Successive percent change net effect: Suman’s income is first increased by 7% and then decreased by 7%. What is the net percentage change in her income?

Introduction / Context:Equal percentage increase and decrease do not cancel out, because the second change is applied on a different base. The net effect is always a small decrease equal to (a^2 / 100)% where a is the percent.

Given Data / Assumptions:

• Increase a = 7% ⇒ factor 1.07.
• Then decrease 7% ⇒ factor 0.93.

Concept / Approach:Net factor = 1.07 * 0.93 = 0.9951. Net % change = (0.9951 − 1) * 100%.

Step-by-Step Solution:

Verification / Alternative check:Start with 100. After +7% → 107. After −7% → 107 * 0.93 = 99.51. Difference from 100 = −0.49%, confirming the formula.

Why Other Options Are Wrong:

• Options claiming increase are incorrect; the net is always a decrease.
• 0.39% miscomputes a^2/100.
• “No change” holds only for +x% and then −x% when x = 0.

Common Pitfalls:Assuming +7% and −7% cancel; they do not because the bases differ.

Final Answer:0.49% (decrease)