Mathematics of FinancePYQ Jan 26Question 4210 of 507
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The net asset value (NAV) of a Mutual Fund is calculated at the end of the financial year. For the last five years following values are computed. Year: 2021(100), 2022(115), 2023(150), 2024(120), 2025(200). Calculate the Compounded Annual Growth Rate of NAV.

Options

A16.92%
B18.92%
C20.92%
D22.92%
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Correct Answer

✅ Option b — 18.92%

All Options:

  • A16.92%
  • B18.92%
  • C20.92%
  • D22.92%

Detailed Solution & Explanation

Compounded Annual Growth Rate (CAGR) is calculated using the formula:
CAGR=(VfinalVinitial)1n−1\text{CAGR} = \left( \frac{V_{\text{final}}}{V_{\text{initial}}} \right)^{\frac{1}{n}} - 1
where:
- Vinitial\displaystyle V_{\text{initial}} is the initial value at the start of the period.
- Vfinal\displaystyle V_{\text{final}} is the final value at the end of the period.
- n\displaystyle n is the number of years in the period.

Given values:
- Initial Year = 2021\displaystyle 2021 with value Vinitial=100\displaystyle V_{\text{initial}} = 100
- Final Year = 2025\displaystyle 2025 with value Vfinal=200\displaystyle V_{\text{final}} = 200
- Number of years n=2025−2021=4\displaystyle n = 2025 - 2021 = 4 years

Substitute these values into the CAGR formula:
CAGR=(200100)14−1\text{CAGR} = \left( \frac{200}{100} \right)^{\frac{1}{4}} - 1
CAGR=(2)14−1\text{CAGR} = (2)^{\frac{1}{4}} - 1

Since 21/4=2≈1.414213≈1.189207\displaystyle 2^{1/4} = \sqrt{\sqrt{2}} \approx \sqrt{1.414213} \approx 1.189207:
CAGR=1.189207−1=0.189207\text{CAGR} = 1.189207 - 1 = 0.189207
Converting to percentage:
CAGR≈18.92%\text{CAGR} \approx 18.92\%

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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