Simple vs Compound Interest
Two accounts can advertise the same rate and pay you very different amounts, because the rate is only half the story. The other half is whether interest is paid on your original deposit alone or on your whole growing balance. Every figure below was produced by the same engine that powers the free compound interest calculator, so the numbers on this page and the numbers in the tool agree exactly.
In short: simple interest pays a flat amount every period, forever. Compound interest pays on principal plus all interest already earned, so each period starts from a larger base. At 5% on $10,000, the two are identical after one year and $6,532.98 apart after twenty.
The two definitions
Simple interest is calculated only on the original principal. If you deposit $10,000 at 5% simple interest, you earn $500 in year one, $500 in year twenty, and $500 in year forty. The formula is a single multiplication: A = P × (1 + r × t), where P is the principal, r is the annual rate as a decimal, and t is the number of years. Growth is a straight line.
Compound interest is calculated on the current balance, which includes every dollar of interest already credited. The same $10,000 at 5% compounded annually earns $500 in year one, but that $500 joins the balance, so year two earns 5% of $10,500 instead of 5% of $10,000. The formula is A = P × (1 + r/n)nt, where n is the number of compounding periods per year. Growth is a curve that bends upward.
The distinction only matters over time. In the first period the two are mathematically identical, which is exactly why the difference is easy to underestimate when you are reading a rate sheet.
Side by side, computed
The table below runs $10,000 at 5% with no deposits, under three treatments: simple interest, compound interest credited once a year, and compound interest credited monthly (the calculator's default setting).
| $10,000 at 5% | Simple | Compound (annual) | Compound (monthly) |
|---|---|---|---|
| After 1 year | $10,500.00 | $10,500.00 | $10,511.62 |
| After 5 years | $12,500.00 | $12,762.82 | $12,833.59 |
| After 10 years | $15,000.00 | $16,288.95 | $16,470.09 |
| After 20 years | $20,000.00 | $26,532.98 | $27,126.40 |
Read the first row and the last row together. After one year, annual compounding produces exactly the same $10,500 as simple interest, and monthly compounding beats it by $11.62. After twenty years, annual compounding is ahead by $6,532.98 and monthly compounding by $7,126.40. Nothing changed except the number of times the interest was allowed to earn interest.
Why the gap widens
The gap is not linear, and that is the whole point. Measured against the simple-interest result, annual compounding is 0.00% ahead at one year, 2.10% ahead at five years, 8.59% ahead at ten, and 32.66% ahead at twenty. Push the same inputs further and the ratio keeps climbing: at thirty years simple interest reaches $25,000 while annual compounding reaches $43,219.42, a gap of $18,219.42. At forty years the figures are $30,000 and $70,399.89, so the compound balance is 2.35 times the simple one.
The mechanism is visible in a single column of the year-by-year table. With simple interest, every year credits exactly $500. With annual compounding on the same $10,000 at 5%, year one credits $500.00, year ten credits $775.66, and year twenty credits $1,263.48. The rate never moved. Only the base did.
A useful way to hold this in your head: simple interest adds, compound interest multiplies. Adding the same quantity repeatedly produces a straight line no matter how many times you do it. Multiplying by the same factor repeatedly produces a curve whose steepness depends on how many multiplications you have room for. That is the entire difference, and it is why every question about compounding eventually turns into a question about the number of periods rather than the size of the rate.
This is also why the shape of the curve is so much more sensitive to time than to small differences in rate, and why the Rule of 72 works as a mental shortcut for compound growth but has no meaning at all for simple interest, which never doubles by itself.
Where simple interest actually appears
Compound interest dominates savings products, but simple interest is not a historical curiosity. It shows up in several ordinary places:
- Some installment loans. Certain fixed-term consumer loans compute a finance charge on the original amount borrowed and divide it evenly across the payments, rather than accruing on the declining balance. The disclosure documents state which method applies.
- Interest that accrues but does not capitalize. Many loans accrue interest on the outstanding principal each day and collect it at the next payment. If the borrower pays it, the interest never joins the principal, so nothing compounds. If it is left unpaid and later added to principal, it does.
- Bond coupon framing. A bond's coupon is quoted as a fixed percentage of face value, paid on a schedule. That coupon is the same dollar amount each period regardless of how long the bond is held, so nothing compounds inside the bond itself. Whether the money compounds depends entirely on what the holder does with each payment when it arrives.
- Accounts that sweep interest out. If interest is paid into a different account rather than left in place, the original balance never grows, and the arrangement behaves like simple interest from the first account's point of view.
None of these are better or worse in the abstract. They are different accounting conventions, and the only thing that matters is knowing which one governs the money in front of you.
Which one this calculator models
The calculator on the home page models compound interest, and only compound interest. It walks forward one month at a time, credits interest whenever the chosen compounding period closes, and adds any monthly deposit afterward. Choose annual compounding to reproduce the middle column of the table above; leave it on monthly to reproduce the right-hand column. To see a simple-interest result, do the one multiplication yourself: principal, times one, plus rate times years.
If you want to push the comparison further, the main guide runs the same test at 7%, daily vs monthly compounding shows how little the crediting schedule matters once the rate is fixed, and monthly contributions covers what happens when you keep adding money instead of leaving a lump sum alone.
Frequently asked questions
Is simple interest ever better than compound interest?
For money you are earning on, no: at the same rate and term, compound interest is always equal to or greater than simple interest, and equal only in the very first period. For money you owe, the ranking flips, since a debt that compounds grows faster than one that does not.
Can I use this calculator for simple interest?
Not directly, because the engine always compounds. Use the formula A = P times (1 + r times t) instead, which needs no tool: $10,000 at 5% for 20 years is 10,000 times 2.00, or $20,000.
How long before the difference gets large?
At 5% on $10,000 with annual compounding, the compound balance is 2.10% ahead of simple interest after five years, 8.59% ahead after ten, and 32.66% ahead after twenty. The gap grows slowly at first and then accelerates, which is why long horizons matter more than the early years suggest.
Does compounding frequency change the comparison much?
Slightly. On $10,000 at 5% over 20 years, annual compounding beats simple interest by $6,532.98 and monthly compounding beats it by $7,126.40. The jump from simple to compound is far larger than the jump from annual to monthly crediting.
Related reading: How compound interest works · Compound interest glossary · Monthly contributions · The Rule of 72 · APY vs APR · FAQ
All rates on this page are illustrative and assumed constant so the arithmetic is comparable. Real account rates change and returns vary. Educational only, not investment, tax, or financial advice.
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