Multiple choice

Find the correct relationship between given quantities. Find total interest incurred- Quantity I-Compound interest on Rs. 4800 for two years at rate of 16.67% per annum. Quantity II-Compound interest on Rs. 4000 for three years at rate of 12.5% per annum.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I< Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established
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A Correct answer
Explanation

Quantity I: P = 4800, r = 16.67% = 1/6, t = 2 years. CI for 2 years = P[(1 + r)² - 1] = 4800[(7/6)² - 1] = 4800[49/36 - 1] = 4800 × 13/36 = 1733.33. Quantity II: P = 4000, r = 12.5% = 1/8, t = 3 years. CI for 3 years = P[(1 + r)³ - 1] = 4000[(9/8)³ - 1] = 4000[729/512 - 1] = 4000 × 217/512 ≈ 1696.09. Since 1733.33 > 1696.09, Quantity I > Quantity II.

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