Chapter 1: The math of time
Growth on top of growth
Why a small sum started early can match a big sum started late.
Put $1,000 somewhere that grows 6% a year. After one year you have $1,060. In the second year you earn 6% on $1,060, so you gain $63.60 instead of $60. That extra $3.60 looks like nothing. It is also the whole idea of this course.
When growth starts earning its own growth, that's compounding. In the early years it barely shows. Later it does most of the work.
Before the numbers
Every example in this course uses dollars, but the math works the same in any currency. The returns are illustrations, not forecasts. Past returns don't guarantee future ones, and this course is general education, not personal financial advice.
Two savers
Maya starts at 25. She puts $200 a month into investments that grow 6% a year after inflation. At 35 she stops adding money for good and leaves the account alone. She has put in $24,000.
Sam waits until 35. Then he puts in $200 a month, every month, until he turns 65. He puts in $72,000, three times as much as Maya.
| Saver | Years adding money | Total put in | Worth at 65 |
|---|---|---|---|
| Maya | 10 | $24,000 | about $187,000 |
| Sam | 30 | $72,000 | about $195,000 |
Sam pays three times as much and only just comes out ahead. Maya's money had an extra decade to compound, and over her last ten years her balance grows by more than $80,000 without her adding a cent.
"After inflation" means these figures are in today's money. A later lesson explains why that matters.
Try it
The calculator below adds the same amount every month and grows it at the yearly rate you pick. Gray is what you put in. Green is growth. Start with the defaults, then drag Years from 30 to 40 and watch the green.
With $200 a month at 6% for 30 years, you put in $72,000 and end with about $195,000. Stretch it to 40 years and you put in another $24,000, yet the total jumps to about $382,000. Those last ten years compound on the biggest balance you've ever had.
Now go back to 30 years and double the monthly amount to $400. The result doubles too, to about $390,000. Doubling the money doubles the result. Adding years multiplies it.
Leave the fee button alone for now. Its lesson comes later.
Turn the surface and move the orange dot. Doubling the monthly deposit doubles the height at any year, while extra years follow the upward bend.
What to take from this
The amount you can set aside at 22 may feel too small to bother with. Its size matters less than its head start. A modest sum started young can rival a much bigger one started late, and the years are the one input you can't buy back.
Rabbit holes
Questions worth chasing. In Learnfold, tap one and your tutor answers it as a new lesson in your course.
- Why does compounding look like almost nothing for the first ten years?
- If Maya had kept adding \$200 a month until 65, how much would she have?
- How does compounding work on loans and credit card debt?