Guides
The decisions behind the numbers: how to compare options, which assumption matters most and what commonly goes wrong. Each guide has a worked example you can reproduce with the linked calculators.
- APR vs. APY vs. interest rate: which number to compare
Which rate to compare when you borrow and when you save, what each one includes, and how to convert between them, with worked numbers you can rerun.
- Debt snowball vs. avalanche: which pays off debt faster?
The snowball, the avalanche and minimum payments compared on the same four debts: what each costs, where the interest difference comes from, why rolling payments over matters, and when a minimum payment never clears a balance.
- Extra mortgage payments: what they save and what they cost
What extra principal payments save in interest and time, what they cost in cash you can’t easily get back, and how prepaying compares with investing, recasting and paying other debts first.
- How accurate are BMI, BMR and TDEE estimates?
The equations behind these numbers describe groups of adults, not you. One worked example shows how far each estimate can move, which choices matter most, and how to check the result against real life.
- How much extra flooring, tile, paint and concrete to buy
Published rules of thumb for overage by material and layout, what each one covers, and worked examples that apply the allowance first and round up to whole boxes, cans and bags last.
- Rent vs. buy: the assumptions that decide the answer
Which inputs move a rent-or-buy comparison the most, tested one at a time on a worked $400,000 example with every number shown.
- Scheduling across time zones and daylight saving time
Why a weekly meeting shifts by an hour for some attendees in March, April, September, October and November, what happens to times that are skipped or repeated, and which zone a recurring invite should follow.
- What’s included in a mortgage payment: PITI, PMI and escrow
The parts of a monthly housing payment, worked through for a $360,000 home with 5% down: what each part costs, which parts change, and the payment on which PMI drops off.
- Common percentage mistakes and how to avoid them
Six percentage slips that produce confident wrong answers, from percentage points to negative starting values, each worked with example numbers you can check.
- Dividend yield vs. total return: what’s the difference?
Dividend yield compares a payout with today’s price; total return is what you actually earned. Worked examples show a stock yielding 7% losing 8% in a year, what a dividend cut does next, and why taxes make the source of a return matter.
- How investment fees compound: 0.1% vs. 1% over 30 years
What a yearly percentage fee takes from a long-term balance, why most of the damage lands in the last decade, and how to compare fund, advisory and flat account fees.
- How loan amortization works, with a worked schedule
The payment formula, how each payment splits between interest and principal, why the last payment is off by a few cents, when principal overtakes interest on a long loan, and what extra payments and negative amortization do to the schedule.
- How to compare loan offers: APR, fees and total cost
Match the offers on cash received and term, then compare APR and total cost. A worked $15,000 example shows how fees, longer terms and early payoff can change which offer is cheaper.
- How to measure a room for square footage and volume
Measure, convert inches to decimal feet, split odd shapes into rectangles, then multiply and convert with a squared or cubed factor. Worked with an L-shaped room, a concrete pad and a water tank.
- Margin vs. markup: formulas, conversion chart and discounts
Margin and markup divide the same profit by different numbers. How to convert one to the other, set a price for a target margin, and work out what a discount really costs.
- Mean, median or mode? How to choose a summary statistic
How to pick the center and spread that describe your data fairly, with worked numbers and a side-by-side of the quartile rules that different tools use.
- Nominal vs. real returns: adjusting savings for inflation
How to turn a nominal return into a real one, when subtracting inflation goes wrong, and how to show a 30-year savings projection in today’s dollars.
- Rental property cash flow: NOI, cap rate, cash-on-cash and DSCR
Follow one example duplex from scheduled rent to net operating income to cash flow, see why its cap rate, cash-on-cash return and DSCR disagree, and find out how little it takes to turn the cash flow negative.
- Roth vs. traditional: what the comparison really depends on
The two tax rates that decide Roth vs. traditional, why equal rates tie, when a Roth pulls ahead at the contribution limit, and how splitting hedges an unknown future rate.
- Sequence-of-returns risk: why average returns mislead
Why two retirees with the same average return can end up far apart, what a constant-return projection hides, and how flexible withdrawals move the risk from the balance to the income.
- Solving triangles: which rule to use, and the SSA ambiguous case
A table for choosing the law of sines or the law of cosines, a worked SSA example with two valid answers, and the step-order and rounding traps that make hand-solved triangles go wrong.
- Unit conversion pitfalls: gallons, tons, cups, GB vs. GiB
Nine unit traps with the numbers worked out: US vs. imperial gallons and pints, fluid ounces vs. ounces, three kinds of ton, cups of flour in grams, cup and tablespoon sizes, GB vs. GiB, bits vs. bytes, temperature changes and UK vs. US mpg.