ROI Calculator

Simple ROI has no time in it

Simple ROI is (gain / cost) × 100. It answers “how much did I make” and nothing else. Two investments both returning 50 per cent are not comparable if one took two years and the other ten: the first compounds at 22.5 per cent a year, the second at 4.1 per cent. Any investment return quoted without a period attached is incomplete.

CAGR is the honest single number

Compound annual growth rate is the constant annual rate that would turn the starting value into the ending value over the period: (end / start)^1/years − 1. It smooths away the path, which is its strength for comparison and its weakness for understanding risk — a steady 8 per cent and a wild ride averaging 8 per cent produce identical CAGR and very different experiences.

Real return is what you actually keep

A 6 per cent nominal return during 4 per cent inflation is roughly a 1.9 per cent real return — ((1.06 / 1.04) − 1), not the 2 per cent that subtraction suggests. Over long periods the difference between nominal and real compounds into something very large, which is why serious long-horizon planning is done in real terms.

A percentage without a time period is not a return

Doubling your money is a 100 per cent return whether it took eleven months or eleven years, which is why simple ROI cannot rank investments against each other. The annualised figure converts the result into a compound rate per year, and that is the only one of the three numbers above that is comparable across holdings of different lengths. It is also the number that makes a headline return look ordinary: 100 per cent over eleven years is 6.5 per cent a year.

Two adjustments separate a quoted return from the one you actually received. Fees compound against you in exactly the way returns compound for you, so a one per cent annual fee removes far more than one per cent of a long-run result. And where contributions or withdrawals happened mid-period, a simple beginning-to-end calculation silently credits or blames the investment for the timing of your own cash flows; that case needs an internal rate of return rather than a ratio of two balances.

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