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A sum of money doubles itself at compound interest in 15 years. It will become 8 times in:
1. 30 years
2. 40 years
3. 45 years
4. 60 years

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Correct Answer - Option 3 : 45 years

Formula used:

Amount = Principal × (1 + r/100)n

Calculation:

Given that a sum of money doubles itself at compound interest in 15 years.

⇒ 2P = P(1 + r/100)15

⇒ 2 = (1 + r/100)15       ----(i)

For Sum to become 8 times

⇒ 8P = P(1 + r/100)n

⇒ 8 = (1 + r/100)n

⇒ (2)3 = (1 + r/100)n

⇒ {[1 + r/100]15}3 = (1 + r/100)n    {From (i)}

⇒ (1 + r/100)45 = (1 + r/100)n

⇒ n = 45

∴ Time taken = 45 years

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