A sum of money becomes eight times of itself in 3 years

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A sum of money becomes eight times of itself in 3 years at compound interest. The rate of interest per annum is

1. 100%
2. 80%
3. 20%
4. 10%

Correct Option: A

Let the principal be P and the rate of compound interest be r% per annum. Then,
According to question ,

8P = P		1 +	r		³
			100

⇒ 8 =		1 +	r		³	⇒ 2³ =		1 +	r		³
			100						100

⇒ 2 = 1 +	r
	100

⇒	r	= 1 ⇒ r = 100%
	100

We can find required answer with the help of given formula :
Here, n = 8, t = 3 years.
R% = (n^1/t − 1) × 100%
R% = [(8)^1/3 − 1] × 100%
R% = [(2³)^1/3 − 1] × 100%
∴ R% = 100%