Money & Finance
Budgeting, borrowing, interest and pay — the arithmetic behind the decisions that cost the most.
A rate moving from 4% to 6% rose 2 percentage points and 50 percent. Both statements are true, they are not interchangeable, and the wrong one gets quoted constantly.
How far off was the estimate? The number you divide by decides the answer, and dividing by your own estimate quietly flatters you.
Every line is right, the total is right, and they disagree by a penny. That is rounding doing exactly what it does — plus why half-up and half-even give different answers.
Two discounts applied one after the other multiply, they do not add. “50% off, then an extra 20% off” is 60% off, and here is the arithmetic that shows why — plus the one case where the order really does matter.
Move the decimal point one place and you have 10%; everything else is halves and doubles of that. Then the harder part — splitting a bill where people ordered very differently, and the pre-tax question, both put to you as choices rather than rules.
The common error is multiplying the gross figure by the rate. Divide by 1 plus the rate instead — and the wrong method is always too high by exactly the rate, which is why it survives so long unnoticed.
Miles per gallon measures distance per fuel, so equal steps up the mpg number are not equal savings. Over the same distance, going from 15 to 20 mpg saves more than three times the fuel that going from 40 to 50 does.
The same percentages applied in a different order produce different money. Here are both orders on identical figures, and why only the agreement can say which one is right.
Freight, duty, handling and the exchange spread all land on the same box of goods. A product that looked profitable on the invoice can be a loss by the time it is on the shelf.
You buy a kilo and you serve 800 grams of it. Cost the dish on what you bought, not on what reached the plate, and every price on the menu is quietly wrong.