ $1,540,000

This means that at age 60, your invested contributions would grow to approximately $1.54 million, assuming consistent 6% growth annually.

Comparison of Both Plans

Retirement Savings

Plan 1’s pension is based on a fixed percentage of salary and results in an annuity that requires an estimated $1.44 million at retirement. This aligns with the pension fund needed to provide $112,500 annually over 25 years at 6% interest. Conversely, Plan 2’s cumulative contributions and investment growth lead to approximately $1.54 million in the account by age 60, which could be used to generate similar or higher annual payouts depending on withdrawal strategies.

Post-Retirement Income

Assuming the same 6% interest rate during retirement, the annual withdrawal amount from the $1.54 million can be calculated by dividing the lump sum annuities:

Annual withdrawal = PV × r / [1 - (1 + r)^-n]

Using the PV of $1,540,000 with 25 years of withdrawal at 6%:

Annual withdrawal ≈ 1,540,000 × 0.06 / [1 - (1 + 0.06)^-25]

Calculating denominator:

(1 + 0.06)^-25 ≈ 0.232

Then:

Annual withdrawal ≈ 1,540,000 × 0.06 / (1 - 0.232) ≈ 1,540,000 × 0.06 / 0.768 ≈ 1,540,000 × 0.0781 ≈ $120,033

This annual withdrawal of approximately $120,033 is slightly less than the $112,500 pension offered in Plan 1 but close enough given the assumptions. If the investments perform better or if stock returns exceed 6%, the withdrawal amount could be higher.

Which Plan is Better?

Based on the calculations, Plan 2 offers a higher retirement fund balance at age 60, resulting in potentially higher annual retirement income. While the pension in Plan 1 provides a guaranteed income, it is fixed and possibly less flexible. Additionally, the actual value of the benefits depends on market performance, interest rates, and inflation rates over time.

Plan 2’s advantage lies in the flexibility of the accumulated amount and potential for growth beyond conservative estimates, while Plan 1 offers security and predictability. For an individual comfortable with market risks, Plan 2 seems more advantageous due to higher accumulated savings and the potential for larger retirement income.

Conclusion

In conclusion, the contribution-based savings plan (Plan 2) offers a higher accumulated value at retirement and a potentially larger annual income, assuming consistent investment returns. The fixed pension plan (Plan 1), while providing certainty, may yield lower benefits depending on market performance and interest rates. Therefore, from a financial perspective, investing in a diversified stock fund with employer matching (Plan 2) appears to be the more beneficial strategy for maximizing retirement savings and income.

References

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