The Roth IRA Calculator projects future compound growth and tax-free retirement distributions generated by annual post-tax Roth IRA contributions.

### Roth Compound Growth Modeling The calculator models multi-year investment compounding using iterative annual contributions: - Annual Growth Iteration: For each year $i$ until retirement age: $$\text{Balance}_{i+1} = (\text{Balance}_i + \text{Annual Contribution}) \times (1 + r)$$ where $r$ is the assumed annual investment rate of return (default 8.0%). - Capital Breakdown: Distinguishes cumulative user contributions (tax-paid principal) from investment compound earnings. - Tax-Free Advantage: Because qualified distributions from a Roth IRA are 100% tax-free, the model estimates tax savings compared to a traditional taxable brokerage account: $$\text{Taxes Saved} = \text{Total Capital Gains} \times \left(\frac{\text{Retirement Tax Bracket}}{100}\right)$$ - 4% Safe Withdrawal Equivalent: Translates terminal nest egg balance into estimated monthly passive income ($(\text{Balance} \times 0.04) / 12$).

### Worked Numeric Example - Starting Age: 25 | Retirement Age: 60 (35-year horizon) - Initial Balance: $10,000 | Annual Contribution: $7,000/year - Assumed Return Rate: 8.0% | Retirement Tax Bracket: 22% - Performance Results: - Total Accumulated Balance: $1,402,682 - Cumulative Out-of-Pocket Principal: $255,000 - Tax-Free Investment Earnings: $1,147,682 - Estimated Taxes Saved: $252,490 - Monthly 4% Rule Income: $4,676/month completely tax-free

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