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Percentage

Read a percentage as a ratio per hundred, convert it to a decimal, and apply it to the correct financial base without confusing money, percentage points or basis points.

A percentage expresses a ratio per hundred: p%=p/100p\%=p/100. The percent sign changes the scale of the number, so 5%=0.055\%=0.05. It does not specify a currency, a time period or the amount to which the rate applies.

This matters when a trading fee looks small. A quoted 0.2%0.2\% is a multiplier of 0.0020.002, and the cash charge depends on the stated fee base.

From a rate to a cash amount

For a percentage number pp and reference amount BB,

A=Bp100.A=B\frac{p}{100}.

Here pp is the number before the percent sign. If you already have the decimal rate r=p/100r=p/100, multiply by rr directly; dividing by 100 again would convert twice. Conversely, an amount AA is (100A/B)%(100A/B)\% of a nonzero base BB. The numerator and denominator must use compatible units.

Suppose a hypothetical broker charges a one-off 0.2% fee on USD 25,000 of traded notional, with no minimum fee, fixed charge or tax:
Fee=25,000×0.2100=50 USD.\text{Fee}=25{,}000\times\frac{0.2}{100}=50\text{ USD}.
The equivalent quote is 20 basis points, because one basis point is 0.01%=0.00010.01\%=0.0001. Entering 0.20.2 as the decimal multiplier instead would produce USD 5,000: a charge 100 times too large.
A hypothetical one-off fee of 0.2% equals the decimal multiplier 0.002 and 20 basis points. Applying it to USD 25,000 traded notional gives a USD 50 fee.
A hypothetical one-off fee of 0.2% equals the decimal multiplier 0.002 and 20 basis points. Applying it to USD 25,000 traded notional gives a USD 50 fee.
Original hypothetical fee example. Three rate labels give the same charge on the same base; the fee is one-off, not annual.

Always ask: percent of what?

The fee above is 0.2% of traded notional. If the trader supports that trade with USD 5,000 of equity, the same USD 50 fee is 1% of that equity. Neither calculation changes the broker's assumed fee rule. Notional and account equity answer different questions.

Likewise, a USD 10 profit is a currency amount. It is 10% of USD 100 and 1% of USD 1,000; without a chosen capital base, “10% profit” is incomplete. A zero base makes the ratio undefined. A negative base needs an explicit interpretation before a percentage is useful for comparing performance.

Read the base and period together. For example, a fund's annual expense ratio uses average net assets and annual operating expenses, rather than a single trade's notional. An annual percentage cannot be treated as a one-off charge without a time convention.

A percentage level is different from its change

A rate moving from 5% to 6% illustrates three distinct statements:

MeasureResultWhat it compares
New percentage level6%The new rate itself
Percentage-point change+1 percentage point, or +100 basis pointsThe difference between the two rate levels
Percentage change+20%The increase divided by the original 5% rate

For the last row, (0.06−0.05)/0.05=0.20=20%(0.06-0.05)/0.05=0.20=20\%. Saying only “up 1%” hides which calculation is intended. Use “one percentage point” for the subtraction and “20% relative increase” for the ratio.

For further work with rates, units and fee equations, see Arithmetic, Algebra, Equations and Functions (full lesson requires membership; public preview available).

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