Investing basics · Explainer

Compound
interest.

READ4 min·UPDATED·APPLIES TOAny country·LEVELBeginner
For anyone new to investing math. Sources are listed at the bottom of the page; check their dates before acting.

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. Starting at 22 beats starting at 32 by a factor of 2 or more.

This page covers personal finance fundamentals that apply regardless of your view on Bitcoin or fiat currencyfiat currencyMoney declared legal tender by a government, not backed by a physical commodity. Its value rests on trust in the issuing government.Full definition.

This page explains why compounding works the way it does; run your own numbers in the Compound Interest Visualizer, see what a dollar becomes by retirement with the Wealth Multiplier, or price a specific purchase with the Opportunity Cost Calculator.

Short answer

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 rateSavings rateThe share of income you save or invest, usually (income minus spending) divided by income. Saving $1,000 of $5,000 take-home pay is a 20% rate. Whether you use gross or take-home pay, and whether 401(k) contributions and an employer match count, changes the number, so compare rates only on the same definition.Full definition at 32 does not catch up to 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.

On this page
  1. How compounding actually works
  2. $200 per month at 10% annual return
  3. The rule of 72
  4. Starting at 22 vs starting at 32
  5. Time horizon as the dominant variable

How compounding actually works

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 per month at 10% annual return

$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.

$200/Month at 10% Annual Return
S&P 500 nominal historical average 1928-2024. Real (inflation-adjustedInflation-adjustedAdjusted for rising prices. Some amounts move with inflation, like IRS tax brackets, TIPS principal, or I-bond rates. Others are restated in today's dollars so different years can be compared: by the BLS consumer price index, $30,000 in 1985 bought about what $93,000 buys in 2026.) returns closer to 6-7 percent.
SourceStandard time-value-of-money formula; documented in any CFA / CFP / FRM curriculumUpdated2026-05-17Download .xlsx
Time Horizon Contributed Portfolio Value
10 years $24,000 ~$41,300
20 years $48,000 ~$153,100
30 years $72,000 ~$452,000
40 years $96,000 ~$1,275,000

The rule of 72

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.

KEY FACT

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 exponent at work.

Starting at 22 vs starting at 32

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 $1.1 million. Saver B has roughly $620,000. Saver A contributed less than a third of what Saver B did and ended with about 1.8 times the balance.

This 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 pull this off on an entry-level salary.

Time horizon as the dominant variable

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.

Where to go from here

Do next

Wealth Multiplier

See what a dollar invested today becomes by your own retirement age.

Read next

Human Capital

Your future earning power, the asset compounding can't replace.

Explore further

Sources

Figures, rates and rules change: check each source’s date before acting on it.

  1. NYU Stern S&P 500 historical returns (Aswath Damodaran) - pages.stern.nyu.edu
  2. Investor.gov compound interest calculator - investor.gov
  3. Bogleheads compound interest wiki - bogleheads.org

Last updated . Not financial advice. Do your own research. Disclosures · How pages are reviewed

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