Mathematics of FinanceMCQMTP Oct 21Question 1578 of 512
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Find CAGR, if the operating profit of a manufacturer for five years is given asYr.: 1, 2, 3, 4, 5, 6OP: 90, 100, 106.4, 107.14, 120.24, 157.35

Options

A9%\displaystyle 9\%
B12%\displaystyle 12\%
C11%\displaystyle 11\%
D13%\displaystyle 13\%
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Correct Answer

Option b12%\displaystyle 12\%

All Options:

  • A9%\displaystyle 9\%
  • B12%\displaystyle 12\%
  • C11%\displaystyle 11\%
  • D13%\displaystyle 13\%

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Detailed Solution & Explanation

The Compound Annual Growth Rate (CAGR) is: CAGR=(FVPV)1n1\text{CAGR} = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1 Given: * Initial Value (Year 2 operating profit, PV\displaystyle PV) = 100\displaystyle 100 * Final Value (Year 6 operating profit, FV\displaystyle FV) = 157.35\displaystyle 157.35 * Time (n\displaystyle n) = 62=4\displaystyle 6 - 2 = 4 years Substituting the values: CAGR=(157.35100)0.2511.121=12%\text{CAGR} = \left(\frac{157.35}{100}\right)^{0.25} - 1 \approx 1.12 - 1 = 12\% Hence, **Option B** 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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