Statistics & Applications

Financial Math

Medium

applied

If an investment value get doubled in 10 years then its compound annual growth rate (CAGR) is: (Given $2^{1/10} = 1.0729$ )

10%

12%

7.29%

✅ Correct Option: 4

The investment doubles in 10 years.

Let the initial value be $P$ .

Final value $= 2P$

Time $= 10$ years

Using the compound interest formula:

Final Value $=$ Initial Value $\times (1 + \text{CAGR})^{\text{number of years}}$

$2P = P \times (1 + \text{CAGR})^{10}$

$2 = (1 + \text{CAGR})^{10}$

Taking the 10th root of both sides:

$1 + \text{CAGR} = 2^{1/10}$

Given that $2^{1/10} = 1.0729$ :

$1 + \text{CAGR} = 1.0729$

$\text{CAGR} = 1.0729 - 1$

$\text{CAGR} = 0.0729$

Converting to percentage:

$\text{CAGR} = 0.0729 \times 100$

$\text{CAGR} = 7.29\%$

Therefore, the compound annual growth rate is $7.29\%$ .

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A person invested ₹2,00,000 in a mutual fund in year 2012. The value of the mutual fund increased to ₹3,00,000 in year 2017. The percentage of compound annual growth rate on the investment is:

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	LIST-I		LIST-II
A.	Book value of an asset at a given date	I.	Original value of the asset - scrap value of the asset
B.	Useful life of an asset	II.	The value of a depreciable asset at the end of its useful life.
C.	Total depreciation	III.	An accounting estimate of the number of years an asset is likely to remain in service for the purpose of cost-effective revenue generation.
D.	Residual value	IV.	Original value of the asset - accumulated depreciation at that time

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If an investment value get doubled in 10 years then its compound annual growth rate (CAGR) is: (Given 21/10=1.07292^{1/10} = 1.072921/10=1.0729)

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If an investment value get doubled in 10 years then its compound annual growth rate (CAGR) is: (Given $2^{1/10} = 1.0729$ )