Multiple choice

If a certain sum becomes 3 times in 6 years at compound interest, then in how many years will it become 81 times?

  1. 81

  2. 162

  3. 27

  4. 24
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D Correct answer
Explanation

If a sum becomes 3^1 times in 6 years, it becomes 3^n times in 6*n years. We want 81 times, which is 3^4. So, 6 * 4 = 24 years.

AI explanation

Using the compound interest growth formula A = P(1 + R/100)^n, if the sum becomes 3 times in 6 years, then the 6th root of 3 represents the annual growth multiplier. To find the time it takes for the sum to become 81 times, we set up the equation 3^(n/6) = 81. Since 81 is 3^4, we get n/6 = 4, which means n is 24 years.

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