Money · 3 min read
Compound Interest Explained: Why Growth Speeds Up
Why money growing at 10% a year doesn't add the same each year, the rule of 72, why starting early matters, and how compounding works against you in debt.
By the Cognosc team ·
Put $1,000 somewhere that grows 10% a year. After one year you have $1,100: $100 more. How much will you have after 30 years?
Most people’s gut says something like $4,000: $100 a year for 30 years, plus the $1,000. The real answer is about $17,450. The difference is compounding.
Try it
Simple against compound growth
$1,000, growing each year. Change the rate and the time.
After 30 years, simple growth gives $4,000. Compound growth gives $17,449: 4.4 times as much, all of it growth earned on earlier growth.
Simple versus compound
Simple growth adds the same amount every year: 10% of the original $1,000, so $100 a year forever.
Compound growth adds 10% of whatever you have now. In year one, that’s 10% of $1,000. In year two, it’s 10% of $1,100, which is $110. In year three, 10% of $1,210, which is $121. Each year’s growth is bigger than the last, because you’re earning growth on your earlier growth.
At first the two look almost the same. After a decade they’ve split apart, and after a few decades compound growth is in a different league:
- After 10 years: simple gives $2,000; compound gives about $2,590.
- After 20 years: simple gives $3,000; compound gives about $6,730.
- After 30 years: simple gives $4,000; compound gives about $17,450.
The rule of 72
A handy shortcut: divide 72 by the yearly growth rate to get roughly how many years it takes to double.
- At 6% a year, money doubles in about 12 years.
- At 9%, about 8 years.
- At 3%, about 24 years.
That also shows how powerful compounding is over time. At 7% a year, money doubles about every 10 years. Over 40 years that’s four doublings: 16 times what you started with.
Why starting early matters so much
Because the biggest gains come at the end, time matters more than almost anything else.
Imagine two people, both earning 7% a year. One invests $2,000 a year from age 25 to 35, then stops. The other invests $2,000 a year from 35 until 65: three times as long. At 65, the early starter has more, even though they put in a third as much, because their money had an extra ten years to compound.
(These are illustrations. Real returns go up and down from year to year, and nothing here is advice for your situation.)
Compounding against you
Compounding works the same way on debt, which is why expensive debt is so dangerous.
Credit cards typically charge interest monthly. A rate of 2% a month compounds to about 27% a year, not 24%. And if you only pay the minimum, most of each payment covers interest, so the balance shrinks painfully slowly. A modest card balance paid off at the minimum can take many years and cost more in interest than was originally borrowed.
Fees compound too
A fee of 1% a year sounds small. But it’s taken every year from a growing pot, so its cost compounds. Over 30 years, an extra 1% in annual fees can take roughly a quarter of what you’d otherwise have ended up with.
Inflation is compounding too
Prices also compound. At 3% inflation, prices roughly double in 24 years. So growth only really makes you richer if it beats inflation. See inflation explained.
The pattern is everywhere
Compound growth is exponential growth, and it shows up far beyond money: populations, viruses spreading, bacteria dividing, the lily pad that doubles every day. In each case, the early stages look slow and harmless, and the later stages arrive with surprising speed.
Test yourself
The free money test opens with a doubling question and covers nine other common money traps, from tax brackets to fees.