Mathematics of FinanceMCQPYQ Jun 23Question 1556 of 512
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Ms. Paul invested 1,00,000\displaystyle 1,00,000 in a mutual fund scheme in January 2018\displaystyle 2018. After one year in January 2019\displaystyle 2019, she got a dividend amounting to 10,000\displaystyle 10,000 for first year, 12,000\displaystyle 12,000 for second year, 16,000\displaystyle 16,000 for third year, 18,000\displaystyle 18,000 for fourth year and 21,000\displaystyle 21,000 for fifth year in January 2023\displaystyle 2023. What is Compounded Annual Growth Rate (CAGR) of dividend return? Given 1.20382=2.1\displaystyle 1.2038^2 = 2.1.

Options

A20.38%\displaystyle 20.38\%
B18.59%\displaystyle 18.59\%
C16.36%\displaystyle 16.36\%
D15.89%\displaystyle 15.89\%
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Correct Answer

Option a20.38%\displaystyle 20.38\%

All Options:

  • A20.38%\displaystyle 20.38\%
  • B18.59%\displaystyle 18.59\%
  • C16.36%\displaystyle 16.36\%
  • D15.89%\displaystyle 15.89\%

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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 dividend (January 2019, PV\displaystyle PV) = 10,000\displaystyle 10,000 * Final dividend (January 2023, FV\displaystyle FV) = 21,000\displaystyle 21,000 * Time (n\displaystyle n) = 20232019=4\displaystyle 2023 - 2019 = 4 years * Given factor: 1.20382=2.1\displaystyle 1.2038^2 = 2.1 Substituting the values: CAGR=(21,00010,000)141=(2.1)141\text{CAGR} = \left(\frac{21,000}{10,000}\right)^{\frac{1}{4}} - 1 = (2.1)^{\frac{1}{4}} - 1 Since (1.2038)2=2.1    (2.1)14=1.20381.097\displaystyle (1.2038)^2 = 2.1 \implies (2.1)^{\frac{1}{4}} = \sqrt{1.2038} \approx 1.097: Wait, if (1.2038)42.1\displaystyle (1.2038)^4 \approx 2.1, then (2.1)1/4=1.2038\displaystyle (2.1)^{1/4} = 1.2038. Indeed, 1.203842.1\displaystyle 1.2038^4 \approx 2.1. CAGR=1.20381=20.38%\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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