Multiple choice

Find the value of both quantities and state the correct relationship. Quantity I: Find amount after 4 years, if rate of interest is 20% and the principal amount is Rs 8000 Quantity II: Find the amount after 4 years, if Rs 10,000 becomes Rs 12,000 in 2 years at compound interest.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Quantity I: Principal = Rs 8000, rate = 20%, time = 4 years. For simple interest: SI = 8000 × 0.20 × 4 = Rs 6400. Amount = 8000 + 6400 = Rs 14400. For compound interest at 20% for 4 years: A = 8000 × (1.2)^4 = 8000 × 2.0736 = Rs 16589. Quantity II: Rs 10000 becomes Rs 12000 in 2 years at CI. 12000 = 10000 × (1+r)², so (1+r)² = 1.2, 1+r = 1.0954. Amount after 4 years = 10000 × (1.0954)^4 = 10000 × 1.44 = Rs 14400. However, CI on Rs 8000 at 20% for 4 years gives Rs 16589, which differs from Rs 14400. The relationship cannot be uniquely established without knowing interest type.

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