money
did you know compound interest grows money absurdly fast?
interest earning interest is exponential growth — and exponential growth is the thing human intuition is worst at.
after 30 years at 7%:
£7,612
simple interest would give £3,100. the gap — £4,512 — is the compounding. at 7%, money doubles roughly every 10.3 years.
the idea
earn 7% a year and your money doubles roughly every decade — not because anyone pays you double, but because each year’s growth starts earning its own growth.
how it works
simple interest adds the same amount every year. compound interest multiplies by the same factor every year — and repeated multiplication is exponential growth.
go deeper
growth that feeds itself
£1,000 growing at 7% a year becomes about £1,070 after one year. boring. but year two earns 7% on £1,070, and year three on that, and so on.
after 30 years it’s about £7,600. after 40, about £15,000. the curve bends upwards because the base keeps growing.
multiply, don’t add
simple interest adds the same amount every year. compound interest multiplies by the same factor every year — and repeated multiplication is exponential growth.
a handy shortcut: the rule of 72. divide 72 by the annual rate and you get the rough doubling time. 72 ÷ 7 ≈ 10 years.
final amount = starting amount × (1 + rate) ^ years
why time beats amount
because growth is exponential, the years matter more than the pounds. starting at 25 instead of 35 can roughly double the outcome at the same monthly saving.
the exponent does the heavy lifting: (1.07)¹⁰ ≈ 2, but (1.07)³⁰ ≈ 7.6 and (1.07)⁴⁰ ≈ 15.
this is why “i’ll start later and catch up” is mathematically expensive.
A = P(1 + r)ᵗ doubling time ≈ 72 ÷ (100r)
things to wonder about next
- the same curve describes debt in reverse — compounding works for whoever is on the receiving end.
- fees compound too: a 1% annual fee can eat a quarter of a 40-year outcome.
- real returns vary year to year; the smooth curve is an average, not a promise. this is maths, not financial advice.
sources & further reading
concepts: exponential growth · percentages · compound interest
4 minute read