Mathematics for FinancePYQ July 21Question 3960 of 507
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Operating profit of a manufacturer for five years\n\n| Year | Operating Profit (in lakh Rs.) |\n|---|---|\n| 1 | 90 |\n| 2 | 100 |\n| 3 | 106.4 |\n| 4 | 107.14 |\n| 5 | 120.24 |\n| 6 | 157.35 |Then the operating profit of Compound Annual Growth Rate (CAGR) for year 6 with respect to year 2 is given that:

Options

A9%\displaystyle 9\%
B12%\displaystyle 12\%
C11%\displaystyle 11\%
D13%\displaystyle 13\%
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Correct Answer

Option b12%\displaystyle 12\%

All Options:

  • A9%\displaystyle 9\%
  • B12%\displaystyle 12\%
  • C11%\displaystyle 11\%
  • D13%\displaystyle 13\%

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 Value (Year 2 operating profit, PV\displaystyle PV) = 100\displaystyle 100 * Final Value (Year 6 operating profit, FV\displaystyle FV) = 157.35\displaystyle 157.35 * Time period (n\displaystyle n) = 62=4\displaystyle 6 - 2 = 4 years Substituting the values: CAGR=(157.35100)141=(1.5735)0.2511.121=12%\text{CAGR} = \left(\frac{157.35}{100}\right)^{\frac{1}{4}} - 1 = (1.5735)^{0.25} - 1 \approx 1.12 - 1 = 12\% Hence, **Option B** is the correct answer.

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