Multiple choice

Rs. $1000$ invested at $5\%$ p.a simple interest, if the interest is added to the principle after every $10$ years, the amount will become Rs. $2000$ after

  1. $15$ years
  2. $\displaystyle 16\frac{2}{3}$ years
  3. $18$ years
  4. $20$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial 1000. After 10 years, interest = 1000 * 0.05 * 10 = 500. New principal = 1500. We need 500 more interest. 500 = 1500 * 0.05 * t. t = 500 / 75 = 6.66 years. Total time = 10 + 6.66 = 16.66 years.

AI explanation

Using the simple interest formula, the interest generated on Rs. 1000 over the first 10 years at 5% is (1000 * 10 * 5) / 100 = 500, making the new principal after 10 years equal to Rs. 1500. The remaining amount needed to reach Rs. 2000 is 500, and the time required to earn this interest is calculated as 500 = (1500 * 5 * t) / 100. Solving for t gives t = 20 / 3, which equals 6 2/3 years; adding this to the initial 10 years gives a total time of 16 2/3 years.

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