Mathematics for FinancePYQ 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 b — 18.36%\displaystyle 18.36\%

All Options:

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

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 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)13−1=(1.6667)0.3333−1≈1.1856−1=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.

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