The 8th wonder of the world, supposedly according to Einstein, probably not. Doesn't matter. The math is the closest thing to magic in finance. Here is how it actually works and why starting at 22 beats starting at 32 by a factor of 2 or more.
READING TIME: ~7 MIN
Compound interest is returns earning returns on previous returns. Over 40 years at a 10 percent annual return, more than 90 percent of the ending balance comes from growth, not contributions. Doubling your savings rate at 32 does not catch up to simply starting at 22 with half the contribution. Time horizon is the dominant variable. The cheapest year of compounding is the year you did not start.
Simple interest: $1,000 at 10 percent earns $100 a year, forever. After 40 years, $4,000 of interest on $1,000 of principal. That is linear growth.
Compound interest: $1,000 at 10 percent earns $100 in year one. Year two, you earn 10 percent on $1,100, which is $110. Year three, you earn 10 percent on $1,210, which is $121. The growth rate is constant; the absolute growth keeps expanding because the base keeps expanding. After 40 years at 10 percent, $1,000 becomes roughly $45,000. That is exponential growth.
The formula is FV = PV x (1 + r)^n. Future value equals present value times one plus the rate, raised to the number of periods. The exponent is what makes it nonlinear. Small changes to r or n produce enormous changes in the output.
$200 a month is $2,400 a year. Over 40 years that is $96,000 contributed. But the ending balance is roughly $1.27 million. More than 92 percent of the outcome was compounding, not contribution.
A quick mental shortcut. Divide 72 by the annual return rate to get the approximate number of years for money to double. At 10 percent, money doubles every 7.2 years. At 7 percent, every 10 years. At 4 percent, every 18 years. It is a decent first-order estimate for any rate between 2 and 15 percent.
At a 10 percent long-run nominal return, a dollar invested today is worth $2 in 7 years, $4 in 14 years, $8 in 21 years, $16 in 28 years, $32 in 35 years. That is the power of the exponent.
Saver A starts at 22. Contributes $200/month for 10 years ($24,000 total), then stops contributing entirely. Leaves the balance invested at 10 percent until age 65.
Saver B starts at 32. Contributes $200/month for 33 years ($79,200 total), through age 65.
At 65, Saver A has roughly $1.2 million. Saver B has roughly $500,000. Saver A contributed less than a third of what Saver B did and ended with more than double the balance.
This is not a gimmick. It is what compounding does when you give it an extra 10 years at the front. The 22-year-old did not need to save more. They just started. See New Graduate for how to actually pull this off on an entry-level salary.
Three variables drive the ending balance: contribution rate, rate of return, and time. Of those, people obsess over returns (the part they cannot control) and time (the part they are actively losing every year they delay). Contribution rate is the middle lever.
You cannot control the next decade of S&P returns. You cannot go back and start at 22 if you are 32. You can start this month. The cheapest year of compounding is the one you did not start. The second cheapest is this one.
Last updated 2026-04-14. Not financial advice. Do your own research.