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How to calculate retirement, which runs two chained phases: years of compound interest while you save, then years of withdrawals while you spend. Worked across starting at 30 with $50,000 and adding $1,000 a month at a 7% return - $2,376,362 by 65, of which $1,906,362 (80.2%) is interest - the 4% rule saying you need 25 times your annual spending ($1,200,000 for $4,000 a month), how the same plan built at 40 or 50 falls to $1,096,343 or $459,410, and why inflation turns that 7% into only about 4.4% in real terms.

How to calculate credit card payoff month by month: each month the card adds the balance times the monthly rate (the APR divided by 12, so 19.99% is about 1.67%) as interest, then your payment comes off the top, which is why early payments go mostly to interest. Worked across $5,000 at 19.99% paying $250 a month - 25 months, $1,132.29 of interest, $6,132.29 paid - why the 2% minimum payment never reaches zero and the interest runs past $20,000 over 50 years, how adding just $100 a month saves $373.96, when to pay the smallest or the highest-rate card first, and what the freed-up $250 a month can earn once invested.

How to calculate CAGR, the compound annual growth rate: the working formula (ending value divided by beginning value)^(1/n) - 1, worked across $10,000 to $20,000, $50,000 and $100,000, why CAGR is the geometric mean of growth rather than the arithmetic one, how it differs from the total return and a simple average (the -50% then +100% path that nets to zero), when a CAGR can be negative and how to handle fractional years, why irregular cash flows require IRR or its money-weighted annualized cousin XIRR instead, and why a CAGR should always be read next to maximum drawdown and the Sharpe ratio.

How to calculate the rule of 72: divide 72 by the whole-number annual rate to get the years to double, worked across 4%, 6%, 8% and 10%, why the true constant is 69.3 and 72 is used for its divisibility, when the rule of 70 or 73 is a closer fit, tripling with 114 and quadrupling with 144, using the rule in reverse to find the return you need, and how a nominal return silently ignores inflation so long-horizon goals should work in the real rate.

How to calculate stop loss and take profit: the two levels in percentage and price mode, a worked $100 long and short example (stop $95, take $110, risk $500, reward $1,000, ratio 1:2), how to read the risk/reward ratio and the break-even price, sizing the stop off ATR instead of a round number, the risk amount and the risk percentage, how much of the account to risk per trade, and where the stop must sit relative to the liquidation price.

Black-Scholes option pricing explained: the full formula with every symbol, a worked $100 at-the-money call with 60 days to expiry (d1, d2, N(d1), N(d2), call $4.45, put $3.63), how each of the five inputs moves the price, the Greeks, implied volatility as the formula run in reverse, the model assumptions, and where it breaks for American and crypto options.

Staking APY explained: the difference between APR and APY, the compounding formula for any frequency V = P · (1+r/n)^(n·t), a fully worked $10,000 example at 10% across four frequencies, what sets a chain's staking yield, how to reverse-convert an advertised APY to its quoted rate, and the comparison against liquidity provision, lending and borrowing cost.

Impermanent loss explained: the AMM formula 1 − 2√r/(1+r) and the weighted general case, a worked $10,000 50/50 example at 2x, 4x and 10x price moves, how pool weights (50/50 vs 80/20 vs 95/5) dampen the loss, why Uniswap v3 out-of-range moves lock it in, and how to check whether trading fees actually cover your exposure.

Funding rate explained: the payment formula notional × rate × (hours held / 8) × sign, a worked $10,000 example at baseline and elevated rates, what positive and negative funding say about positioning, how to annualize the 8-hour rate, and why funding arbitrage is not risk-free.

Liquidation price explained: the formula entry × (1 − collateral / position size ± maint margin), a worked BTC example at 10x, why the buffer shrinks as 1/leverage, how maintenance margin and fees close the gap, how to push the price further away, and why your stop-loss must sit before it.

Position sizing explained: the formula shares = (account × risk%) / stop distance, a worked example for long and short, why the 1–2% rule exists, where the stop comes from, how to use a position sizing calculator, and how it combines with the Kelly criterion.

The Kelly criterion defined, the formula (b·p − q)/b step by step, worked examples, full vs fractional Kelly, what a negative Kelly means, how to apply it to betting and trading, and how to calculate it in Excel.

The Sharpe ratio defined, the formula (Rp − Rf) / σ step by step, four worked examples, what counts as a good Sharpe, how to calculate it in Excel, and how it compares to Sortino, Calmar, Treynor and information ratio.

Maximum drawdown (MDD) defined, the formula step by step, a full worked example, drawdown duration and recovery, and what counts as an acceptable MDD for funds, prop firms and crypto.

How to write prompts for text-to-image models: the eight-part structure, the visual vocabulary image models respond to, worked examples, and mistakes to avoid.

How to write prompts for text-to-video and image-to-video models: the six-part structure, camera vocabulary, worked examples, and mistakes to avoid.

Convert between decimal, fractional and American betting odds with the exact formulas, worked examples, and implied-probability math.

Learn how to calculate the difference between two dates in days, weeks, months and business days, with a worked example, common pitfalls like inclusive counting and timezones, and tools that do it for you.

Learn what IRR (internal rate of return) is, how the NPV = 0 equation works, a five-year worked example with trial rates, and when to prefer IRR over ROI.

Learn how to calculate ROI (return on investment) with the exact formula, worked examples for stocks and real estate, and how ROI differs from CAGR and ROE.

Learn how to calculate pip value in forex with the exact formula, worked examples for major and JPY pairs, and how to use it to size positions with a 1% risk rule.

Generate strong, random passwords instantly with our free online password generator. Learn what makes a password secure and how to create unique passwords for every account.

Learn the compound interest formula with step-by-step examples. Use our free calculator to see how your investments grow over time with daily, monthly, or annual compounding.

Compare the best free loan calculators online. Learn how to calculate monthly payments, total interest, and amortization schedules without entering your bank details.

How to calculate market cap, which is one multiplication: the current stock price times the total shares outstanding. A stock at $150 with 8,000,000,000 shares has a $1,200,000,000,000 market cap, a mega cap, since the tier starts at $200 billion. Two companies can both trade at $20 a share and be 25 times different in size because size is set by the share count, a $50,000,000,000 large cap versus a $2,000,000,000 mid cap. With the share count fixed, a 50% move is the same 50% move in market cap, and the P/E divides the $1.20 trillion by a year of earnings, 12 if the company earns $100,000,000,000 a year.