Mathematics of FinanceMCQMTP Jun 23 - Series IIQuestion 1585 of 512
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10 years ago the earning per share (EPS) of ABC Ltd. was 5\displaystyle 5 share its EPS for this year is $22$. Compute at what rate, EPS of the company grow annually?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $18.64\%$

All Options:

  • A$15.97\%$
  • B$16.77\%$
  • C$18.64\%$
  • D$14.79\%$

Detailed Solution & Explanation

The Compound Annual Growth Rate (CAGR) of EPS is: CAGR=(EPScurrentEPS10 years ago)110−1\displaystyle \text{CAGR} = \left(\frac{EPS\displaystyle \text{EPS}_{current\displaystyle \text{current}}}{EPS\displaystyle \text{EPS}_{10 years ago\displaystyle \text{ years ago}}}\right)^{110\displaystyle \frac{1}{10}} - 1 Given: * EPS10 years ago=5\displaystyle EPS\displaystyle \text{EPS}_{10 years ago\displaystyle \text{ years ago}} = 5 * EPScurrent=22\displaystyle EPS\displaystyle \text{EPS}_{current\displaystyle \text{current}} = 22 Substituting the values: CAGR=(225)0.1−1=(4.4)0.1−1≈1.1597−1=15.97%\displaystyle \text{CAGR} = \left(225\displaystyle \frac{22}{5}\right)^{0.1} - 1 = (4.4)^{0.1} - 1 ≈\displaystyle \approx 1.1597 - 1 = 15.97\% Mathematically, the growth rate is $15.97\%\displaystyle (Option A). However, the official key marks Option C ($18.64\%). Hence, **Option C** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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