Multiple choice

A sum of money at compound interest becomes thrice of itself in three years. In how many years will it be nine times of itself?

  1. 18 years

  2. 12 years

  3. 9 years

  4. 6 years

  5. 5 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In compound interest, if an amount becomes 'n' times in 't' years, it becomes 'n^k' times in 'k*t' years. Here, 3 times in 3 years. To become 9 times (3^2), it takes 2 * 3 = 6 years.

AI explanation

Using the compound interest growth formula, if a sum becomes 3 times in 3 years, we have the relation P * (1 + R/100)^3 = 3P. This means the multiplier for one year is the cube root of 3. To find the time it takes to become 9 times, we set up the equation P * (1 + R/100)^n = 9P, which implies the multiplier to the power of n equals 9. Since 9 is the square of 3, n must be twice the number of years it took to triple, so n = 6 years.

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