At what per cent annual compound interest, rate, a certain

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At what per cent annual compound interest, rate, a certain sum amounts to its 27 times in 3 yr?

1. 100%
2. 150%
3. 75%
4. 200%

Correct Option: D

Let sum = P
and given that n = 3 yr
According to the question,
Amount = 27 P
According to the formula,
Amount = P (1 + R/100)ⁿ
⇒ 27 P = P (1 + R/100)³
⇒ 27 = (1 + R/100)³
⇒ (1 + R/100)³ = (3)³
⇒ 1 + R/100 = 3
⇒ R/100 = 3 - 1 = 2
∴ R = 200%