At what percent annual compound interest rate, a certain sum amounts to its 27 times in 3 years

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

Let sum = P and given that n = 3 yr According to the question, Amount = 27 PAccording 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%

Correct Answer:

Description for Correct answer:

Let sum = P and given that n = 3yr According to the question Amount = 27 P According to the formula, Amount = \( \Large P \left(1+ \frac{R}{100}\right)^{n} \) => 27P= \( \Large P \left(1+ \frac{R}{100}\right)^{3} \) => 27=\( \Large \left(1+ \frac{R}{100}\right)^{3} \) => \( \Large \left(1+ \frac{R}{100}\right)^{3}=(3)^{3} \) => \( \Large 1+ \frac{R}{100} \)=3 => \( \Large \frac{R}{100} \)=3-1=2

R=200%

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