Articles
Money, housing and energy in numbers from official sources. Every article leads to a calculator where you can put in your own figures.
- Data
How much electricity does a heat pump use? By month and by year
How many kWh of electricity a heat pump uses in a family house month by month, what it costs, why winter takes the most, how house size matters and how much less it uses with underfloor heating.
- Guide
How a neural network recognises a digit, step by step
We follow a handwritten digit through a real neural network: what it sees, how a neuron adds up, how the network learned its weights and which digits it mixes up most.
- Comparison
Heat pump or gas furnace: when does a heat pump pay off?
When a heat pump saves against gas heating, why the electricity-to-gas price ratio and the COP decide, and how it works out in the US and 8 European countries.
- Data
Do solar panels pay off? Payback in the US and Europe
How many years rooftop solar takes to pay back in the US and 8 European countries, how much of the power you use yourself and what shortens the wait.
- Guide
When an adjustable-rate mortgage resets: your new payment
How much an ARM payment rises or falls when the fixed period ends, why the new rate applies to almost the whole loan, and what you can do before the reset.
- Data
How many years to financial independence by savings rate
How many years until you can live off investments if you save 10, 20, 30 or 50% of your income, why the share matters more than the salary, and what changes it.
- Data
Stocks, bonds and cash since 1928: what earned the most
What $100 in stocks, bonds and cash since 1928 would be today, what was left after inflation, how long losses lasted and what it means for investors.
- Comparison
Password or passphrase: which is stronger?
How many random words match how many password characters, how long a passphrase would take to guess, why a made-up sentence falls short and when to use which.
- Data
What $1,000 from 2000 is worth today: US inflation and other countries
How many dollars it takes today to buy what $1,000 bought in 2000, how much buying power cash lost, what $1,000 from other years is worth now and how US prices rose against other countries.
- Guide
A million dollars for your kid at 21: how much to invest
What it takes to give your child $1,000,000 at 21 at the average historical returns of US stocks, bonds and cash: one deposit at birth, a monthly amount from birth or from age 10, and what inflation does to the million.
- Guide
Extra mortgage payments: what $100 or $200 a month really saves
How much sooner you pay off a 30-year mortgage and how much interest you save with $100 to $1,000 extra a month or a one-off lump sum, plus prepayment penalties and recasting.
- Comparison
Lump sum or dollar-cost averaging? What S&P 500 history says
Should you invest a windfall at once or spread it over a few months? Every start since 1993 compared: how often the lump sum came out ahead, by how much, and when spreading it out helped.
- Guide
The rule of 72: how many years it takes your money to double
How the rule of 72 works, how accurate it is at different returns, how fast US stocks, bonds, cash and prices have doubled and why fees stretch the doubling time.
- Data
US home prices by state: how much they have risen since 2015
How home prices have changed in the US and in every state according to the FHFA index, how much of the rise inflation took and where prices rose the most.
- Guide
The 4% rule: how much you need to retire early
Where the 4% rule comes from, how it holds up in market history since 1928, what fees and the share of stocks do to it and what to watch out for.
- Comparison
Electric or gas car at 12,000 miles a year?
What running an electric and a gas car costs a month at today’s prices, how long the electric car’s higher price takes to pay back and how charging at home and mileage change it.
- Guide
How to make a strong password: length, a password manager and two-step verification
Why length matters more than complexity for a password, how long it takes to guess one according to published benchmarks, what CISA and NIST recommend and what to do today.
- Guide
Sign in with Google, Apple or Facebook: how it works, the benefits and the risks
How the “Sign in with Google” button works, what a site learns about you, where the benefits and the risks are and how to use it safely.
- Data
Buying bitcoin every month since 2014: what it would be worth today
What a fixed monthly purchase of bitcoin since 2014 would be worth today, how deep it fell along the way, how much the start year matters and how it did against the S&P 500.
- Guide
How much do you need to retire early? Your FIRE number by monthly spending
How much you need to live off your investments, when 25 times your yearly spending is enough and when it is not, what Social Security changes and how much sooner you get there by spending less.
- Comparison
A 0.2% or a 1.5% fund fee: what the difference costs over 30 years
How much a yearly fund fee takes from regular investing: the numbers for fees from 0 to 2%, a front-end load, a lump sum and where to find what a fund costs.
- Comparison
Start investing at 25 or 35: what ten years of waiting costs
How much less you end up with if you start investing ten years later, how much more you would have to put in to catch up and why even ten years of investing while young make a big difference.