Compound interest: the engine of the Singularity

Most people picture money growing in a straight line: invest $10,000, earn $700 a year, repeat. That is simple interest. Compound interest works differently. Each year's growth is added to the pile, and next year you earn returns on the bigger pile. Growth starts earning growth, and over long stretches the straight line bends into a curve that climbs faster and faster.

Banks show this effect on savings accounts as APY, a yearly rate that already includes interest earned on interest. Investments compound the same way when you reinvest their gains, although their returns arrive unevenly rather than at a fixed rate.

The same $10,000, two different paths

Here is $10,000 earning 7% a year with nothing added. Simple interest pays 7% of the original amount; compounding pays 7% on whatever the balance has become.

The gap is small at first and enormous later. In the first decade, compounding adds about $2,700 over simple interest; by year 30 it has added more than $45,000. The most powerful ingredient is not a clever stock pick. It is a long time horizon.

Compounding also works against you. Credit card debt at 24% compounds too, which is why high-interest debt is the first fire to put out (see Pay yourself first).

The Rule of 72

You can feel compounding without a calculator. The Rule of 72 says: divide 72 by the annual growth rate to estimate how many years it takes to double.

• At 4%, money doubles in about 18 years.
• At 7%, about every 10 years.
• At 10%, about every 7 years.

So $10,000 at 7% becomes roughly $20,000, then $40,000, then $80,000 over three decades, close to the table above. Try your own rates with the Rule of 72 tool.

Your financial singularity

Now add steady contributions: say $6,000 a year, about $500 a month. Early on, your deposits do nearly all the work; after year one, 7% growth on $6,000 is just $420. But the balance keeps building, and eventually the portfolio's yearly growth becomes larger than what you put in. We call that crossover your financial singularity. Past it, your money does more of the lifting than your paycheck.

Here is a neat piece of math: if you start from zero and contribute the same amount every year at a steady return, the crossover arrives at about the Rule of 72 doubling time. At 7%, that is a little over 10 years, when the balance passes about $86,000 and 7% of it tops $6,000. Real markets never deliver smooth returns, so treat this as a map, not a schedule. Keep going for 30 years and those deposits could grow to roughly $567,000, of which only $180,000 came from you.

Escape velocity

The next milestone is escape velocity: the point where your portfolio could fund your life. A popular guideline, the 4% rule, comes from research on historical U.S. returns: withdrawing about 4% in the first year, then adjusting for inflation, has historically lasted around 30 years. Flip it around and your target is roughly 25 times your annual spending. Spend $40,000 a year and escape velocity is about $1,000,000. It is a rule of thumb, not a guarantee, but it turns a fuzzy dream into a number.

What actually moves the needle

• Start early. At 7%, ten extra years roughly doubles a lump sum.
• Contribute automatically. Money that moves before you see it rarely gets spent.
• Keep costs low. Fees compound against you; check the fee-drag calculator.
• Do not interrupt it. Panic-selling resets the clock.

Plug your own numbers into the Find your singularity calculator to see your crossover year and your escape-velocity target.