Money that earns a return produces new money, and compounding is what happens when that new money is left in place to earn returns of its own. Year one, $10,000 at 7% earns $700. Year two, the 7% applies to $10,700, earning $749. Each year's growth is calculated on a slightly larger base, so the dollar gains keep swelling even though the percentage never changes. Over a few years the difference from simple interest is pocket change; over a few decades it is most of the money. Nothing in personal finance rewards patience more mechanically than this.
Compound Interest
Compound interest is growth earned on both your original money and on all the growth it has already produced--interest on interest--which makes balances accelerate over time rather than grow in a straight line.
Reviewed by
Steven Fox, CFP®, EA
Updated
Quick Summary
- Simple interest pays only on the original amount; compound interest pays on the original amount plus every dollar of growth so far.
- The effect starts small and accelerates, which is why the final decade of a long investment typically adds more dollars than the first two combined.
- The Rule of 72 gives a quick estimate--divide 72 by the annual return to approximate the years it takes money to double.
- Time invested drives the outcome more than timing, so starting early beats starting big.
- The same force runs in reverse on debt, which is how credit card balances outrun their borrowers.
Definition
Advanced Explanation
The variables are the return, the time, and how often growth is credited, and time is the one that dominates. Growth at a steady rate is exponential: a balance compounding at 7% doubles roughly every decade, and each doubling doubles everything that came before. That is why the curve looks flat for years and then steep, and why the honest summary of most retirement math is that the early dollars are the valuable ones. A dollar invested at 25 has twice the doublings ahead of it as a dollar invested at 45.
The Rule of 72 is the standard mental shortcut: divide 72 by the annual percentage return to estimate the years to double. At 7%, about 10.3 years (72 divided by 7); at 3%, 24 years; at 9%, 8 years. It is an approximation, tightest for single-digit returns, but accurate enough to do the planning arithmetic in your head.
Two sober footnotes. Investment returns are not the smooth fixed rates of textbook examples; markets compound irregularly, with losing years that make long horizons, not lucky timing, the reliable ingredient. And compounding is indifferent to whose side it is on. A credit card balance compounds against you at rates several times what diversified investments have historically returned, which is why carrying high-interest debt while investing is usually rowing against the current.
Used in a Sentence
“When Priya's niece started her first job, Priya's only advice was to respect compound interest: automate a retirement contribution now, because the dollars invested at 22 would do more than the much bigger dollars she would invest at 40.”
How It Works
A hypothetical example at a steady 7% annual return, no new contributions. A single $10,000 investment grows to about $19,700 in 10 years, $38,700 in 20 years, $76,100 in 30 years, and $149,700 in 40 years. Each decade the balance roughly doubles, just as the Rule of 72 predicts (72 divided by 7 is about 10.3 years per double). Notice the shape: the first decade adds about $9,700, while the fourth adds about $73,600, more than seven times as much, from the same $10,000 and the same 7%.
The same engine works against borrowers. A $5,000 credit card balance at a 22% APR, left unpaid with interest compounding monthly, grows by roughly $1,200 in a single year. The card compounds at triple the rate of the investment example, and monthly rather than annually, which is why paying down high-rate debt is one of the highest-return moves available.
Pros and Cons
Pros
- Turns modest, consistent saving into large sums given enough decades.
- Rewards starting early more than saving heroically later.
- Requires no skill, activity, or forecasting, only leaving the money alone.
- Works in every account type, and tax-advantaged accounts protect the compounding from annual tax drag.
Cons
- Runs in reverse on credit cards and other high-rate debt, compounding against the borrower.
- The payoff is heavily back-loaded, which tests patience precisely when balances still look unimpressive.
- Annual costs and taxes compound too; a recurring 1% fee removes a large slice of the ending balance.
- Inflation compounds alongside your returns, so real purchasing power grows slower than the statement balance.
People Also Asked
Answers to the most frequently asked questions.
What is the difference between simple and compound interest?
Simple interest is paid only on the original principal, so $10,000 at 7% simple earns a flat $700 every year, reaching $31,000 after 30 years. Compound interest is paid on principal plus accumulated growth, so the same money reaches about $76,100 in 30 years. The gap is the interest earned by prior interest, and it widens every year the money stays put.
How does the Rule of 72 work?
Divide 72 by an annual growth rate to approximate the years needed for money to double: about 10.3 years at 7%, 9 years at 8%, 24 years at 3%. It also runs backward, dividing 72 by a number of years to find the return needed to double in that time. It is an approximation that works best for ordinary single-digit rates, and it is a useful lens on debt too: at a 22% card APR, an unpaid balance doubles in a little over three years.
Why does starting early matter so much?
Because compounding's biggest gains arrive in the final doublings. At 7%, money doubles roughly every decade, so a 25-year-old's dollar has about four doublings before 65 while a 45-year-old's has two, making the early dollar worth roughly four times as much at retirement. Waiting a decade cannot be fully repaired by saving more later; the arithmetic of lost doublings is unforgiving.
Does compound interest apply to my investments or just bank accounts?
The mechanism applies to anything whose growth is reinvested: savings account interest, reinvested dividends, and the appreciation of index funds all compound. The difference is smoothness. A savings account compounds at a posted rate on a schedule, while market investments compound irregularly through up and down years, arriving at their long-run average only over long holding periods.
How does compounding work against me in debt?
Unpaid interest gets added to your balance, and the next month's interest is charged on that larger balance, the identical mechanism that grows investments. Credit cards are the sharpest case, typically compounding daily or monthly at rates far above what diversified investments have historically returned. That mismatch is why paying off a high-rate card is, dollar for dollar, one of the best guaranteed returns in personal finance.
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