Mathematics of FinanceMCQPYQ Jun 23Question 1556 of 512
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Ms. Paul invested $1,00,000$ in a mutual fund scheme in January $2018$. After one year in January $2019$, she got a dividend amounting to $10,000$ for first year, $12,000$ for second year, $16,000$ for third year, $18,000$ for fourth year and $21,000$ for fifth year in January $2023\displaystyle . What is Compounded Annual Growth Rate (CAGR) of dividend return? Given $1.2038^2 = 2.1.

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

✅ Option a — $20.38\%$

All Options:

  • A$20.38\%$
  • B$18.59\%$
  • C$16.36\%$
  • D$15.89\%$

Detailed Solution & Explanation

The Compound Annual Growth Rate (CAGR) is: CAGR=(FVPV)1n−1\displaystyle \text{CAGR} = \left(FVPV\displaystyle \frac{FV}{PV}\right)^{1n\displaystyle \frac{1}{n}} - 1 Given: * Initial dividend (January 2019, PV\displaystyle PV) = $10,000$ * Final dividend (January 2023, FV\displaystyle FV) = $21,000$ * Time (n\displaystyle n) = $2023 - 2019 = 4$ years * Given factor: $1.2038^2 = 2.1$ Substituting the values: CAGR=(21,00010,000)14−1=(2.1)14−1\displaystyle \text{CAGR} = \left(21,00010,000\displaystyle \frac{21,000}{10,000}\right)^{14\displaystyle \frac{1}{4}} - 1 = (2.1)^{14\displaystyle \frac{1}{4}} - 1 Since (1.2038)2=2.1  ⟹  (2.1)14=1.2038≈1.097\displaystyle (1.2038)^2 = 2.1 \implies (2.1)^{14\displaystyle \frac{1}{4}} = 1.2038\displaystyle \sqrt{1.2038} ≈\displaystyle \approx 1.097: Wait, if (1.2038)4≈2.1\displaystyle (1.2038)^4 ≈\displaystyle \approx 2.1, then (2.1)1/4=1.2038\displaystyle (2.1)^{1/4} = 1.2038. Indeed, $1.2038^4 ≈\displaystyle \approx 2.1$. CAGR=1.2038−1=20.38%CAGR=1\displaystyle \text{CAGR} = 1.2038 - 1 = 20.38\% Hence, **Option A** 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.

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