Simple interest is calculated only on your original principal, so it adds the same amount every period; compound interest is calculated on the principal plus all the interest already earned, so the amount it adds grows each period and the balance accelerates over time.
That single difference, whether interest is paid only on what you started with or also on the interest you have already earned, is one of the most consequential ideas in long-term investing. Over a year or two the two barely differ. Over decades they diverge dramatically, because compound interest keeps earning returns on its own past returns while simple interest never does.
This guide explains what each one means, walks through a worked example where the two visibly pull apart year by year, and shows when each is the more useful lens, under a clear set of assumptions rather than as a rule about which is "correct."
The short answer
Both methods start the same way: you have a principal, it earns a rate, and time passes. The difference is what the rate is applied to.
- Simple interest applies the rate only to your original principal, every single period. The interest earned in year 10 is exactly the same as the interest earned in year 1.
- Compound interest applies the rate to your principal plus all the interest accumulated so far. Each period's interest is slightly larger than the last, because the base it is calculated on keeps growing.
With simple interest your balance grows in a straight line. With compound interest it grows on a curve that steepens over time. The longer the horizon and the higher the rate, the wider the gap between the two.
Side-by-side comparison
| Aspect | Simple Interest | Compound Interest |
|---|---|---|
| Interest is calculated on | The original principal only | Principal plus all interest already earned |
| Interest earned each period | The same fixed amount every period | A growing amount, larger each period |
| Shape of the balance over time | A straight line (linear growth) | An upward curve (exponential growth) |
| Formula | A = P × (1 + r × t) | A = P × (1 + r) to the power of t |
| Effect of a longer horizon | Adds interest at a steady, flat rate | Accelerates, because returns earn their own returns |
| Usually higher or lower | Lower over long periods | Higher over long periods, by a widening margin |
| Commonly seen on | Some bonds, car loans, short-term notes | Investment accounts, reinvested returns, many savings products |
| Equal to the other when | The very first period, or when t is tiny | The very first period, or when t is tiny |
The table describes how each behaves, not a ranking. Which one applies to you is usually set by the product or investment itself, not chosen, as covered in the decision summary below.
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Try the Compound Interest CalculatorWhat simple interest measures
Simple interest is the more intuitive of the two, because the interest never changes. You take the principal, multiply by the rate, and that is the interest for every period.
The plain-text formula is:
A = P × (1 + r × t)
where A is the final amount, P is the principal, r is the rate per period, and t is the number of periods. The interest itself is just P × r × t.
Because the rate only ever touches the original principal, the interest you earn in the final year is identical to the interest you earned in the first year. Nothing you have already earned goes on to earn more. That makes simple interest easy to predict, and it is common on instruments like some bonds and fixed-term loans, where the interest is paid out rather than added back to the balance.
What compound interest measures
Compound interest answers a different question: what happens when the interest you earn is left in place and starts earning interest of its own?
The plain-text formula for compounding once per period is:
A = P × (1 + r) to the power of t
The key is the exponent. Each period, the whole balance, principal and accumulated interest together, is multiplied by (1 + r). So the interest earned in period two is calculated on a slightly bigger base than in period one, and so on. This is the mechanism behind Compound Interest, and it is why reinvesting returns matters so much over long horizons: every dollar of interest becomes principal that earns its own future interest.
A useful shorthand for how fast compounding works is the Rule of 72: divide 72 by the annual rate to estimate the years it takes a balance to double. At a steady rate that doubling repeats, which is what produces the curve. You can model any principal, rate, and horizon yourself with the Compound Interest Calculator.
A worked example
Assume you put $10,000 into an account earning 5% per year, and you leave it untouched for 30 years. Under these simplified, steady-rate assumptions, here is how the two methods compare.
Simple interest adds a flat 5% of the original $10,000 every year, which is $500 per year, no matter how large the balance gets:
$10,000 + ($500 × 30) = $25,000
Compound interest multiplies the whole balance by 1.05 each year, so the interest grows as the balance grows:
$10,000 × (1.05) to the power of 30 = about $43,219
Same principal, same rate, same 30 years. $25,000 one way, about $43,219 the other. The extra roughly $18,000 is entirely interest earning interest, money that simple interest structurally cannot produce.
The gap is small at first and widens the whole way. Watch the two diverge:
| End of year | Simple interest balance | Compound interest balance | Gap |
|---|---|---|---|
| Start | $10,000 | $10,000 | $0 |
| Year 5 | $12,500 | $12,763 | $263 |
| Year 10 | $15,000 | $16,289 | $1,289 |
| Year 20 | $20,000 | $26,533 | $6,533 |
| Year 30 | $25,000 | $43,219 | $18,219 |
In year 5 the two are within a few hundred dollars, which is why the difference feels trivial early on. By year 30 the compound balance is worth about 73% more than the simple one, from the same inputs. The longer the money stays invested, the more of the final result comes from compounding rather than from the original principal.
Which to use when
In practice you usually do not "choose" between simple and compound interest, the product or investment sets it. What matters is recognising which one is in play and reading the numbers accordingly. Under a given set of assumptions:
- Simple interest tends to apply when interest is paid out rather than reinvested, for example certain bonds that pay a fixed coupon, some fixed-term loans, and short-dated notes. If the interest leaves the account each period, it cannot compound.
- Compound interest tends to apply when returns stay in the account and are reinvested, which describes most long-term investing: reinvested dividends, growth left to accumulate, and many savings products. This is the setting where the curve does its work.
- The two are effectively equal when the horizon is very short or the rate is very low, because there is little accumulated interest for compounding to act on. The more time and the higher the rate, the more they diverge.
The reliable habit is to check whether a stated rate is simple or compound before comparing two options, and to confirm how often compounding happens (yearly, monthly, or daily), since more frequent compounding raises the effective result. Comparing a simple rate on one product to a compound rate on another is not a like-for-like comparison.
Frequently asked questions
Is compound interest better than simple interest?
For a saver or investor whose returns stay invested, compound interest produces a larger balance over long periods under the same rate, because it earns returns on past returns. But "better" depends on the context: on money you owe, compounding works against you, and simple interest costs less. Rather than ranking them, the useful question is which one applies to your specific product and whether the interest is being reinvested or paid out.
What is the formula for simple and compound interest?
Simple interest uses A = P × (1 + r × t), where the interest is just principal times rate times time. Compound interest (compounding once per period) uses A = P × (1 + r) to the power of t, where the whole balance is multiplied by (1 + r) each period. In both, P is the principal, r is the rate per period, and t is the number of periods. The exponent in the compound formula is what makes it accelerate.
How much faster does compound interest grow than simple interest?
It depends entirely on the rate and the horizon, and the gap widens the longer you stay invested. In the example above, $10,000 at 5% for 30 years reaches $25,000 with simple interest and about $43,219 with annual compounding, roughly 73% more, but at year 5 the two are within a few hundred dollars. You can test any rate and horizon with the Compound Interest Calculator to see how wide the gap becomes under your own assumptions.
Do savings accounts use simple or compound interest?
Many savings products credit interest that is then left in the account, so it compounds, and they often state how frequently (for example monthly or daily). That said, terms vary by product and provider, so the reliable step is to check whether a quoted rate is simple or compound and how often it compounds, since more frequent compounding raises the effective annual result.
When are simple and compound interest the same?
They are effectively identical over a single period, and nearly identical over very short horizons or at very low rates, because there is little or no accumulated interest for compounding to build on. The two only diverge to the extent that interest is left in place to earn further interest, which is why more time and higher rates widen the gap.
Put this into practice.
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