· 2 min read
The 50/30/20 Budget Rule
Split after-tax income into 50% needs, 30% wants, 20% savings. Here's how the buckets work, what counts as each, and how to adapt it to your life.

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· 2 min read
Split after-tax income into 50% needs, 30% wants, 20% savings. Here's how the buckets work, what counts as each, and how to adapt it to your life.
· 3 min read
Your break-even point is where revenue equals costs. Here's how to find it in units and revenue, and how to use it to make pricing decisions.
· 2 min read
Credit utilization is the share of your credit limit you're using. Here's what counts as good, why it matters for your score, and how to lower it.
· 3 min read
Save around 15% a year and aim for roughly 25 times your annual spending. Here's the rules of thumb, why starting early matters, and how to find your monthly number.
· 2 min read
Simple interest grows in a straight line; compound interest snowballs. Here's how each works, a worked example, and which one you meet in real life.
· 2 min read
Three to six months of essential expenses is the usual rule. Here's how many months fit your situation, where to keep the money, and how to build it.
· 13 min read
What Google's own documentation says about rewriting title links and about the meta description, rather than what SEO folklore says. Then the measurable part: titles are truncated by pixel width, so two titles of exactly sixty characters can render 204.55 pixels apart and only one of them survives.
· 3 min read
ROI measures your gain relative to what you invested, as a percentage. Here's the formula, a worked example, and what ROI leaves out.
· 2 min read
Your debt-to-income ratio compares your monthly debt payments to your income. Here's how to calculate it, why lenders use it, and how to improve it.
· 11 min read
Constant additions against a proportional loss rate do not grow forever — they converge on a ceiling equal to additions divided by the loss rate. Here is that ceiling computed for six loss rates, why a list can grow while its engaged half shrinks, and the feedback loop that makes a bought list self-defeating.
· 11 min read
The overall rate is the product of the stage rates, which makes a percentage gain anywhere worth the same percentage overall — and a ten-point gain worth wildly different amounts depending on where you put it. Plus the lag that makes a growing business look worse than it is.
· 12 min read
Impressions divided by reach is frequency — one identity that decides what a campaign actually is. The same impression budget split five ways, what a frequency cap really costs you, and why the three-exposure rule is a 1970s heuristic rather than a law.
· 11 min read
A fund can return 9.49 percent a year while its investor earns −1.77 percent. Time-weighted versus money-weighted, nominal versus real, gross versus net — four questions inside one number, separated with arithmetic.
· 10 min read
Four balances of $20,000 at 20.6 percent blended, cleared on a $680 budget, cost $7,085 in interest. One loan at 9.9 percent over seven years cuts the payment to $330.99 — and costs $7,803. The break-even term is 77 months.
· 2 min read
Multiply the bill by the tip percentage, add it on, then divide by the number of people. Here's the method, an example, and how tipping norms differ.
· 12 min read
The rule is the output of a named backtest on US data. Its inversion, 1 ÷ w, gives the multiple: 25× at 4 percent, 33.3× at 3 percent. And two paths with the same 4.7676 percent geometric mean end one at zero and one at $2,031,661.
· 16 min read
Liquidation distance is (1 ÷ L − m) ÷ (1 − m): at 20× that is 2.56 percent on a 2.5 percent maintenance margin, inside a normal day. Recovering a loss needs 1 ÷ (1 − L) − 1, so 90 percent lost needs 900 percent back. Combined, repeated leveraged bets on a market with a genuine +0.08 percent edge compound at −1.23 percent per period at 10×.
· 14 min read
Spending a fixed amount each period buys more units when the price is low, so your average cost is the harmonic mean of the prices while the average price is the arithmetic mean — always lower, by 4.10 percent on the path worked through here. Against a lump sum, a 200,000-path simulation puts DCA's standard deviation 41 percent lower and its expected terminal wealth $337 lower on $12,000.
· 15 min read
Annualised volatility = period standard deviation × √(periods per year), and that √t scaling assumes independent increments. It is a model, not arithmetic: at a daily autocorrelation of 0.1 a 60 percent annualised figure should read 66.3. The payload is volatility drag — the arithmetic mean exceeds the geometric by about σ²/2, so at 8 percent average return and 40 percent volatility the compound outcome is zero.
· 2 min read
The rule of 72 estimates how long money takes to double: divide 72 by the interest rate. Here's why it works, when it's accurate, and how to flip it.
· 15 min read
Sharpe = (return − risk-free) ÷ standard deviation, so it prices return per unit of volatility — and volatility is symmetric. Two funds can share a Sharpe of 0.4939 while their Sortino ratios are 8.59 and 0.74. Annualising by √12 assumes independent returns: at an autocorrelation of 0.2 the published figure is 20 percent too high.
· 3 min read
Net worth is what you own minus what you owe. Here's how to total your assets and debts, what to include, and why the trend matters more than the number.
· 3 min read
Charging cost is energy added times your electricity price. Here's the sum, home vs public charging, cost per 100 miles, and how it compares to gas.
· 3 min read
Inflation quietly cuts what your money can buy. Here's what it is, how it erodes cash, the rule of 72 for prices, and how to protect your savings.