Statistics & Applications

Financial Math

Medium

applied

Anisha invested Rs.20000 in a mutual fund in the year 2016, which increased to Rs.36000 in the year 2024. The percentage compounded annual growth rate(CAGR) of her investment is:

(Given: $(1.8)^{1/8} = 1.076$ )

13.8% p.a

7.6% p.a

8.6% p.a

10.76% p.a

✅ Correct Option: 2

Anisha's investment grew from Rs. 20,000 to Rs. 36,000 from 2016 to 2024.

The compound annual growth rate (CAGR) formula is:

Final Amount $=$ Initial Amount $\times (1 + r)^n$

where $r$ is the annual growth rate and $n$ is the number of years.

Given values:

Initial Amount $=$ Rs. 20,000

Final Amount $=$ Rs. 36,000

Number of years $= 2024 - 2016 = 8$ years

Substituting into the formula:

$36,000 = 20,000 \times (1 + r)^8$

Dividing both sides by 20,000:

$\dfrac{36,000}{20,000} = (1 + r)^8$

$1.8 = (1 + r)^8$

Taking the 8th root of both sides:

$(1.8)^{1/8} = 1 + r$

Using the given value $(1.8)^{1/8} = 1.076$ :

$1.076 = 1 + r$

$r = 1.076 - 1$

$r = 0.076$

Converting to percentage:

$r = 0.076 \times 100 = 7.6\%$

Therefore, the CAGR is 7.6% p.a.

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Choose the correct answer from the options given below:

Anisha invested Rs.20000 in a mutual fund in the year 2016, which increased to Rs.36000 in the year 2024. The percentage compounded annual growth rate(CAGR) of her investment is: (Given: (1.8)1/8=1.076(1.8)^{1/8} = 1.076(1.8)1/8=1.076)

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Anisha invested Rs.20000 in a mutual fund in the year 2016, which increased to Rs.36000 in the year 2024. The percentage compounded annual growth rate(CAGR) of her investment is:

(Given: $(1.8)^{1/8} = 1.076$ )