A sum of money placed at compound interest doubles itself

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A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times itself in ?

1. 15 years
2. 20 years
3. 12 years
4. 10 years

Correct Option: A

Let the principal be P and rate be r%.Then
2P = P(1 + r/100)⁵
⇒ (1 + r/100)⁵ = 2
Let it be 8 times in t years, then
∵ 8P = P(1 + r/100)^t
⇒ (1 + r/100)^t = 8
⇒ (2)³ ⇒ (1 + r/100)¹⁵
∴ t =15 year.