Multiple choice

The difference between the compound interest on a certain sum for the second year and the third year at 5% p.a. is Rs.42. Find the sum.

  1. Rs. 12000

  2. Rs. 15000

  3. Rs. 16000

  4. Rs. 20000
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C Correct answer
Explanation

For compound interest, the CI for the second year on principal P at 5% is P(1.05)² - P(1.05) = P(0.05)(1.05). The CI for the third year is P(1.05)³ - P(1.05)² = P(0.05)(1.05)². The difference is P(0.05)(1.05)² - P(0.05)(1.05) = P(0.05)(1.05)(1.05 - 1) = P(0.05)(1.05)(0.05) = 0.002625P. Given this difference is Rs. 42, we have 0.002625P = 42, so P = 42/0.002625 = Rs. 16,000.

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