Multiple choice

A sum of money doubles itself in 3 3 years at CI, when the interest is compounded annually. In how many years will it amount to $16$ times of itself?

  1. $6$ years
  2. $8$ years
  3. $12$ years
  4. $16$ years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the sum doubles every 3 years, it becomes 4 times in 6 years, 8 times in 9 years, and 16 times in 12 years. Therefore, the required time is 12 years.

AI explanation

Using the compound interest formula, A equals P times (1 plus R over 100) raised to the power of n. Since the sum doubles in 3 years, 2 raised to the power of n over 3 gives the final multiplier. To make the sum 16 times itself, we set 2 raised to the power of n over 3 equal to 16, and since 16 is 2 to the 4th power, we equate the exponents to get n over 3 equals 4. Solving this gives n equals 12 years.

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