Lesson 04 · 4 min · 6 things to do
Doubling, and why it sneaks up
Work out how long a rate takes to halve what money buys.
Prices rise 7% a year, every year. Roughly how many years before the same basket costs twice as much?
yearsYes.Divide 70 by the rate and you get the doubling time: 70 ÷ 7 = 10. It is a rule of thumb, and it is accurate enough to do in your head at any rate under about 15%.That is the rule of 70. Seventy divided by the rate gives the years until prices double — and until money buys half as much.
Slide the rate and watch how long a doubling takes.
2%3.5%7%14%Until prices double35 yearsUntil they double again (4× the price)70 years2%35 years to double. A whole working life, and it still halves what a pension is worth.
Until prices double20 yearsUntil they double again (4× the price)40 years3.5%20 years. A child born today would see it before they finished university.
Until prices double10 yearsUntil they double again (4× the price)20 years7%10 years. Two doublings in a career: four times the price.
Until prices double5 yearsUntil they double again (4× the price)10 years14%5 years. Money stops being a way to hold value at all; people spend it the day they get it.
Going from 2% to 7% multiplies the rate by three and a half. What does it do to the doubling time?
- Yes.Doubling time is 70 divided by the rate, so it moves the opposite way and in proportion. A small-sounding change to the rate is a large change to the clock.
- Not quite.That would be subtracting from the years. The rate divides into 70; it does not subtract from the answer.
- Not quite.35 years and 10 years are the difference between 'my pension survived' and 'my pension did not'.
Move the control to see what changes.
- At 2%, after 35 years2×
one doubling
At 4%, after 35 years4×two doublings
Twice the rate, four times the price. The gap is a doubling, not a difference. Two countries hold prices steady for 35 years — one at 2% a year, the other at 4%. How much dearer is the second country at the end?
- Yes.At 4% the doubling takes about 17 years, so 35 years is two doublings: ×4. Twice the rate is not twice the damage — it is the damage squared.
- Not quite.That is what a straight line would give. Doubling stacks on doubling, so the gap widens the longer you wait.
- Not quite.That is roughly the extra you would get by adding the difference each year. Compounding multiplies rather than adds.
£1,000 goes under a mattress for 24 years. Prices rise 3% a year throughout. What is it worth at the end, in today's money, to the nearest £50?
£Yes.At 3%, prices double in about 23 years — so the same £1,000 buys about half of what it did. The note is untouched. What it commands has halved.Prices rise 3% a year for 25 years. Which of these are true at the end?
The £50 note in a drawer is still a £50 note.
That £50 buys roughly what £25 bought at the start.
Anyone who owed a fixed £50 has an easier debt to repay.
Somebody must have taken money out of the drawer.
Wages will have risen by the same 3% every year.
Yes.Inflation moves value between people rather than destroying it. The saver holding a fixed number loses; the borrower owing a fixed number gains; the worker depends entirely on whether pay kept up.Country A runs 2% for 35 years. Country B runs 7% for 10 years. Which one's money has lost half its value faster in calendar time?
- Yes.Both lose half, and the only difference is the clock. It is the same arithmetic that makes a 'moderate' 7% year feel violent and a 2% decade feel like nothing.
- Not quite.It takes longer to arrive at the same place. Duration is not severity.
- Not quite.The destination is the same. How fast you get there is exactly what people mean by an inflation crisis.
Lesson complete
Divide 70 by the rate and you have the years until your money buys half as much.
Next: The rate you get and the rate you keep →