Skip to main content Skip to main content
Not investment advice. Educational reading. See Disclaimer.
L.2 · BEGINNER · 4 MIN

Compound Interest: The Eighth Wonder of the World

Einstein allegedly called compound interest the eighth wonder of the world. Whether or not he said it, the math is extraordinary: money earning returns on returns creates exponential growth that accelerates over time.

Quiz · 5 questions ↓

Formula

Future Value = Present Value × (1 + Rate)ⁿ

Compare

Start AgeMonthly InvestmentAt Age 65Total Invested
25$300/month$1,050,000$144,000
35$300/month$447,000$108,000
45$300/month$177,000$72,000
25 (same total as 35)$225/month$785,000$108,000

Key point

Starting 10 years earlier at $300/month produces $1.05M vs. $447K — well over twice the money despite only investing $36K more. (All rows: 8% nominal, compounded monthly, contributions at month-end, to age 65.) One honest caveat up front: 8% is a NOMINAL rate — after ~2-3% inflation the real, purchasing-power figure is closer to 6%, which roughly halves these dollar amounts in today's money (the $1.05M is more like $600K real). The lesson is the same — starting early is the most powerful variable in the compound interest formula, and the one you can never get back — but read the headline numbers as nominal, not as today's spending power.

Formula

Rule of 72: Years to Double ≈ 72 / Annual Return %

Try it

Use the calculator above with your actual savings rate and expected return. See what your current savings path produces at retirement. Then try increasing the monthly contribution by $100 — notice how small changes compound into huge differences.

Check-in

At 10% annual returns, how long does it take for $10,000 to become $1,000,000?

Key insight

Compound interest works against you just as powerfully with debt. Credit card debt at 20% doubles in 3.6 years. Paying off high-interest debt is a risk-free cost reduction equivalent to that interest rate (subject to the loan terms) — in most personal-finance scenarios, it dominates investing.

Note

What this calculator hides

The 8–10% figure is nominal. Real returns — after 2–3% average inflation — run closer to 6% historically (S&P 500, 1926–2023, Ibbotson SBBI). At 6% real, the $1.05M starting-at-25 example shrinks to roughly $600K in today's purchasing power. Volatility matters: the S&P 500's annual standard deviation is ~16%, so one year in six delivers a loss. A Monte Carlo model using the historical return distribution places the 10th-percentile outcome near $450K and the 90th-percentile near $2.1M — a nearly 5x spread around the point estimate. The flat 8% line is the median story; the real story is a band, not a point. One reframe before the down years scare you off: while you are still contributing monthly, the loss years are when each contribution buys the most shares — module pfvi-17 (Why Falling Markets Help the Accumulator) works that arithmetic in full.

Check your understanding

Sit with the ideas.

Twin A invests $10,000 at age 25 at 8% and adds nothing else. Twin B waits until age 35, invests $10,000 at 8%, then adds $100/month for 30 years. At age 65, who has more?

Why:
Continue this lesson in the app →See it on a real ticker →