Compound interest case studies — six concrete examples that show how it works

Compound interest is easy to understand abstractly and almost impossible to internalize. The math says one thing; the human brain shrugs. The fix is concrete examples — six of them, covering the most common real-world saving patterns. All numbers use a 7% real (after-inflation) return, which is a conservative US stock-market historical average.

Case 1: $100/month for 40 years (the "young person who barely contributes")

Start at age 22 with $0. Save $100/month into an index fund inside a Roth IRA. Total contributed over 40 years: $48,000. Final balance: about $263,000. The growth (~$215,000) is 4.5× the contributions. This is the case for "even a small amount, started early, becomes meaningful."

Case 2: $500/month for 30 years (the "average professional")

Start at age 35 with $0. Save $500/month for 30 years. Total contributed: $180,000. Final balance: about $612,000. Growth is 3.4× contributions. This is the standard "save through your career and retire OK" case. Most middle-class American retirees who didn't inherit money landed near here.

Case 3: $1,000/month for 25 years (the "high earner who started late")

Start at age 40 with $0. Save $1,000/month for 25 years. Total contributed: $300,000. Final balance: about $810,000. Growth is 2.7× contributions. Note that doubling the monthly amount doesn't fully compensate for the lost decade — Case 2 ($500 for 30 years) ends close to Case 3 ($1,000 for 25 years). Time matters more than the contribution rate.

Case 4: $50,000 lump sum, no additions, 40 years (the "inheritance left alone")

A 25-year-old inherits $50,000 and invests it in an index fund inside a Roth IRA. Never contributes another dollar. After 40 years: about $750,000. The Rule of 72 explains it — at 7%, money doubles every ~10 years. Four doublings: $50K → $100K → $200K → $400K → $800K. Only the doubling period not being exactly 10 years brings it slightly below.

Case 5: $500/month from 25 to 35, then stop (the "Anna" case from compound interest folklore)

Save $500/month from age 25 to 35 — only 10 years. Then stop contributing entirely. Total contributed: $60,000. Let it grow until age 65. Final balance: about $611,000. Compare to Ben who started at 35 and saved $500/month for 30 years ($180K contributed): also about $611,000. Anna invested 1/3 as much and matched Ben's ending balance — purely from a 10-year head start.

Case 6: 1% extra in fees, $500/month for 30 years (the "fee tax" case)

Same Case 2 ($500/month for 30 years), but the investor uses a 1.0% expense ratio fund instead of a 0.05% index fund. Effective return drops from 7.0% to 6.0%. Final balance: about $502,000 instead of $612,000. The 1% fee cost $110,000 — over 60% of the entire contribution amount, vanished into the fund's expense ratio. This is why every dollar of expense ratio matters.

What these cases share

All six follow the same math: A = P(1 + r/n)^(nt) plus the future-value-of-an-annuity formula for monthly contributions. The difference is which lever was pulled — time, amount, lump vs recurring, fees. Understanding which lever produces which result is the entire game of personal finance.

The takeaways

(1) Time is worth more than amount. (2) Starting early — even with tiny contributions — beats starting later with bigger ones. (3) A single lump sum compounded for decades produces shocking results. (4) Fees consume far more of your money than most people realize. (5) Stopping contributions doesn't stop compounding — Anna proved that. (6) Doubling your contribution doesn't double your final balance unless you also keep the same time horizon.