Compound interest in investing: how reinvested returns drive long-run wealth
Compound interest—the mechanism by which earnings on previous earnings drive long-run wealth—is the single most important quantitative idea in personal finance. Its effect is easy to underestimate over short windows and impossible to ignore over long ones.
What compound interest is
Compound interest is the process by which the return earned in each period is added to the principal, so that the next period's return is calculated on a larger base. In contrast to simple interest, where the return is computed on the original principal alone, compound interest produces a return on the return—and over multiple periods, this nesting produces growth that is exponential rather than linear.
The mathematics is straightforward. If a sum P earns a return r each period, after n periods it grows to P × (1 + r)n. The exponent is the source of the asymmetry: each additional period multiplies the previous total, not the original principal. Albert Einstein is widely (if apocryphally) credited with calling compound interest the eighth wonder of the world; the mathematics, at least, justifies the description.
How it works
Consider a USD 10,000 portfolio earning 7% per year. After ten years, simple interest would produce USD 17,000 (the principal plus 7 × 10 = 70% in interest). Compound interest produces USD 19,672—about 16% more, because each year's return is calculated on the prior year's larger base. After thirty years, the simple-interest figure rises to USD 31,000; the compound-interest figure to USD 76,123—a 145% larger outcome.
The gap widens with both the rate and the horizon. A higher rate compounds more aggressively; a longer horizon allows more cycles of compounding to occur. The doubling time—how long it takes a balance to double at a constant rate—can be approximated by the rule of 72: divide 72 by the percentage rate. At 7%, a balance doubles every ten years and three months; at 10%, every seven years and two months.
The geometric mean is the appropriate single-period rate to use when summarising a compounded return series. The arithmetic mean of period returns systematically overstates the realised compounded outcome whenever volatility is non-zero, because the volatility itself introduces a drag on long-run growth. This is the so-called volatility tax: a return series with the same arithmetic mean but lower volatility produces a higher compounded outcome.
The same mathematics applies in reverse. Costs that are charged as a percentage of assets each year—fund expense ratios, advisor fees, transaction costs—also compound. A 1% annual fee on a USD 100,000 portfolio earning 7% pre-fee for 30 years reduces the terminal balance by approximately 25%, which is more than its naive expectation might suggest.
What the evidence shows
Compounding's empirical importance is most visible in long-run equity studies. The Dimson, Marsh, and Staunton global dataset documents real annualised equity returns of around 5–6% across more than a century in major markets. Compounded over a 40-year working life, that produces a real wealth multiple of roughly 8–10×—meaning each unit invested at the start of a career produces 8–10 units of inflation-adjusted purchasing power at retirement.
The same dataset documents the corresponding figures for cash and bonds: real annualised returns of approximately 1% and 2% respectively. Compounded over the same 40 years, those produce wealth multiples of approximately 1.5× and 2.2×. The cumulative gap between equities and cash over a working life is not a 4-percentage-point gap; it is a 6× to 8× gap. That is compounding doing its work over time.
Reinvestment of distributions matters in the same way. Equity returns measured on a price-only basis understate total returns by the dividend yield each year—and over decades, the reinvested dividend stream becomes a meaningful share of the cumulative return. Total return measures (which assume dividend reinvestment) are typically 1–2 percentage points higher than price-only returns on diversified equity indices, and over 40 years that gap compounds to 50–100% of the price-only terminal value.
Limitations and trade-offs
Compound interest assumes returns are positive in expectation and that they can be reinvested at the same expected rate as the original principal. Neither assumption is automatic. Drawdowns interrupt the compounding sequence—and once principal has been lost, the recovery requires a return larger than the loss to restore the balance. A 50% drawdown requires a 100% gain to recover; a 75% drawdown requires a 300% gain. Sequence-of-returns risk is the formal name for this asymmetry, and it is most acute for investors withdrawing from a portfolio in retirement.
Compounding also assumes the investor stays the course. The strategy that produces an n-period compounded return is the strategy held for n periods. An investor who panics out at the first drawdown crystallises the loss without participating in the subsequent recovery, capturing only a portion of the long-run rate. The structural argument for systematic, rules-based investing is that it removes the discretionary moments at which investors are most likely to break the chain.
Compound interest in pfolio
pfolio's analytics report cumulative return and CAGR, both of which are direct expressions of compound growth applied to the asset or portfolio over the chosen analysis period. The choice of close or adjusted close price as input—which determines whether dividend reinvestment is captured in the return series—is configurable via advanced settings.
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