The central difference
Simple interest is always calculated on the original principal. Compound interest is calculated on the accumulated balance, including previous returns.
With principal P, rate r and t periods, simple growth is P × (1 + r×t), while compound growth is P × (1 + r)^t. Simple interest adds the same monetary amount each period; compound interest changes the period’s monetary gain as the balance changes.
At $10,000 and 5% a year, simple interest adds $500 each year. Compound interest adds $500 in year one, $525 in year two and $551.25 in year three because earlier returns remain in the calculation base.
Compare both methods
Use the same capital, annual rate and duration below. The comparison assumes no contributions, fees, inflation or taxes so that the compounding effect remains visible.
For $10,000, 5% and 20 years, the simple model gives $20,000: the original $10,000 plus twenty additions of $500. Annual compounding gives about $26,532.98. The $6,532.98 difference is the mathematical effect of reinvesting returns under these fixed assumptions.
At one period the results are identical, and at a zero rate they remain identical for every duration. As the positive rate or horizon increases, the gap normally widens nonlinearly. The interactive comparison lets one input change at a time so the cause of the difference remains visible.
When each model is used
Simple interest describes situations where returns are not reinvested. Compound interest describes balances where returns stay invested. Loans also require an amortisation schedule and should not be assessed with this comparison alone.
The simple formula can be appropriate for a clearly specified contract that calculates interest only on original principal. The compound formula is appropriate only when returns are actually credited to the balance at the stated interval. Labels in a product document and local disclosure rules take precedence over a generic model.
For debt, repayments reduce principal while interest accrues on an outstanding balance. Fees, payment dates and day-count conventions can also matter. A side-by-side savings illustration therefore cannot provide the total cost of credit or replace an amortisation table.
Frequent mistakes
Compare like with like: the same effective rate, period and cash flows. Mixing nominal and effective rates can make the result misleading.
Do not read the compound-minus-simple gap as a promised bonus. Both lines assume a constant rate and omit uncertainty. If the rate is negative, the simple formula can eventually reach zero or become negative while multiplicative compounding remains above zero for rates greater than −100% per period; that mathematical divergence may not describe a real contract.
Also distinguish interest generated from total final capital. Contributions are transfers of the saver’s own money, not returns. When deposits are added, a fair comparison must use exactly the same amounts and dates under both methods.
Simple interest—
Compound interest—
Difference—
How to interpret the difference
The gap is not an extra guaranteed return. It isolates the mathematical effect of reinvesting returns under a constant rate. Real outcomes can differ because returns vary, costs and taxes apply, and money may enter or leave at different times.