Selling 100 a day with a ten-day lead time and 300 units of safety stock, you reorder at 1,300 — not because 1,300 is a comfortable level, but because that is what ten days of selling costs.
Buy and sell fees of 0.5 % each need a 1.005 % gain to break even. Triple them to 1.5 % and you need 3.046 % — more than triple, because the two fees multiply rather than add.
Ten shares at 100 plus twenty at 80 gives an average of 86.67. Buy forty at 50 instead and it falls to 60 — but the money at risk goes from 2,600 to 3,000.
A payment of 1,000 a year is worth 20,000 at a 5 % discount rate and 25,000 at 4 %. The formula is a single division, and that is exactly why the input matters more than the arithmetic.
CAPM and the dividend growth model both compute the cost of equity. On one set of inputs they give 9 % and 7 % — and the choice between them decides a valuation more than any figure inside either.
Two sides both priced at -110 imply 52.4 % each. That adds to 104.8 %, and the 4.8 points that should not exist are the margin — visible the moment you convert the odds.
Over fourteen years the same French dog costs 4,387 more insured if it stays healthy and 15,124 less if it develops a chronic condition. Every other input is arithmetic; the claim curve is the whole decision.
End minus start minus break is the easy part. Whether a break is paid and whether it counts as working time are two different questions with different answers by country — plus rounding, where timesheets actually go wrong, and what the tool does with a shift that crosses midnight.
Nine absences give five different rates depending on what you divide by — scheduled days, sessions, weekdays, calendar days, or a part-timer's own diary. What the tool computes, the three places it misleads, and why the Bradford Factor makes short repeated absences look ten times worse than one long one.
The addition is the easy half. Turning balances into the fewest possible transfers is a different, and much harder, computation — and the tool's own note claims a minimum it does not deliver. Plus uneven shares, and why the awkwardness is ambiguity rather than money.
The number is large because it is a daily number multiplied by 260 or 365 — and the same arithmetic works on anything daily, which is the part worth keeping. With the home-brewing comparison done properly, and a plain statement of what the number is not.
The addition is trivial. What people miss is the annual plan billed once, the trial that converted, the conversion fee on a service billed abroad — and the break-even month that decides whether a yearly plan was ever a saving.
Salary is not the cost. The ticker applies no loaded-cost multiplier of its own, so the rate box is where you have to put it. And the number is for one comparison: a recurring meeting against the written update that would replace it.
The hourly rate is the small part. Minimum hours, the late-return surcharge, the ride home — and the question that changes the number most: casual help, or a declared employee? Six markets, named, with the thresholds that could be verified.
A local two-bedroom move estimates at $954–$1,347. Four boxes ticked on a three-bedroom move — peak week, full packing, two flights, full-value cover — take it from $1,730 to $3,162. Quotes differ on exclusions, not on price.
Score both wrappers on the same rows and the pension plan wins the arithmetic at almost every horizon and almost every combination of tax rates — including when the rate does not fall at all. Which is exactly why the deduction is the wrong thing to decide on.
The product paying the second-highest headline rate finishes last, and the reason is a tax change that took effect in January 2026. The three French savings vehicles scored on identical criteria: rate, tax, net return, real return, and what each one costs you in access.
You do not need a penalty clause. A European directive gives every business creditor a statutory interest rate and a fixed recovery sum, both due automatically, and a term in the contract trying to take them away is void or presumed unfair. Here are the current rates and what they produce on a real invoice.
The usual advice is that a buy-back gets worse with age, because the price rises. The French scale is written to be actuarially neutral, so that is not quite what is happening — and once you see what actually moves the answer, the decision changes. Computed on the current parameters.
The same company, the same year, reads 1.02×, 1.52× or 2.56× depending on where rent is put and whether principal is grossed up for tax. Two of those pass a 1.25 covenant and one does not.
A missing quarter in France costs you twice over, through two separate mechanisms that most explanations mention only one of. A German point is a single arithmetic step and much easier to price. Both are computable, and the 2026 figures changed more than usual.
Overpaying earns exactly your mortgage rate, certainly and untaxed. An investment must therefore beat that rate divided by one minus the tax on its return — which at a 3.2 % mortgage means 4.57 % in a French ordinary account and 3.20 % inside the German savings allowance, before any reward for taking risk.
Two regimes get merged into one paragraph everywhere, and they behave nothing alike. Selling a service to a business abroad and selling to a private customer abroad are governed by different articles, different thresholds and different filings. Here is the split, with the current figures.
The rule of thumb everyone repeats — one point of rate gap — is not a rule and gets the timing wrong. What decides it is how much interest you have not yet paid, and the three countries answer the cost side in three completely different ways. Here is the arithmetic, computed.