Compound Interest Methodology — Formula, Assumptions, Sources

By Duc Nguyen X.· Founder, worth101.com·Last reviewed: June 7, 2026

Every projection on worth101.com follows the same standard compound interest math published by the SEC Office of Investor Education. This page documents the exact formula, the rate and inflation assumptions, the data sources, and the limitations you should keep in mind when interpreting results.

1. The formula

Worth101 uses the canonical compound interest formula:

A = P (1 + r/n)^(n·t)

A — final value (future value)
P — principal (initial deposit)
r — annual interest rate (decimal, e.g. 7% = 0.07)
n — compounding periods per year (Worth101 pSEO scenarios use annual compounding for lump sums and monthly compounding when monthly contributions are present)
t — time horizon in years

For a monthly-contribution scenario, Worth101 uses the ordinary-annuity formula with deposits added at the end of each monthly period:

FV = P(1+i)^N + PMT · [((1+i)^N − 1) / i]

where i = r/12, N = 12 × t, and PMT is the monthly contribution. This is monthly compounding with end-of-period contributions, matching the scenario engine and embedded calculator.

2. Default rate assumptions

Scenario pages cover 5%, 7%, 8%, 10%, 12%, and 20% so you can model conservative through aggressive outcomes. The defaults map to historically defensible long-run averages:

5% — typical HYSA / short-duration bond ladder.
7% — common "real" equity assumption (long-run S&P 500 nominal return ~10% minus ~3% long-run US CPI per FRED).
10% — long-run nominal S&P 500 average (1926–present per S&P / NYU Stern data).
12% / 20% — stress scenarios. Not a forecast. Included so readers can see the asymmetry of high-rate compounding and the risk of relying on outlier returns.

Worth101 does not adjust returns for sequence-of-returns risk, taxes, or fund expense ratios in the headline calculation. Where relevant, scenario pages include a separate "Tax & Account" section calling out the after-tax drag in a taxable brokerage versus a Roth IRA / 401(k).

3. Inflation and purchasing-power adjustment

For real (inflation-adjusted) figures we default to 3% annual inflation — the long-run average US CPI per BLS data series. A 5% scenario is also shown for stress-testing the purchasing-power outcome.

4. Tax / account assumptions

Account-specific guidance (Roth IRA, 401(k), HYSA, taxable brokerage) references the 2026 IRS contribution limits: $7,500 for an IRA and $24,500 for a 401(k). Standard age-50+ catch-ups are $1,100 and $8,000, for totals of $8,600 and $32,500 respectively. Tax-free / tax-deferred treatment described on scenario pages reflects current IRS rules and may change.

5. Limitations — what this model does not know

The primary calculator output is deterministic — it assumes a fixed annual rate, not year-to-year market volatility. The "Worth101 Research" section on this page models sequence-of-returns risk and a Monte Carlo return distribution separately; treat that as illustrative range-finding, not a guarantee.
Taxes are modeled as flat effective rates where offered. State income tax, the Net Investment Income Tax, and bracket changes over time are not modeled.
Contribution behavior is assumed perfectly consistent for the whole horizon — pauses, raises, and panic-selling in downturns are real-world factors outside the formula.
Fund expense ratios, advisory fees, and trading costs are not subtracted unless you reduce the input rate yourself (e.g. enter 6.5% to model a 0.5% fee drag on a 7% gross return).
Tax law, contribution limits, and inflation are point-in-time references. Bump the "Last reviewed" date on the calculator pages when you confirm these are still current.
Past performance does not guarantee future results. Educational use only — not personalised financial advice.

6. Sources

Sources cited

Worth101 cites public-domain government data (SEC, IRS, Federal Reserve FRED, BLS CPI) on every calculator page. We do not cite paywalled research or vendor whitepapers as primary sources.