Multiple choice

Sushma invested a fixed amount of money at compound interest for 2 years and got an amount of Rs. 4080 as compound interest. Find the rate of interest and sum, if simple interest on the same amount for the same period of time is Rs. 4000.

  1. 4%, Rs. 40,000

  2. 5%, Rs. 50,000

  3. 6%, Rs. 40,000

  4. 4%, Rs. 50,000

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple interest for 2 years is 4000, so SI for 1 year is 2000. Compound interest for 2 years is 4080. The difference between CI and SI for 2 years is (P * r^2) / 100^2 = 80. Since SI = (P * r * 2) / 100 = 4000, we have P * r = 200,000. Substituting into the difference formula: (200,000 * r) / 10,000 = 80, so 20r = 80, r = 4%. Then P = 200,000 / 4 = 50,000.

AI explanation

The difference between compound interest and simple interest for two years is calculated as Rs. 4080 - Rs. 4000 = Rs. 80. Using the formula for this difference, Principal * (Rate / 100)^2 = Rs. 80. Substituting the principal from the fourth option gives 50000 * (Rate / 100)^2 = 80, which simplifies to (Rate / 100)^2 = 0.0016 and a rate of 4%. To verify, the simple interest on Rs. 50000 at 4% for two years is (50000 * 4 * 2) / 100 = Rs. 4000, confirming the principal is Rs. 50,000 and the rate is 4%.

Keep practicing — related questions