How compound interest grows
The short answer
Compound interest is interest earned on interest. Leave $1,000 at an example rate of 7% a year and it earns $70 in year one. In year two it earns $70 again plus 7% of the first $70, $4.90, and that extra keeps growing because every dollar of interest earns interest too. The balance nearly doubles every 10 years: $1,967 after 10, $3,870 after 20 and $7,612 after 30, of which $4,512 is interest on interest. Simple interest, paid only on the original $1,000, would reach $3,100. Starting 10 years later ends with about half.
Chapters and transcript
- 0:00
Leave $1,000 alone at 7% a year.
Put $1,000 away at an example rate of 7% a year, paid once a year, and add nothing more. The rate is an example, not a forecast.
- 0:06
Each square is $10.
On screen each square is $10, so $1,000 is a block of 100 squares.
- 0:11
Year 1: it earns $70.
After one year, 7% of $1,000 is $70, so the balance is $1,070.
- 0:17
Year 2: $70 again, plus 7% of that $70.
In year two, the original $1,000 earns another $70, and last year's $70 earns 7% too.
- 0:24
That $4.90 is interest on interest: compounding.
That extra $4.90 is interest earned on interest, which is what compound interest means. The balance is now $1,144.90. Investor.gov's example works the same way: $100 at 5% becomes $105, then $110.25.
- 0:31
Every year, every square earns 7%. Even the gold ones.
Each year the whole balance earns 7%, including all the interest already added, so the interest on interest grows faster every year.
- 0:41
Year 10: $1,967. It has almost doubled.
After 10 years the balance is $1,000 × 1.07¹⁰ = $1,967.15, almost twice the start.
- 0:46
Rule of 72: 72 ÷ 7 is about 10 years to double.
The Rule of 72 estimates the years to double by dividing 72 by the rate: 72 ÷ 7 ≈ 10.3. The exact time at 7% is ln 2 ÷ ln 1.07 = 10.24 years.
- 0:52
Year 20: $3,870. Year 30: $7,612.
The balance keeps doubling about every 10 years: $3,869.68 after 20 years and $7,612.26 after 30.
- 1:03
Interest on interest is now the biggest part.
After 30 years, the $7,612 is $1,000 of your own money, $2,100 of interest on that $1,000, and $4,512 of interest on interest.
- 1:10
Without it, simple interest stops at $3,100.
Simple interest pays only on the original $1,000: $70 a year, or $3,100 after 30 years, a straight line instead of a curve.
- 1:18
The last 10 years add $3,743, more than the first 20.
From year 20 to year 30 the balance grows by $3,743, more than the $2,870 it grew in the first 20 years together.
- 1:26
Start 10 years later, and you end with about half.
The same $1,000 left for 20 years instead of 30 reaches $3,870, about 51% of $7,612.
- 1:35
Interest on interest needs one thing: time.
Compound interest is interest earned on interest, and the longer it runs, the larger that part becomes.
Sources
Every figure in the film comes from these. The animation is illustrative.