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Compound interest is the interest calculated on the initial principal which also includes all of the accumulated interest from previous periods. The amount accrued is determined by the formula: A = P(1 + r/n)nt where A is the final amount, P is the principal, r is the annual interest rate (decimal), n is the compounding frequency, and t is the time in years. Compound interest differs from simple interest in that the interest-on-interest effect produces exponential rather than linear growth of the principal balance.
Forget the formula for a sec. Imagine you have €100 and a friend pays you 10% interest a year.
After year one: you have €110. Easy.
But here's the trick — in year two, the 10% is calculated on €110, not €100. So you earn €11, not €10. The interest itself starts earning interest.
That's why €100 left alone for 30 years at 10% becomes €1,745 — not €400 like simple math would suggest.
Money grows on top of money. That's the whole idea.
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