Finance, worked out with actual numbers
Every article takes one money question and works it through with explicit arithmetic: the formula, the assumptions, a table of outcomes, and the point where the answer flips. No tips, no stock picks, no affiliate links. Start with the topic index, or read the newest below.
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Treasury Auctions: 2 Bid Types and What You GetWork out the exact price you pay in a T-bill auction under both bid types, see where competitive bids fail, and track settlement to maturity. -
Rule 10b5-1 Trading Plans: What Insiders Are Actually Allowed to DoLearn how 10b5-1 plans let insiders pre-schedule stock sales, what the 90-day cooling-off means, and the 2022 rules that tightened the safe harbor. -
Dark Pools: Why Your 50,000-Share Order HidesHow off-exchange venues fill big orders without moving the quote, what price they use, and what it costs a retail trader in reported spread. -
Ex-Dividend Date: Why the Stock Price Drops by (Roughly) the DividendWork out why a $0.90 dividend knocks about $0.90 off the open, why your account value barely moves, and what taxes do to the gap. -
Stock Splits: Why 4x the Shares Is Worth the SameWork out exactly what a 4-for-1 split does to your share count, cost basis, dollar P/L and percentage return, using one $12,400 position tracked through split day. -
TIPS Principal Adjustment: How Inflation Changes What You're Paid at MaturityFollow a $10,000 TIPS through five years of inflation to see exactly how the index ratio changes your coupons, your maturity payment, and your tax bill. -
Money Market Funds Breaking the Buck: What a Drop Below $1 NAV MeansHow a money market fund's $1.00 share price is maintained, what happens when it falls to $0.97, and what a redemption gate costs you in real dollars. -
FDIC Insurance: What the $250,000 Limit Really CoversWork out exactly how much of your bank money is insured, why two accounts at one bank can share a single $250,000 cap, and what falls outside it. -
Series I Bonds: How the Fixed and Inflation Rate CombineWork out the exact composite rate on an I bond, why 1.20% fixed plus 1.50% semiannual inflation isn't 2.70%, and what your $10,000 actually earns. -
RMD Penalty Math: What a 25% Excise Tax Costs If You Miss the DeadlineWork out exactly what a missed required minimum distribution costs, how the 25% excise tax shrinks to 10%, and how the correction window works. -
401(k) Vesting: What You Forfeit by Leaving at Year 2Work out exactly how much employer match you lose by quitting before a cliff or graded vesting schedule finishes, using a $9,000 balance. -
Social Security at 62 vs 70: Where Breakeven LandsWork out the exact age your delayed Social Security benefit overtakes an early one, using the 30% cut, the 24% credit, and simple arithmetic. -
HSA Triple Tax Advantage: What It's Actually Worth in DollarsWork out the dollar value of an HSA's three tax breaks using one $4,300 contribution held 20 years, and see which break does most of the work. -
Mortgage Points Breakeven: How Long Until Buying Down Your Rate Pays OffWork out the exact month a mortgage point pays for itself, using a $400,000 loan, real amortization math, and the tax and opportunity-cost catches most calculators skip. -
Cost Basis Methods: How FIFO vs Specific ID Changes Your Tax BillSee exactly how much tax FIFO versus Specific Identification costs across share counts and brackets, with full worked math. -
Qualified vs Ordinary Dividends: The Tax Rate Gap on the Same PayoutWork out what the same $4,000 dividend costs after tax when it counts as qualified versus ordinary, and why the holding period decides it. -
Closed-End Fund Discounts: Why You Can Buy a Dollar of Assets for 90 CentsWork out what a closed-end fund discount is actually worth to you after fees, and when a 10% discount returns nothing at all. -
Roth vs Traditional: The Bracket Math That Decides Which WinsWork out whether Roth or Traditional wins for you using your current bracket, your expected retirement bracket, and the exact break-even gap. -
Annuity Surrender Charges: How the Penalty Shrinks Year by YearWork out exactly what a 7-year surrender schedule costs you in dollars, and how much longer you'd wait to drop that penalty to zero. -
Currency-Hedged ETFs: What the Hedge Actually Costs You Per YearWork out the yearly cost of a currency hedge from expense ratio, roll cost, and rate spread, with tables covering every realistic combination. -
Currency Conversion Fees: What a 2% Spread Costs on an International TradeWork out exactly what a 0.25% to 3% FX conversion spread costs on trades from $500 to $250,000, round trip, with the arithmetic shown. -
Forex Pip Value: What 1 Pip Costs at Every Lot SizeWork out exactly what one pip is worth in dollars for micro, mini, and standard lots, including JPY pairs and non-USD quote currencies. -
Contango and Backwardation: The Rollover Cost Futures Traders Pay MonthlyWork out what rolling a futures position costs you each month, using a full sweep of contango and backwardation spreads with the arithmetic shown line by line. -
IPO Lock-Up Expiry: How Much Stock Unlocks Day 181Work out how many shares hit the float when an IPO lock-up ends, using share-count math, a full-range table, and staggered-release scenarios. -
Reg SHO Locate Requirements: What 'Hard to Borrow' Actually MeansHow locate rules, borrow fees and buy-ins work, with rate tables showing what a 3% versus 300% borrow costs you per day on real position sizes. -
Trailing Stops: How the Trigger Price Recalculates as the Market MovesWork out exactly where your trailing stop sits after any price path, using percent and dollar offsets, gaps, and intraday spikes. -
Futures Margin: The Difference Between Initial and Maintenance RequirementsWork out exactly how far an E-mini S&P 500 position can move before a margin call, using index points, dollars, and account size. -
Pin Risk: Why an Option Can Get Assigned Right at the StrikeWork out your assignment odds and overnight exposure when a stock closes within pennies of the strike, using tables of real dollar gaps. -
Circuit Breakers: The Exact Percentage Drops That Halt the Whole MarketLevel 1, 2 and 3 market-wide halts trigger at 7%, 13% and 20% below the prior S&P 500 close. Here are the exact price levels and timings. -
Extended-Hours Trading: Why the Spread Triples After 4pmWork out what a wider after-hours spread costs on your own order size, from 100 to 5,000 shares, with the arithmetic shown line by line. -
Good-Til-Cancelled vs Day Orders: What Happens When the Order Type ExpiresWork out exactly when your resting order dies, how many trading days a GTC survives, and what 60-day and 90-day broker caps cost you in re-entries. -
Odd Lots: Why Under 100 Shares Fills DifferentlyHow orders under 100 shares get routed, priced, and reported, with tables showing spread cost per share across 12 price levels. -
Payment for Order Flow: What It Means for the Price You Actually GetWork out what price improvement and spread capture are worth on your own order size, from 10 shares to 5,000, with the arithmetic shown. -
401(k) Match: The Return You Forfeit Under 6%Work out the exact dollar amount your employer match leaves on the table at your salary, and what it compounds to over 30 years. -
Share Dilution: How New Stock Issuance Shrinks Your PercentageWork out exactly what your ownership stake and per-share earnings become after a company issues new shares, using tables covering 1% to 50% issuance. -
ETF Premium and Discount: Why the Price You Pay Differs From NAVWork out what a 0.15% ETF premium actually costs you in dollars, and when the price-NAV gap is noise versus a real problem. -
Margin Call Math: The Exact Price Drop That Forces a Broker SaleWork out the exact percentage drop that triggers a maintenance margin call at 25%, 30%, 35% and 40% house rules, with full sweep tables. -
Rebalancing Cost: The Tax and Transaction Drag of Staying on TargetWork out what rebalancing actually costs you per year, in basis points, from spreads, commissions, and capital gains tax at your own bracket. -
Bond Duration: How a 1% Rate Rise Moves Your Bond PriceWork out what a 1% rate move does to your bond's price using duration, with full-range tables from 1 to 30 years and the cases where the estimate breaks. -
Short vs Long-Term Capital Gains: The Tax Gap From One DaySee the exact tax dollars one extra day of holding saves at every income level, from $0 to $700,000, with the math shown. -
SIPC Coverage: What Is and Is Not Protected If Your Broker FailsSee exactly what SIPC pays back if your brokerage collapses, with tables by account size, cash mix, and account type. -
The Wash Sale Rule: When a Realized Loss Gets DisallowedLearn when the wash sale rule blocks a tax loss, how the 61-day window works, and how to calculate the disallowed amount. -
The Pattern Day Trader Rule: Why $25,000 Is the Hard CutoffLearn how the pattern day trader rule works, why $25,000 is the line, and what happens to your account below it. -
Short Selling: What the Stock Borrow Fee Actually Costs Per DayLearn how to calculate the daily stock borrow fee for a short position, with a worked example across four rate tiers. -
T+1 Settlement: What Happens Between Your Trade and Your MoneySee exactly how a stock trade moves from execution to settled cash in one business day, with a worked timeline and a real slip-up scenario. -
Car Loan vs Cash: The Total Interest You Pay to DriveA worked comparison of car loan interest versus paying cash, showing what financing actually costs over the life of the loan. -
How One Extra Mortgage Payment Per Year Cuts Total InterestA worked example shows how adding one extra mortgage payment a year can shave years off a loan and cut total interest by roughly a fifth. -
What a 1% Advisory Fee Costs vs 0.05% Over 20 YearsA worked example shows how a 1% advisory fee versus a 0.05% index fund fee can cost tens of thousands of dollars over 20 years of compounding. -
How Your Fund's Turnover Ratio Quietly Creates a Tax BillA worked example showing how a mutual fund's portfolio turnover generates capital gains distributions and a tax bill you never asked for. -
Sequence of Returns: Why the Order of Gains and Losses MattersA worked example showing how two retirees with identical average returns end up with different account balances, purely from the order the returns arrived in. -
The Full Round-Trip Cost: Spread, Commission, and SlippageA worked breakdown of what a buy-then-sell trade really costs once spread, commission, and slippage are added together. -
What Overnight Financing Charges Cost on a Leveraged PositionA worked breakdown of how overnight financing fees on leveraged trades accumulate daily and erode returns over time. -
How Theta Decay Drains a Long Option Every Day It SitsA worked example showing how theta decay chips away at a long option's value daily, and why that erosion accelerates near expiration. -
The Minimum Payment Trap: How Long It Actually Takes to ClearA worked example shows why paying only the credit card minimum can stretch a $5,000 balance past a decade in interest charges. -
Diversification: What It Protects You From and What It Does NotHow diversification reduces single-stock risk but not market-wide risk, with a worked example showing where the benefit runs out. -
Early On, Your Savings Rate Matters More Than Your ReturnsA worked example showing why saving $100 more a month beats chasing a 2% higher return in the first decade of investing. -
Stop Losses: The Trade-Off Between Protection and WhipsawHow stop orders actually fill, why tight stops get triggered by normal noise, and the math behind picking a stop distance. -
Tax Drag: How Frequent Trading Shrinks What You KeepA worked comparison of short-term versus long-term capital gains tax shows how trading frequency quietly erodes compounding over time. -
Why Backtests Look Great and Live Results Do NotHow overfitting, survivorship bias, and hidden costs turn a beautiful backtest into a mediocre live strategy, explained with a worked example. -
What Inflation Does to Cash Savings Over a DecadeA worked example showing how inflation erodes the purchasing power of cash savings over ten years under different rate assumptions. -
Position Sizing: The Part Beginners Skip and RegretLearn how to calculate trade size from risk per trade instead of gut feeling, with a worked example and its limits. -
The Bid-Ask Spread: The Fee Nobody Puts on Your StatementHow the bid-ask spread quietly costs traders money on every trade, with a worked example showing the real dollar impact. -
Leverage and Liquidation: The Move Size That Wipes You OutA worked example showing exactly what price move erases a leveraged position, and why the math gets worse as leverage rises. -
How to Read a Fund Fact Sheet Without Getting MisledLearn to spot which numbers on a fund fact sheet matter, which are marketing, and how to check a fund's real costs before you commit. -
How Big Should an Emergency Fund Be? Working From Your Actual BillsA method for sizing an emergency fund from your real monthly expenses instead of a generic multiple, with a worked example. -
Index Funds vs Picking Stocks: What the Long-Run Evidence ShowsHow index funds and stock picking compare over decades, with a worked cost example and the caveats the averages hide. -
Drawdown Explained: Why a 50% Loss Needs a 100% GainHow percentage losses and gains scale asymmetrically, why drawdown recovery gets harder the deeper it goes, and how to read the math. -
Dollar-Cost Averaging vs Lump Sum: What the Arithmetic Actually SaysA worked comparison of investing a lump sum at once versus spreading it out, showing exactly what each approach does to your average cost and final share count. -
How a 0.75% Expense Ratio Quietly Eats a Third of Your ReturnsA worked example showing how a small annual fee compounds over decades into a large share of your final balance. -
Market Order vs Limit Order: When Each One Loses You MoneyLearn the mechanics of market and limit orders and the specific conditions where each type silently costs you money. -
What Slippage Actually Costs You (And When It Bites Hardest)Learn what slippage is, how to calculate its real cost, and which conditions make it worst. -
Why Most Day Traders Lose: The Numbers Behind the AttritionA numbers-based look at why the majority of active day traders lose money, using costs, sample studies, and a worked example.