Compounding
Mechanism by which interest accumulates on both the initial capital and previously earned interest, producing exponential growth.
Textbook case: 1,000 euros invested at 5 percent for twenty years. With simple interest, you get back 2,000 euros. With annual compounding, 1,000 × 1.05^20, about 2,653 euros, and a little over 2,712 euros if compounding is monthly. Compounding is the reinvestment of interest so that it earns interest in turn. The future value of a capital C at rate r over n periods is C × (1 + r)^n. At the same nominal rate, the more frequent the compounding, the higher the final value, up to the limit of continuous compounding, C × e^(r×n). The gap is small over one year and widens with time, which is why the rate assumption weighs so heavily on pension liabilities running forty or fifty years. The trap is in the convention: a quoted rate means nothing without its compounding frequency, and two rates that look identical on paper can deliver different returns. In actuarial work, compounding is the inverse of discounting, and discounting a future cash flow means dividing it by its compounding factor.
Textbook case: 1,000 EUR invested at 5% for 20 years. Simple interest gives 2,000 EUR; annual compounding, 1,000 × 1.05^20 ≈ 2,653 EUR; monthly compounding, ≈ 2,712 EUR.
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