Multiple choice

If a sum becomes 2 times its original value in 7 years at a certain rate of compound interest, then in how many years will it become 8 times the original value?

  1. 14

  2. 21

  3. 28

  4. 35

  5. 42
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For compound interest, A = P(1 + r/100)^t. Given 2P = P(1 + r/100)^7, so (1 + r/100)^7 = 2. We want 8P = P(1 + r/100)^t, so 8 = (1 + r/100)^t. Since 8 = 2^3, 8 = ((1 + r/100)^7)^3 = (1 + r/100)^21. Thus, t = 21 years.

AI explanation

According to the laws of exponents, if a sum becomes 2 times in 7 years, it will become 2 cubed times in three times that period. Because 2 cubed equals 8, the sum will become 8 times its original value in 3 multiplied by 7 years, which is 21 years.

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