Mathematics of FinanceMCQPYQ Sep 24Question 1563 of 512
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The Earning Per Share (EPS) of a company for five years is given below:YearEPS201940202025202140202240202390Calculate the Compounded Annual Growth Rate (CAGR) of EPS

Options

A23.47%\displaystyle 23.47\%
B24.47%\displaystyle 24.47\%
C22.47%\displaystyle 22.47\%
D21.47%\displaystyle 21.47\%
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Correct Answer

Option c22.47%\displaystyle 22.47\%

All Options:

  • A23.47%\displaystyle 23.47\%
  • B24.47%\displaystyle 24.47\%
  • C22.47%\displaystyle 22.47\%
  • D21.47%\displaystyle 21.47\%

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Detailed Solution & Explanation

The Compound Annual Growth Rate (CAGR) of EPS is: CAGR=(EPS2023EPS2019)1n1\text{CAGR} = \left(\frac{\text{EPS}_{2023}}{\text{EPS}_{2019}}\right)^{\frac{1}{n}} - 1 Given: * EPS2019=40\displaystyle \text{EPS}_{2019} = 40 * EPS2023=90\displaystyle \text{EPS}_{2023} = 90 * Time (n\displaystyle n) = 20232019=4\displaystyle 2023 - 2019 = 4 years Substituting the values: CAGR=(9040)141=(2.25)0.2511.22471=22.47%\text{CAGR} = \left(\frac{90}{40}\right)^{\frac{1}{4}} - 1 = (2.25)^{0.25} - 1 \approx 1.2247 - 1 = 22.47\% 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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