Mathematics for FinancePYQ June 24Question 1560 of 512
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If the initial investment of 4,00,000\displaystyle 4,00,000 becomes 6,00,000\displaystyle 6,00,000 in 24\displaystyle 24 months, then CAGR is

Options

A30.33%\displaystyle 30.33\%
B22.4%\displaystyle 22.4\%
C19.46%\displaystyle 19.46\%
D14.47%\displaystyle 14.47\%
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Correct Answer

✅ Option b — 22.4%\displaystyle 22.4\%

All Options:

  • A30.33%\displaystyle 30.33\%
  • B22.4%\displaystyle 22.4\%
  • C19.46%\displaystyle 19.46\%
  • D14.47%\displaystyle 14.47\%

Detailed Solution & Explanation

The Compound Annual Growth Rate (CAGR) is: CAGR=(FVPV)1n−1\text{CAGR} = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1 Given: * Initial investment (PV\displaystyle PV) = 4,00,000\displaystyle 4,00,000 * Final value (FV\displaystyle FV) = 6,00,000\displaystyle 6,00,000 * Time (n\displaystyle n) = 24\displaystyle 24 months = 2\displaystyle 2 years Substituting the values: CAGR=(6,00,0004,00,000)12−1=(1.5)0.5−1≈1.2247−1=22.47%\text{CAGR} = \left(\frac{6,00,000}{4,00,000}\right)^{\frac{1}{2}} - 1 = (1.5)^{0.5} - 1 \approx 1.2247 - 1 = 22.47\% This is closest to Option B (22.4%\displaystyle 22.4\%). Hence, **Option B** is the correct answer.

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