Compound Interest Explained (With Examples)
Compound interest is "interest on interest": each period, you earn a return not just on your original money but on all the returns you have already banked. Over decades, that feedback loop is what turns modest savings into real wealth.
The formula
A = P × (1 + r/n)(n × t)
A = final amount
P = principal (starting amount)
r = annual interest rate
n = times compounded per year
t = years
The exponent n × t is the total number of compounding periods. More frequent compounding (monthly vs. yearly) means interest starts earning its own interest sooner — a small but real boost.
Worked example: $10,000 at 7% for 20 years
| Compounding | Final amount | Interest earned |
|---|---|---|
| Annually (n = 1) | $38,690 | $28,690 |
| Monthly (n = 12) | $40,390 | $30,390 |
Simply by compounding monthly instead of yearly, the same deposit earns about $1,700 more over 20 years — with no extra risk or contribution. That gap widens as the balance grows.
The Rule of 72
A quick mental shortcut: divide 72 by your annual return to estimate how many years it takes to double your money. At 7%, 72 ÷ 7 ≈ 10.3 years to double. At 9%, it is about 8 years. The rule is approximate but remarkably handy for gut-checking any "get rich" claim.
Why it matters
Compounding rewards two things you control: a decent rate and time. Starting 10 years earlier often beats saving 50% more per month later, because the early dollars get the longest run of reinvestment. This is the entire argument for starting a retirement or savings plan now rather than later.
Frequently asked questions
Compound vs. simple interest?
Simple interest is charged only on the original principal for the whole term. Compound interest is charged on the growing balance, so it accelerates. Loans usually compound; so do most savings and investment vehicles.
Does more frequent compounding always win?
Within the same nominal rate, yes — but the edge shrinks as frequency rises (daily vs. monthly is tiny). Always compare using the effective annual yield (APY), which bakes compounding in.
What reduces compounding?
Withdrawals, fees, and inflation. A 7% nominal return with 3% inflation is really ~4% in purchasing power — still compounding, just on a smaller real base.
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