Multiple choice

A sum of money, if invested at a rate of 12% compounded annually for a period of two years, yields Rs. 684 less when it is invested for the same time period at a simple interest of 15%. Find the amount.

  1. Rs. 15,000

  2. Rs. 12,500

  3. Rs. 13,000

  4. Rs. 14,000

  5. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let sum be P. CI for 2 years at 12% = P * (1.12^2 - 1) = 0.2544P. SI for 2 years at 15% = P * 0.15 * 2 = 0.3P. Difference = 0.3P - 0.2544P = 0.0456P = 684. P = 684 / 0.0456 = 15000.

AI explanation

Let the principal sum be P. The simple interest at 15% for two years is P multiplied by 15 multiplied by 2 divided by 100, which equals 0.30P. The compound interest at 12% for two years is P multiplied by (12/100) squared plus P multiplied by 24 divided by 100, which simplifies to 0.2544P. The difference between the two interests is 0.30P minus 0.2544P, equalling 0.0456P, which we are told equals 684. Solving for P gives 684 divided by 0.0456, which results in Rs. 15000.

Keep practicing — related questions