Multiple choice

A certain sum of money, when invested for 5 years at an annual simple interest rate of 6%, yields an amount that exceeds the amount obtained by investing the same principal at an annual compound interest rate of 10% over 2 years by Rs. 900. Determine the principal amount.

  1. Rs. 8,000

  2. Rs. 9,000

  3. Rs. 10,000

  4. Rs. 10,500

  5. Rs. 11,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the principal. SI = P * 0.06 * 5 = 0.3P. CI = P * (1.10^2 - 1) = 0.21P. Difference = 0.3P - 0.21P = 0.09P. 0.09P = 900, so P = 10000.

AI explanation

The amount from simple interest over 5 years is P multiplied by (1 plus 0.30), which is 1.30P. The amount from compound interest over 2 years is P multiplied by 1.10 squared, which equals 1.21P. The problem states the simple interest amount exceeds the compound interest amount by 900, so 1.30P minus 1.21P equals 900. Solving 0.09P equals 900 gives a principal of Rs. 10,000.

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