Investment Calculator
Model exponential compound interest, recurring cash contributions, intra-year compounding frequencies, and multi-decade tax drag across taxable, tax-deferred, and tax-free account structures.
Effective CAGR (Net): 18.46%
1. Mathematical Foundations of Capital Accumulation
Derivations of future value, annuity due timing, effective annual rates, and Euler limits
Investment modeling is anchored in the mathematics of discounted cash flows and geometric progression. When capital is deployed over an extended multi-year horizon, wealth creation separates into two distinct mechanisms: the geometric expansion of the starting lump-sum principal and the cumulative summation of recurring periodic deposits compounded forward.
Lump-Sum Future Value Equation
Where PV is initial capital, r is nominal annual rate, k is compounding frequency per year, and t is total years invested.
Periodic Contribution Annuity Equation
Where PMT is periodic deposit, i = r / m is rate per period, n = m × t is deposit count, and timing = 1 for annuity due (beginning of period) or 0 for ordinary annuity (end of period).
Total gross portfolio terminal wealth represents the sum of both components: FV_total = FV_lump + FV_annuity. When intra-year compounding frequencies converge toward infinity (continuous compounding), the compounding multiplier reaches the mathematical Euler limit: lim_(k→∞) (1 + r/k)^(k×t) = e^(r×t).
2. Asset Class Return, Volatility & Tax Location Matrix
Long-term historical nominal returns, inflation-adjusted returns, risk metrics, and optimal account placement
| Asset Class / Index | Hist. Nominal Return (CAGR) | Hist. Real Return (After CPI) | Annual Volatility (σ) | Tax Efficiency Profile | Optimal Asset Location |
|---|---|---|---|---|---|
| U.S. Broad Equities (S&P 500 / VTI) | 10.1% – 10.5% | 6.8% – 7.2% | 15.2% – 16.5% | High (Qualified Divs / LTCG) | Taxable Brokerage / Roth IRA |
| International Developed Equities (MSCI EAFE) | 7.8% – 8.4% | 4.9% – 5.5% | 17.1% – 18.3% | Moderate-High (Foreign Tax Credit) | Taxable (Recovers Foreign Credit) |
| Emerging Markets (MSCI Emerging) | 8.9% – 9.8% | 5.8% – 6.6% | 21.5% – 23.0% | Moderate (Higher Turn & Divs) | Roth IRA / 401(k) |
| U.S. Intermediate Aggregate Bonds (BND) | 4.5% – 5.2% | 1.5% – 2.1% | 5.4% – 6.2% | Low (Ordinary Income Tax) | Traditional 401(k) / Traditional IRA |
| Public Real Estate (REITs / VNQ) | 8.5% – 9.3% | 5.2% – 6.0% | 17.8% – 19.5% | Very Low (90% Non-Qual Divs) | Roth IRA / Traditional IRA |
| Cash Equivalents & Short T-Bills | 3.2% – 4.8% | 0.2% – 1.0% | 0.8% – 1.5% | Moderate (State-exempt if Treasuries) | Emergency Reserves / HYSA |
Frequently Asked Questions
Authoritative answers regarding compound interest, tax drag, and portfolio mathematics
How does recurring contribution timing (beginning vs. end of period) alter terminal portfolio wealth?
Contributions deposited at the start of each compounding interval (annuity due) earn returns immediately across that full period, compounding into noticeably higher terminal wealth than deposits made at period-end (ordinary annuity).
What is tax drag, and why does it significantly depress long-term taxable compound growth?
Tax drag represents the compound friction of annual taxes assessed on realized dividends, interest distributions, and capital gains rebalancing, which prevents those subtracted tax dollars from compounding in future cycles.
What is the mathematical difference between APR, nominal return, and effective annual rate (EAR)?
Nominal APR ignores intra-year compounding, whereas Effective Annual Rate (EAR) explicitly calculates the true compounding yield: EAR = (1 + r/k)^k - 1, generating higher realized returns as intra-year frequency k increases.
How do expense ratios and investment management fees compound against asset returns over decades?
An annual asset management fee or fund expense ratio of 1% does not merely consume 1% of profits; over a 30-year horizon, it typically erodes 20% to 26% of potential terminal portfolio wealth due to forfeited compound acceleration.
Is any personal financial or portfolio data saved on external servers during calculation?
No. All financial mathematical projections, cash flow calculations, and tax drag analyses are computed 100% client-side in your local browser sandbox, ensuring absolute data privacy.