Mathematics of FinanceMCQPYQ June 22Question 1555 of 512
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The CAGR of a initial value of a investment of 15,000\displaystyle 15,000 and final value of 25,000\displaystyle 25,000 in 3\displaystyle 3 years is:

Options

A19%\displaystyle 19\%
B18.36%\displaystyle 18.36\%
C17.56%\displaystyle 17.56\%
D17%\displaystyle 17\%
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Correct Answer

Option b18.36%\displaystyle 18.36\%

All Options:

  • A19%\displaystyle 19\%
  • B18.36%\displaystyle 18.36\%
  • C17.56%\displaystyle 17.56\%
  • D17%\displaystyle 17\%

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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 (PV\displaystyle PV) = 15,000\displaystyle 15,000 * Final Value (FV\displaystyle FV) = 25,000\displaystyle 25,000 * Time (n\displaystyle n) = 3\displaystyle 3 years Substituting the values: CAGR=(25,00015,000)131=(1.6667)0.333311.18561=18.56%\text{CAGR} = \left(\frac{25,000}{15,000}\right)^{\frac{1}{3}} - 1 = (1.6667)^{0.3333} - 1 \approx 1.1856 - 1 = 18.56\% This is closest to Option B (18.36%\displaystyle 18.36\%). 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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