One deposit · 10% a year · 30 years
Time multiplies money. Inflation quietly divides it.
Put 100,000 away once and leave it to earn 10 percent a year. Each ring of this tree is one year. A wider ring means that year added more money.
Inflation is how fast prices rise. At 7 percent a year, a basket that costs 100 today costs 761 after 30 years. The frost shows the part of the tree that no longer buys anything extra.
It says 1.7 million on paper, but buys what 229 thousand buys today.
The last 10 rings hold 65 percent of all the growth. The widest years come at the end, so the years you wait are the ones that pay.
Simple vs compound · 100,000 for 30 years
Interest that earns interest
Simple interest pays only on the money you put in. Compound interest also pays on the interest you already earned, so each year starts from a bigger amount.
simple = P × (1 + r × t) · compound = P × (1 + r)t
Year 30, compound, split by source
- Interest on interest00%
- Interest on your money00%
- Your money00%
At 10 percent, interest on interest is 77 percent of the final amount.
A shortcut you can do in your head
The rule of 72
Divide 72 by the yearly rate in percent. The answer is roughly how many years it takes for money to double.
exact = ln 2 ÷ ln(1 + r)
How far the shortcut drifts, 1% to 20%
At 8 percent, money doubles about every 9 years. Over 40 years it grows 21.7 times.
The rule works for prices too. At 7 percent inflation, prices double in about 10 years.
Two savers · 10,000 a month each
The early starter
Saver A invests from 25 to 35, then stops and leaves the money alone. Saver B starts at 35 and keeps going until 65.
monthly rate = yearly ÷ 12 · balance = balance × (1 + monthly) + deposit
- Measure
- Saver A
- Saver B
- Invests
- age 25 to 35
- age 35 to 65
- Total put in
- 0
- 0
- Value at 65
- 0
- 0
- Growth
- 0×
- 0×
Saver A wins by 5.1 million.
The two finish level at about 6.1 percent a year.
Cash under the mattress
The silent shrink
Cash keeps its number but loses its reach. Every year prices rise, the same notes buy a little less. That loss is called losing purchasing power.
At 7 percent, cash loses half its buying power in about 10 years.
What your money gains in things it can buy
The real return
The return you are quoted is the nominal return. The real return is what is left after prices rise.
real = (1 + return) ÷ (1 + inflation) − 1
In words: divide how much your money grows by how much prices grow. Whatever is left above 1 is your real gain. 12 percent return with 8 percent inflation gives 1.12 ÷ 1.08 = 1.037, a real return of 3.7 percent.
Along the outlined diagonal, return equals inflation and the real return is zero. Every frost cell below it loses buying power, even when the balance goes up.
The quick shortcut, return minus inflation, says 4 percent for that example. It overstates gains and losses a little, and the gap grows when inflation is high.
Tap any cell · 12% return, 8% inflation
Real return in % · yearly return → across · inflation ↓ down
Illustrative model · try your own numbers
Your savings over time
monthly growth = (return − fee) ÷ 12
today's money = balance ÷ (1 + inflation)years
Time is the one ingredient you cannot add later.
- Start early
- Stay invested
- Beat inflation
- Watch fees
Educational illustration, not financial advice. Returns are never guaranteed.
Sources: All figures computed from the formulas shown.
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