Multiple choice

The compound interest for two years is Rs. 525 on a certain sum of money at 10% annual interest rate. If the same amount of money is lent for double the time and at half the annual rate of interest, then what will be the simple interest?

  1. Rs. 250

  2. Rs. 300

  3. Rs. 400

  4. Rs. 500

  5. Rs. 550
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For CI: 525 = P * ((1 + 0.1)^2 - 1) = P * (1.21 - 1) = 0.21P. P = 525 / 0.21 = 2500. For SI: P = 2500, T = 4 years (double), R = 5% (half). SI = (2500 * 4 * 5) / 100 = 500.

AI explanation

Using the compound interest formula for two years, CI = P * (R / 100)^2 + P * 2R / 100, which simplifies to 525 = P * (10 / 100)^2 + P * (20 / 100). This equation becomes 525 = 0.21P, giving the principal P as Rs. 2500. The new conditions are double the time (4 years) and half the rate (5%), so applying the simple interest formula SI = (P * R * T) / 100 yields SI = (2500 * 5 * 4) / 100. The calculation results in Rs. 500.

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