What Compound Interest Actually Is
Simple interest pays you interest only on your original deposit. Compound interest pays you interest on your deposit PLUS on all the interest you've already earned. That feedback loop is what makes it so powerful.
| Year | Simple (5% on $10k) | Compound (5% on $10k) | Difference |
|---|---|---|---|
| 1 | $10,500 | $10,500 | $0 |
| 5 | $12,500 | $12,763 | $263 |
| 10 | $15,000 | $16,289 | $1,289 |
| 20 | $20,000 | $26,533 | $6,533 |
| 30 | $25,000 | $43,219 | $18,219 |
After 30 years, compound interest at 5% produces $43,219 from a $10,000 investment. Simple interest produces only $25,000. The difference of $18,219 cost you exactly nothing — it came from letting interest compound.
The Rule of 72: Mental Math That Actually Works
Divide 72 by your annual return rate to get the years to double your money. • 6% return → 72÷6 = 12 years to double • 8% return → 72÷8 = 9 years to double • 10% return → 72÷10 = 7.2 years to double • 24% credit card APR → 72÷24 = 3 years for debt to double
$5,000 in credit card debt at 22% APR grows to $10,000 in 3.3 years if you only make minimum payments. The same math that builds wealth destroys it when rates are high and you're on the wrong side.
How Compounding Frequency Changes Your Return
The more often interest compounds, the more you earn. On $10,000 at 5% for 10 years:
| Compounding frequency | Final balance | vs Annual |
|---|---|---|
| Annual | $16,289 | — |
| Quarterly | $16,436 | +$147 |
| Monthly | $16,470 | +$181 |
| Daily | $16,487 | +$198 |
The gap between monthly and daily compounding on $10,000 over 10 years is just $17. Compounding frequency matters far less than the rate and how long you stay invested.
The Single Biggest Factor: Time
Starting 10 years earlier is worth more than doubling your contributions. Here's the proof:
| Investor | Starts at | Monthly contribution | Stops at | Balance at 65 |
|---|---|---|---|---|
| Early starter | 25 | $300/month | 65 (40 years) | $792,000 |
| Late starter | 35 | $600/month | 65 (30 years) | $679,000 |
The late starter invests TWICE as much money per month but still ends up with $113,000 less at retirement. Those 10 extra years of compounding the early starter had are worth more than all the extra contributions.
Can only afford $50/month right now? Start anyway. $50/month at 7% for 40 years = $131,000. Waiting 5 years to afford $100/month = $127,000. The early small amount beats the later larger amount.
What 100 Years of Market History Says About the 7% Assumption
Every projection in this guide leans on a return assumption, so it's worth knowing where the standard numbers come from. The S&P 500 has returned roughly 10% per year nominal over the last century — about 7% after inflation. That 7% real figure is the honest one to plan with, because your retirement is priced in future dollars.
| Assumption | What it represents | $500/mo for 30 years becomes |
|---|---|---|
| 4% | Bond-heavy portfolio, real terms | $347,000 |
| 7% | Stock index funds, after inflation | $610,000 |
| 10% | Stocks, nominal (ignores inflation) | $1,139,000 |
That 10% nominal average includes 2008 (−37%) and 2022 (−18%) as well as 2013 (+32%) and 2023 (+26%). Compounding only works if you stay invested through the down years — an investor who sold in March 2009 and bought back in 2012 missed a 100%+ recovery and permanently broke the compounding chain.
Project with 10% and you're planning in inflated future dollars — $1.1 million in 2056 buys what roughly $450,000 buys today at 3% inflation. Using 7% real keeps the answer in today's purchasing power, so the number you see is the lifestyle you actually get.
Tax Drag: Why the Same Return Ends Up 25% Smaller in a Taxable Account
Where you hold an investment changes how fast it compounds. In a taxable account, dividends and fund distributions are taxed every single year — each tax bill is money that can never compound again. In a 401(k), IRA, or Roth, growth compounds untouched.
| Account | Tax during growth | $10,000 + $300/mo, 7%, 30 yrs |
|---|---|---|
| Roth IRA / Roth 401(k) | None — and withdrawals tax-free | $416,000 spendable |
| Traditional 401(k) / IRA | None until withdrawal | $416,000, then ordinary tax on withdrawal |
| Taxable brokerage (~0.6%/yr drag) | Dividends + distributions taxed annually | ≈ $371,000 before capital gains tax at sale |
A ~0.6% annual tax drag sounds trivial, but over 30 years it costs about $45,000 on this portfolio — 11% of the final balance — before you even pay capital gains on the way out. This is why the standard order is: max tax-advantaged space first ($7,500 IRA, $24,500 401(k) employee deferral), taxable brokerage only after.
Broad index ETFs distribute little and rarely fire capital gains, cutting the drag to ~0.3–0.5%/year. Actively managed funds that churn holdings can push drag past 1%/year — the same destructive math as a 1% advisory fee, stacked on top of it.