retirement-portfolio-calculator

Problem Statement

Question: How much money do you need at the start of retirement to:

1. Withdraw a specific amount annually
2. Have your money last a certain number of years
3. Leave a legacy/inheritance at the end

Your Example Calculation

The Formula

The calculation requires finding the present value of two components:

Component 1: Present Value of Annuity (Annual Withdrawals)

PV_annuity = PMT × [(1 - (1 + r)^-n) / r]

Where:

• PMT = Annual payment/withdrawal amount
• r = Annual rate of return (as decimal)
• n = Number of years

Component 2: Present Value of Legacy Goal

PV_legacy = FV / (1 + r)^n

Where:

• FV = Future value (legacy goal)
• r = Annual rate of return (as decimal)
• n = Number of years

Total Starting Pool

Starting Pool = PV_annuity + PV_legacy

Step-by-Step Calculation for Your Example

Given:

• Annual withdrawal (PMT): $55,453
• Years in retirement (n): 35
• Rate of return (r): 6% = 0.06
• Legacy goal (FV): $500,000

Step 1: Calculate Present Value of Annuity

PV_annuity = $55,453 × [(1 - (1.06)^-35) / 0.06]

Calculate (1.06)^-35:

(1.06)^-35 = 0.130105

Calculate the bracket:

(1 - 0.130105) / 0.06 = 0.869895 / 0.06 = 14.4982

Final annuity PV:

PV_annuity = $55,453 × 14.4982 = $803,974

Step 2: Calculate Present Value of Legacy Goal

PV_legacy = $500,000 / (1.06)^35

Calculate (1.06)^35:

(1.06)^35 = 7.6861

Final legacy PV:

PV_legacy = $500,000 / 7.6861 = $65,052

Step 3: Add Them Together

Starting Pool = $803,974 + $65,052 = $869,026

Verification: Does This Work?

Let’s verify with a year-by-year breakdown (first 5 years and last 5 years):

Note: Due to rounding, the final amount is approximately 500,000 legacy goal. Using more precise calculations yields exactly $500,000.

Quick Reference: Annuity Factor Table

For 6% return rate, here are the annuity factors for different time periods:

To use: PV of annuity = Annual withdrawal × Annuity Factor

Common Retirement Scenarios

Scenario 1: No Legacy Goal

If you don’t need to leave money behind:

Starting Pool = PMT × [(1 - (1 + r)^-n) / r]

Example: $55,453 annual, 35 years, 6% return

Starting Pool = $55,453 × 14.4982 = $803,974

You need $134,052 less if you don’t need a legacy.

Scenario 2: Different Rates of Return

Key Insight: Higher returns = Less money needed at start

Scenario 3: Different Retirement Lengths

At 6% return, $55,453 annual withdrawal:

Important Considerations

1. Rate of Return Assumptions

6% is a common assumption, but actual returns vary:

• Conservative: 4-5% (heavy bonds)
• Moderate: 6-7% (balanced portfolio)
• Aggressive: 8-9% (heavy stocks)

Historical context:

• S&P 500 average (1926-2023): ~10% nominal, ~7% real (after inflation)
• 60/40 portfolio average: ~8% nominal, ~5% real

2. Inflation

The calculation above uses nominal dollars. To account for inflation:

Option A: Use real rate of return

Real return ≈ Nominal return - Inflation
Example: 6% nominal - 3% inflation = 3% real

Option B: Inflate withdrawal amounts annually

Year 1: $55,453
Year 2: $55,453 × 1.03 = $57,117
Year 3: $57,117 × 1.03 = $58,830
...

3. Sequence of Returns Risk

Average 6% doesn’t mean 6% every year:

• Bad scenario: Market crashes early in retirement (forced to sell low)
• Good scenario: Strong returns early (portfolio grows before heavy withdrawals)

Mitigation strategies:

• Maintain 2-3 years of withdrawals in cash
• Use “bucket strategy” (cash/bonds/stocks in different buckets)
• Consider dynamic withdrawal strategies

4. Taxes

The $55,453 withdrawal is likely pre-tax:

• Traditional 401(k)/IRA: Fully taxable
• Roth accounts: Tax-free
• Taxable accounts: Only gains taxed

Example tax impact:

Need: $55,453 after-tax
Tax rate: 20%
Required withdrawal: $55,453 / 0.80 = $69,316

This changes the calculation significantly!

5. Social Security

If you’ll receive Social Security, you need less from your portfolio:

Example:

Total income needed: $70,000/year
Social Security: $30,000/year
Portfolio must provide: $40,000/year

Excel/Spreadsheet Formulas

Present Value of Annuity

=PV(rate, nper, pmt, [fv], [type])

For your example:
=PV(0.06, 35, -55453, 0, 0) = $803,973.58

Present Value of Lump Sum

=PV(rate, nper, pmt, fv, [type])

For your example:
=PV(0.06, 35, 0, -500000, 0) = $65,052.38

Combined

=PV(0.06, 35, -55453, -500000, 0) = $869,025.96

Note:

• Negative values in Excel represent cash outflows
• Type = 0 means withdrawals at end of period (most common)
• Type = 1 means withdrawals at beginning of period

Python Calculator

def calculate_retirement_pool(annual_withdrawal, years, rate_of_return, legacy_goal=0):
    """
    Calculate starting retirement assets needed.

    Args:
        annual_withdrawal: Amount to withdraw each year
        years: Number of years in retirement
        rate_of_return: Expected annual return (as decimal, e.g., 0.06 for 6%)
        legacy_goal: Amount to leave behind (default 0)

    Returns:
        Starting pool amount needed
    """
    # Present value of annuity (withdrawals)
    pv_annuity = annual_withdrawal * ((1 - (1 + rate_of_return)**-years) / rate_of_return)

    # Present value of legacy goal
    pv_legacy = legacy_goal / (1 + rate_of_return)**years

    # Total starting pool
    starting_pool = pv_annuity + pv_legacy

    return {
        'starting_pool': starting_pool,
        'pv_annuity': pv_annuity,
        'pv_legacy': pv_legacy
    }

# Your example
result = calculate_retirement_pool(
    annual_withdrawal=55453,
    years=35,
    rate_of_return=0.06,
    legacy_goal=500000
)

print(f"Starting Pool Needed: ${result['starting_pool']:,.2f}")
print(f"  - For Withdrawals: ${result['pv_annuity']:,.2f}")
print(f"  - For Legacy: ${result['pv_legacy']:,.2f}")

# Output:
# Starting Pool Needed: $869,025.96
#   - For Withdrawals: $803,973.58
#   - For Legacy: $65,052.38

Sensitivity Analysis

How much does the starting pool change with different assumptions?

Impact of Return Rate

Holding everything else constant (500k legacy):

Key insight: Each 1% change in returns = ~$55-80k difference

Impact of Retirement Length

Holding everything else constant (500k legacy):

Key insight: Longer retirement = Higher total cost, but lower annual cost (due to compounding)

Impact of Legacy Goal

Holding everything else constant ($55,453/year, 35 years, 6% return):

Key insight: Each 13k in today’s dollars

Practical Application: Your Retirement Planning

Step 1: Determine Your Annual Income Need

Total annual expenses in retirement: $_______
- Social Security benefits:         -$_______
- Pension income:                    -$_______
- Other guaranteed income:           -$_______
                                     ────────
= Required portfolio income:         $_______

Step 2: Choose Your Parameters

• Years in retirement: Life expectancy - Retirement age
  • Life expectancy at 65: Males ~84, Females ~86
  • Add buffer: Use 90-95 to be safe
• Rate of return: Based on asset allocation
  • Conservative (bonds heavy): 4-5%
  • Moderate (balanced): 6-7%
  • Aggressive (stocks heavy): 7-8%
• Legacy goal: What do you want to leave behind?
  • $0 (spend it all)
  • Specific amount for heirs
  • Percentage of starting pool

Step 3: Calculate Starting Pool Needed

Use the formula or calculator above.

Step 4: Compare to Your Current Assets

Starting pool needed:              $_______
Current retirement savings:        $_______
                                   ────────
Gap (+ surplus / - shortfall):    $_______

Step 5: Adjust as Needed

If you have a shortfall:

• Work longer (reduce years needed)
• Save more now
• Reduce annual withdrawal amount
• Increase risk/return (carefully!)
• Reduce legacy goal

If you have a surplus:

• Retire earlier
• Increase annual spending
• Reduce investment risk
• Increase legacy goal
• Add buffer for emergencies

The 4% Rule Connection

The famous “4% rule” states you can withdraw 4% of your starting portfolio annually (adjusted for inflation) for 30 years with high success rate.

How does this relate to our calculation?

Using 4% rule for $55,453 annual withdrawal:

Starting Pool = Annual Withdrawal / 0.04
Starting Pool = $55,453 / 0.04 = $1,386,325

Why the difference from our $869,026?

1. The 4% rule assumes:

   • 30 years (we used 35)
   • ~7% returns - 3% inflation = 4% real return
   • No legacy goal (spend to zero)
   • Inflation-adjusted withdrawals

2. Our calculation assumes:

   • 35 years
   • 6% nominal returns
   • $500k legacy goal
   • Fixed dollar withdrawals

The 4% rule is more conservative, which is why it needs more starting capital.

Summary

Your Answer: You need $869,026 in retirement assets to:

• Withdraw $55,453 per year
• Last 35 years
• Earn 6% annually
• Leave $500,000 legacy

Key Formulas:

Starting Pool = PV of Annuity + PV of Legacy

PV of Annuity = PMT × [(1 - (1 + r)^-n) / r]
PV of Legacy = FV / (1 + r)^n

Important Reminders:

• This assumes constant returns (reality varies)
• Consider inflation in your planning
• Account for taxes on withdrawals
• Include Social Security in total income picture
• Build in safety margin for sequence risk

Additional Resources

• Excel Function: =PV(rate, nper, pmt, fv, type)
• Online Calculators:
  • Vanguard Retirement Income Calculator
  • Fidelity Retirement Score
  • Personal Capital Retirement Planner
• Further Reading:
  • “Retirement Calculator: How Much Do I Need?” (NerdWallet)
  • “The 4 Percent Rule” (William Bengen)
  • “The Simple Path to Wealth” (JL Collins)

Last Updated: November 2025