Multiple choice

A certain sum is to be invested for a certain time at Compound interest at $12$% p.a., such that there is an increase of $40.4$% in the sum. Find the time.

  1. $2.5$ years
  2. $3$ years
  3. $3.5$ years
  4. $2.75$ years
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B Correct answer
Explanation

Compound interest formula: A = P(1 + r/100)^n. Given A/P = 1.404 and r=12. (1.12)^n = 1.404. Testing values: 1.12^2 = 1.2544, 1.12^3 = 1.4049. Thus, n is approximately 3 years.

AI explanation

An increase of 40.4% means the amount ratio is 1.404, which can be written as the fraction 1404 divided by 1000, simplifying to 351 divided by 250. Setting up the compound interest relationship, the principal multiplied by (1 plus 0.12) raised to the time t equals the principal multiplied by 351 divided by 250; solving this gives t equal to 3 years.

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