Monthly Deposit Discussion And Solution Bruce W Norcise Exce

Monthly Deposit Discussion And Solutionbruce W Norciseexcelsior Coll

Suppose my current age is 25 years and I plan to retire at age 60. I want to accumulate a retirement fund that can generate an annual interest income of $150,000, which is $12,500 per month. The annual percentage rate (APR) is 3.5%. I need to determine the required retirement account balance to sustain this interest income, and then calculate the necessary monthly deposits to reach this goal by my retirement age.

Paper For Above instruction

Retirement planning involves crucial calculations to ensure sufficient funds upon retirement, especially when relying on investment income. The problem entails calculating how much money an individual needs at retirement and the monthly deposits required to reach that amount, considering specific financial parameters.

First, the desired annual interest income determines the necessary principal balance at retirement. Given an annual APR of 3.5%, the principal must be sufficient to generate $150,000 annually. The formula to determine this retirement fund is:

Retirement Fund (P) = Annual Interest Income / Interest Rate

Plugging in the values:

P = $150,000 / 0.035 = $4,285,714.29

Thus, to produce an annual interest of $150,000 at 3.5%, the retirement account must hold approximately $4,285,714.29 by the time of retirement.

Next, to determine the monthly deposit needed to accumulate this amount over the 35-year period from age 25 to 60, assuming consistent monthly contributions and a fixed interest rate, we utilize the future value of an ordinary annuity formula:

FV = Pmt × [(1 + r)^n - 1] / r

Where:

  • FV = Future value needed ($4,285,714.29)
  • Pmt = Monthly deposit (unknown)
  • r = Monthly interest rate = APR / 12 = 0.035 / 12 ≈ 0.0029167
  • n = Total number of deposits = 35 years × 12 months/year = 420 months

Rearranged to solve for Pmt:

Pmt = FV × r / [(1 + r)^n - 1]

Calculating step-by-step:

  • (1 + r)^n = (1 + 0.0029167)^420 ≈ e^{420 × ln(1 + 0.0029167)} ≈ e^{420 × 0.002913} ≈ e^{1.223} ≈ 3.396
  • Numerator: FV × r = 4,285,714.29 × 0.0029167 ≈ 12,501.71
  • Denominator: 3.396 - 1 = 2.396

Therefore, the monthly deposit is:

Pmt ≈ 12,501.71 / 2.396 ≈ $5,220.66

Rounding to two decimal points, the required monthly deposit is approximately $5,220.66.

This calculation assumes consistent contributions and the power of compound interest over time, emphasizing the importance of disciplined savings and investment planning for retirement.

In conclusion, to retire at age 60 with a fund that yields $150,000 annually at 3.5% interest, an individual must accumulate about $4,285,714.29 by retirement. Achieving this through monthly deposits of approximately $5,220.66 over 35 years ensures a sustainable income stream during retirement, exemplifying effective financial planning for long-term financial security.

References

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