Compound Growth, explained.
Compound growth applies each period's percentage change to the current total, so earlier gains also participate in later growth.
Why it happens
Simple interest adds the same amount based on the starting balance. Compounding uses a changing base. The gap can be small initially and large later; inflation separately changes the purchasing power of the nominal total.
Compounding applies each period's change to the current total. The gap from simple interest widens with time because earlier gains also earn gains.
Read the result
Compare the compounded balance, simple-interest balance, and inflation-adjusted value at the same horizon. A growing nominal number does not necessarily mean equivalent growth in what it can buy.
A worked example
Two years at a fixed 10%
Start with 100 units and apply a 10% increase: the first-year total is 110.
The second increase is 10% of 110, or 11, producing 121. Simple interest would produce 120.
The extra unit comes from growth on the previous gain, not an increase in the assumed rate.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Starting with 1,000 units, nominal balance is 1,000(1+r)^t; simple interest is 1,000(1+rt). Purchasing power divides the nominal balance by (1+inflation)^t. Rates are fixed and there are no deposits.
Where this idea is useful
A practical use
Compare long-term savings scenarios, or explore how a recurring percentage increase changes a bill over time.
A common misconception
“A smooth growth curve predicts actual returns.”
The curve shows arithmetic under fixed rates. Real returns, costs, and inflation can vary, so the model is a scenario rather than a forecast.
What this explanation leaves out
- This is arithmetic under assumed constant rates, not an investment forecast. Taxes, fees, changing inflation and uncertain returns are excluded.
Can compounding work against me?
Yes. Recurring charges, debt interest, and repeated percentage losses can also compound. The same multiplication rule applies even when the resulting change is unwanted.
Is the percentage change applied to the initial amount or to the evolving total?
Further reading
Explore the original research or the teaching reference behind this experiment.