Articles
Practical guides to the calculations behind everyday decisions: the formulas, worked examples, the assumptions each one makes on your behalf, and the mistakes that produce a confident-looking wrong answer.
Every article here starts from a question someone actually needs answered — what a pay rise is worth after inflation, whether the larger pack is really cheaper, how much a set of small subscriptions costs over a year, what a discount stacked on a discount actually comes to. Each one gives the formula, walks through a realistic example with numbers, and then does the part that matters most: explains where the calculation stops being reliable.
Where a calculator on this site covers the same ground, the article links to it, so you can read the reasoning first and then run your own figures. Results throughout are estimates for planning and educational purposes; rates, taxes, fees and personal circumstances change the outcome.
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A loan officer looks at one number before almost anything else: how much of your monthly income already goes to debt. Here is how that number is calculated and why it can matter more than your income.
A lender will tell you the biggest loan they're willing to give you. That number and the mortgage payment you can actually live with comfortably are often not the same figure.
A minimum payment is designed to keep an account in good standing, not to pay off the balance in a reasonable time. Here is the arithmetic that explains why.
Before you reach for a calculator, there's a shortcut that gets you a surprisingly close answer to one specific question: how long will it take this to double?
"Four interest-free payments" sounds like the cost of borrowing is zero. Sometimes it is — and sometimes the real cost only shows up if a payment is late or the promotional period ends.
An extra $100 a month doesn't just chip away at the balance — it removes every future interest charge that would have been calculated on that $100. Here's how to put a number on it.
Two stocks can both pay a $2 annual dividend and represent completely different value, because yield depends on what you paid, not just what's paid out.
After a dozen small purchases at different prices, "what did I actually pay?" stops being a simple question — unless you know which average to calculate.
The same $5,000 profit can be taxed completely differently depending on one detail most investors don't track closely enough: exactly how long the asset was held.
A card advertising 3% cashback and a $95 annual fee sounds simple to evaluate. It takes an actual calculation of your own spending to know whether that fee pays for itself.
The same 25,000 miles can be worth $150 on one flight and $500 on another. The only way to know which is a good use of them is to run the numbers before you book.
The exchange rate posted at an airport kiosk and the real market rate are rarely the same number. The gap between them is a cost you're paying without a visible fee.
Read the assumptions and limitations section before trusting any number for a real decision. Most of these calculations are short — a division, a multiplication, occasionally an exponent — and the arithmetic is rarely where things go wrong. What goes wrong is using a figure that does not match the situation: an advertised fuel-consumption number instead of your own, a total-spending figure where essential spending was needed, or a rate quoted on a different basis from the one you are comparing it against.
Several of the articles overlap on purpose. Percentage change, reverse percentages and stacked discounts are the same underlying idea applied to three different problems, and reading two of them together tends to make the third obvious.