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A sum becomes 8 times of itself in 7 years at the rate of compound interest (interest is compounded annually). In how many years will the sum becomes 4096 times of itself?

A sum becomes 8 times of itself in 7 years at the rate of compound interest (interest is compounded annually). In how many years will the sum becomes 4096 times of itself? Correct Answer 28

Given :

Principal = Rs. P

Rate of interest = R%

Time = t years

Amount after 7 years = Rs. 8P

Formula used:

Amount = (P) × (1 + (R/100))T

Calculation :

According to question,

⇒ P(1 + (R/100))7 = 8P

⇒ (1 + (R/100))7 = 8

⇒ 1 + (R/100) = 81/7 --- (1)

Let Amount after T years be Rs. 4096P

⇒ P(1 + (R/100))T = 4096P

⇒ (1 + (R/100))T = 4096

Substituting (1) in above equation

⇒ (81/7)T = 84

⇒ (8T/7) = 84

⇒ T/7 = 4

⇒ T = 28

∴ In 28 years, the given principal will become 4096 times of itself.

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