Compound Interest, Explained With Real Numbers
Compound interest is the difference between earning interest on your principal and earning interest on everything you've accumulated so far — including yesterday's interest. Over short horizons it barely matters. Over 30 years it dwarfs the principal you contributed. Here's the math, with worked examples.
Simple vs compound interest
If you put $10,000 in an account earning 7% annually:
- Simple interest: you earn $700 every year, regardless of how long the money's been in. After 30 years you'd have $10,000 + (30 × $700) = $31,000.
- Compound interest: each year's $700 also starts earning 7%. The next year you earn 7% × $10,700 = $749. The year after that, 7% × $11,449 = $801.43. After 30 years you have $76,123.
Same starting principal, same rate, same time horizon — and 2.5× the result. The difference is purely the reinvestment of earnings. That's compounding.
The formula
Future value of a starting principal compounding at rate r over t years, with n compounding periods per year:
FV = P × (1 + r/n)nt
Add a recurring contribution PMT (per period, made at the end of the period — an "ordinary annuity"):
FV = P(1 + r/n)nt + PMT × [((1 + r/n)nt − 1) / (r/n)]
That second formula is what every retirement projector and "what if I save $X/month" calculator runs internally. r is the annual rate as a decimal (0.07 for 7%), n is the number of compounding periods (12 for monthly), and t is years.
Why time matters more than rate
The classic illustration: two savers, both contributing $5,000/year at a 7% real return.
- Saver A starts at age 25, contributes for 10 years (ages 25–34), then stops. Total contributed: $50,000.
- Saver B starts at age 35, contributes for 30 years (ages 35–64). Total contributed: $150,000.
At age 65, who has more?
| Saver | Total contributed | Years invested | Balance at 65 |
|---|---|---|---|
| A (25–34, then untouched) | $50,000 | 40 | $602,070 |
| B (35–64) | $150,000 | 30 | $505,365 |
Saver A contributed one-third as much money but ends up with more, because their first $5,000 had 40 years to compound while Saver B's last $5,000 had only one year. The lesson is not that you should give up if you didn't start at 25 — it's that adding time to the front of the horizon is far more valuable than catching up at the back.
Why rate still matters (a lot)
Time matters more than rate, but rate still matters enormously over long horizons. Same $200/month for 30 years:
| Annual return | Total contributed | Final balance | Growth multiplier |
|---|---|---|---|
| 3% (high-yield savings) | $72,000 | $116,547 | 1.6× |
| 5% (bonds) | $72,000 | $166,452 | 2.3× |
| 7% (mixed portfolio) | $72,000 | $243,994 | 3.4× |
| 10% (aggressive equities) | $72,000 | $452,098 | 6.3× |
Going from 3% to 7% nearly doubles the final balance. Going from 7% to 10% nearly doubles it again. This is why the asset-allocation question (how much in stocks vs bonds vs cash) is so consequential — small rate differences explode over decades.
Compounding frequency
Most banks and funds compound monthly or daily, but it doesn't matter much in practice:
- Compounding annually at 7%: future value of $1 after 1 year = $1.0700.
- Compounding monthly at 7%: future value of $1 after 1 year = $1.0723 (effective annual yield of 7.23%).
- Compounding daily at 7%: future value of $1 after 1 year = $1.0725.
The difference between annual and continuous compounding at 7% is about 0.25 percentage points of effective yield. Not nothing, but not where the action is.
Inflation and real returns
The numbers above are nominal — they don't adjust for inflation. If you earn 7% nominal but inflation runs at 3%, your real return (purchasing power) is closer to 4%. Long-run US stock-market real returns have averaged about 6.5%, not 10%.
For a retirement projection, model in real returns (subtract expected inflation from the nominal rate) and you'll see numbers that look more conservative — but more realistic — than headline charts suggest.
What this means for your savings rate
Three takeaways for the practical question of how much to save:
- Start now, even if it's small. $50/month at 7% from age 22 to 65 is $147,000. The same $50/month from 35 to 65 is $58,800. The first scenario is about 2.5× the second.
- Increase contributions over time. Most calculators assume a flat contribution; in reality, your income should grow with experience. Bumping the contribution by 3%/year — matching expected raises — roughly doubles the final balance.
- Mind fees. A 1% expense ratio sounds tiny but compounds the wrong direction. $200/month over 30 years at 7%: $244K. Same scenario but with a 1% drag (net 6%): $201K. That's $43K of compound interest going to the fund company.
Run your own numbers
Our compound interest calculator handles the formula above with regular contributions, any compounding frequency, and any time horizon. Useful runs:
- "What if I increase my contribution by $50?" — see how marginal savings translate to final balance.
- "What if I retire 5 years later?" — extra compounding time at the end, when balances are largest, has outsized impact.
- "What if returns are 5% instead of 7%?" — sanity-check whether your plan still works under conservative assumptions.