Sudha’s present salary — which statements suffice? I. The salary increases every year by 15%. II. Her starting salary (at joining) was $10,000. III. She joined exactly 5 years ago.

Difficulty: Easy

Correct Answer: All I, II and III

Explanation:


Introduction / Context:
We need to determine which statements allow computation of Sudha’s current salary under compound annual raises.


Given Data / Assumptions:

  • I: Annual raise rate r = 15% per year, compounded yearly.
  • II: Initial salary S0 = $10,000 at joining.
  • III: Time elapsed t = 5 years.


Concept / Approach:
Present salary S = S0 * (1 + r)^t. Therefore, we require S0, r, and t — i.e., all three statements together.


Step-by-Step Solution:

S0 = 10,000; r = 0.15; t = 5.S = 10,000 * (1.15)^5.Numerically, (1.15)^5 ≈ 2.011357 ⇒ S ≈ $20,113.57.


Verification / Alternative check:
Any missing element (rate, initial salary, or years) prevents a unique numeric answer.


Why Other Options Are Wrong:

  • II and III only: Missing raise rate.
  • I and II only: Missing time.
  • I and III only: Missing base salary.


Common Pitfalls:
Using simple interest instead of compounding for annual percentage raises; ignoring the exact number of years.


Final Answer:
All I, II and III

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