Compound Interest Guide
Compound Interest vs Simple Interest
Simple interest is the version of interest you met in school: you earn a percentage of the original amount, every year, forever. Compound interest is the version money actually experiences: each year you earn interest on everything you already have, including the interest from every year before. This article puts the two side by side with identical starting conditions — $10,000 at 5% — and lets the table show exactly when, and how dramatically, they part ways. If you have ever heard compound interest called "the eighth wonder of the world," the numbers below are the evidence for that claim.
What actually differs: interest on interest
Both methods use the same annual rate and the same starting balance. The only difference is the base that the rate is applied to.
With simple interest, the base never changes. Put $10,000 in an account paying 5% simple interest and you earn $500 every year, year after year. After 10 years you have collected $5,000 of interest; after 20 years, $10,000. The math is linear, which is exactly why it is easy to follow.
With compound interest, the base grows. In the first year you still earn $500, but now that $500 stays in the account, so the second year's interest is 5% of $10,500, or $525. The extra $25 is interest being earned on the first year's interest — the thing people mean when they say "the interest earns interest." The formula behind this is the same one used everywhere on this site: A = P(1 + r/n)^(nt), unpacked in detail in the compound interest formula guide. If the account compounded monthly instead of annually, the second year's interest would be even a few dollars higher, but the mechanism would be unchanged: every payment is a percentage of a slightly larger base than the payment before.
It sounds like a small quirk. Over a year it barely matters. Over decades, the quirk becomes the entire difference between the two methods.
Side by side over 30 years
The cleanest way to see the gap is a straight comparison. Both columns below assume $10,000 at 5% per year; the simple column earns $500 a year, and the compound column is compounded once a year so the only variable is the method itself.
$10,000 at 5%: simple interest vs compound interest
Compounding once a year keeps the comparison clean — both sides use the same rate and the same starting balance.
| Year | Simple interest balance | Compound interest balance | Difference |
|---|---|---|---|
| 0 | $10,000 | $10,000 | $0 |
| 5 | $12,500 | $12,762.82 | $262.82 |
| 10 | $15,000 | $16,288.95 | $1,288.95 |
| 15 | $17,500 | $20,789.28 | $3,289.28 |
| 20 | $20,000 | $26,532.98 | $6,532.98 |
| 30 | $25,000 | $43,219.42 | $18,219.42 |
Read the last column on its own. The difference at year 5 is $262.82, at year 10 it is $1,288.95, and at year 30 it is $18,219.42 — more than the entire balance under simple interest. The gap does not grow steadily; it grows faster as time passes, because each year's lead is itself earning interest. Note also what the table does not show: total interest earned. Under simple interest the total is a straight $500 per year, so the interest column of a statement never surprises you. Under compound interest, the yearly interest at year 30 on this balance is about $2,058 — more than four times the $500 of year one.
The first two years, step by step
To see the mechanism in the smallest possible case, use $1,000 at 10% for just two years. The numbers are small enough to follow without a calculator.
Year 1. Both methods start identically. Interest is 10% of $1,000, which is $100, and the balance becomes $1,100.
Year 2, simple. Interest is again 10% of the original $1,000: $100. Balance: $1,200. Total interest earned: $200.
Year 2, compound. Interest is 10% of the new balance of $1,100: $110. Balance: $1,210. Total interest earned: $210.
The extra $10 is the entire secret of compounding. It is 10% of the $100 you earned in year one — interest on interest. Now scale that idea up to $10,000, stretch it over 30 years, and the $10 becomes the $18,219.42 from the table above. The geometry is the same at every size; only the label on the example changes.
Where the difference starts to take off
If you watch the year-by-year numbers, the divergence feels slow for a long time. In the first year the two methods are identical. By year five the gap is only a few hundred dollars on a five-figure balance. The gap only becomes dramatic in the second decade, and it is most dramatic in the third.
That shape is not an accident — it is the defining characteristic of an exponential function. Simple interest grows in a straight line; compound interest grows in a curve whose slope keeps increasing. The practical lesson is that the later years of a savings plan matter more than the early ones, which is why starting earlier beats starting with more, and why regular contributions are so effective: every deposit you make gets pulled along the same curve.
You can locate the "takeoff point" on the table for yourself. Between year 0 and year 5 the difference grows by about $262. Between year 5 and year 10 it grows by about $1,026. Between year 10 and year 15, by about $2,000. Each five-year slice adds more than the previous one — that accelerating rhythm is the telltale sign that you are looking at compound growth rather than linear growth.
One more way to feel the difference: the doubling time. Under simple interest at 5%, $10,000 reaches $20,000 only after 20 years. Under compound interest, the Rule of 72 estimates a doubling in about 72 ÷ 5 ≈ 14 years — and the second doubling after that takes another 14, at which point simple interest is still decades away from its first.
Where simple interest still shows up
Compound interest wins on savings, but simple interest is not extinct. You meet it in consumer finance more often than you might expect: personal loans and auto loans frequently quote simple interest, meaning the interest due is calculated on the outstanding principal rather than compounding on itself. Short-term loans are often simple interest too, and for very short terms the difference between the two methods is small enough that it barely matters.
The trap is assuming a loan is one type when it is actually the other. A loan advertised at 12% simple interest costs 12% of the balance per year; the same 12% with monthly compounding costs about 12.68% effective. Checking which one you are signing up for, and matching it in your calculator, prevents a sour surprise in the final payment.
Frequently asked questions
Which is better for savings?
For a long-term saver, compound interest always produces the larger balance at the same rate, and the advantage grows with time. Savings accounts, high-yield savings accounts, and certificates of deposit all use compounding. Over a term of just a few months the two are nearly identical, so for very short goals either method gives a fair estimate.
Why do some accounts still use simple interest?
Mostly simplicity and short terms. When money is borrowed for a few months, the compounding difference is tiny, so lenders can quote and explain simple interest more easily. Many car loans and personal loans work this way, and for those products the statement "interest is calculated on the principal" is genuinely accurate.
Does the compounding frequency change the comparison?
It only widens it. Compounding more often than once a year — monthly or daily — makes compound interest outperform simple interest by an even larger margin. The compounding frequency guide shows exactly how much.
Key takeaways
1. Simple interest pays on the principal only; compound interest pays on the principal plus every bit of interest already earned.
2. At $10,000 and 5%, the two methods are $1,288.95 apart at year 10 and $18,219.42 apart at year 30.
3. The difference accelerates over time, so the later years of a plan do the heavy lifting.
4. Loans often use simple interest; savings accounts essentially always compound. Know which one your numbers describe.