Statistics & Applications

Financial Math

Medium

applied

A person invested ₹ 20000 in a mutual fund in year 2018. The value of the mutual fund increased to ₹ 32000 in year 2023. The compound annual growth rate of his investment is:

[Given that $(1.6)^{1/5} = 1.098]$

9.8%

8.7%

10 %

7.8 %

✅ Correct Option: 1

Initial Investment = ₹20,000

Final Value = ₹32,000

Time Period = 2023 - 2018 = 5 years

Given: $(1.6)^{1/5} = 1.098$

The compound growth formula is:

Final Value = Initial Value × $(1 + r)^n$

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

Substituting the values:

$32000 = 20000 \times (1 + r)^5$

$\dfrac{32000}{20000} = (1 + r)^5$

$1.6 = (1 + r)^5$

Taking the 5th root of both sides:

$(1 + r) = (1.6)^{1/5}$

Using the given value $(1.6)^{1/5} = 1.098$ :

$(1 + r) = 1.098$

$r = 1.098 - 1$

$r = 0.098$

Converting to percentage:

$r = 0.098 \times 100 = 9.8\%$

Therefore, the compound annual growth rate is 9.8%.

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A person invested ₹ 20000 in a mutual fund in year 2018. The value of the mutual fund increased to ₹ 32000 in year 2023. The compound annual growth rate of his investment is: [Given that (1.6)1/5=1.098](1.6)^{1/5} = 1.098](1.6)1/5=1.098]

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CUET Mathematics Past Year Questions (Topic-Wise)

A person invested ₹ 20000 in a mutual fund in year 2018. The value of the mutual fund increased to ₹ 32000 in year 2023. The compound annual growth rate of his investment is:

[Given that $(1.6)^{1/5} = 1.098]$