Transparency first
How FinancialDepth calculations work
Every result is an estimate built from the numbers you enter and the assumptions shown beside the calculator. This page explains the common formulas, modeling choices, source standards, and limits behind the tools.
Our modeling principles
Financial calculators can create false confidence when they hide assumptions behind one large result. FinancialDepth takes the opposite approach: show the important inputs, make the formula understandable, and clearly separate a deterministic projection from a real-world forecast. We favor a useful range over a single promise and encourage users to test conservative, base, and optimistic cases.
- Inputs stay visible. A result should be traceable to the starting balance, contributions, spending, rate, time horizon, inflation, fees, or withdrawal rate that produced it.
- Units stay explicit. Rates are annual unless the page says otherwise. Monthly models convert annual rates before compounding.
- Nominal and real values are not mixed. When inflation is included, the page explains whether a number is shown in future dollars or today's purchasing power.
- Risk is not reduced to an average. Historical tools show drawdowns and weak periods alongside long-run growth.
Core formulas
Compound growth
A lump sum is modeled with FV = PV × (1 + r/n)^(n×t). When regular deposits are included, the calculator adds the future value of those deposits using the ordinary-annuity formula. Some tools run month by month instead, which produces the same result when timing and rate conversion are aligned.
Debt and mortgage payoff
Installment-loan tools convert the annual percentage rate to a monthly rate, apply interest to the outstanding balance, subtract the scheduled payment, and repeat until the balance reaches zero. Extra payments are applied to principal. Debt comparison tools use the same account-level engine but change the order in which surplus cash is allocated.
Retirement withdrawals
Withdrawal-rate pages calculate first-year portfolio income as portfolio × withdrawal rate. Longevity simulations then grow the remaining balance and subtract spending over time. A constant-return model is useful for sensitivity testing but does not reproduce the order of real market returns; that limitation is especially important near retirement.
Real return and inflation
Where a real return is required, the preferred relationship is (1 + nominal return) / (1 + inflation) − 1. A simple subtraction is a close approximation at moderate rates but is not identical. Pages state which convention they use.
Historical market data
The S&P 500 backtest uses annual total returns, including reinvested dividends. Historical return series are checked against Aswath Damodaran's public U.S. investment-return dataset at NYU Stern. Backtests describe what happened during selected historical periods; they do not estimate the probability that the same path will happen again.
What the calculators usually omit
Most tools intentionally isolate one decision. Unless a calculator explicitly includes an item, its projection may omit taxes, trading costs, fund expenses, advisory fees, changing contribution levels, variable interest rates, irregular income, required minimum distributions, Social Security taxation, Medicare premiums, and state-specific rules. A cleaner model helps explain one relationship, but it is not a full financial plan.
Updates and quality checks
Pages are reviewed when formulas change, an important source releases a new annual figure, a browser dependency changes, or a material error is reported. Each calculator is checked with boundary values such as zero return, zero contributions, and short time horizons. Internal links, canonical URLs, structured data, and sitemap coverage are checked as part of each site release.
How to use the results responsibly
- Run a base case using inputs you can explain.
- Run a conservative case with lower returns, higher costs, or a longer retirement.
- Look for the input that changes the result most; that is usually the assumption worth researching further.
- Verify major decisions with account statements, lender documents, tax guidance, or a qualified professional.