A rate goes from 4% to 5%, how much did it rise?

Question

A subtle interview favourite: distinguishing a change in percentage points from a relative percentage change. Solve in your head.

An interest rate moves from $4\%$ to $5\%$ . By what percentage did the rate increase (relatively)? Aim: under 10 seconds.

Accepted Answer

The absolute move is 1 percentage point. But the relative increase divides by the starting rate: \frac{5 - 4}{4} = \frac{1}{4} = 25\%. So the rate rose by \mathbf{25\%} relative, while only \mathbf{1} percentage point in absolute terms. Both answers are "correct" for different questions. Takeaway. "Percentage points" is the raw difference; "percent increase" divides by the base. A move from 4% to 5% is +1 point but +25% relative, always clarify which is being asked.

A rate goes from 4% to 5%, how much did it rise?

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