Aman invested ₹2,00,000 at an annual compound interest

Solution

Compound interest = Sum X {1 + (rate of interest/100) }^time – Sum Since, the interest is compounded every four months, it is compounded 3 times a year. For I: Effective rate of interest = 18 ÷ 3 = 6% per term Effective time period = (12/12) X 3 = 3 terms So, sum at the end of 12 months = 200000 X {1 + (6/100) }³ = Rs. 2,38,203.2 So, interest earned = 2,38,203.2 - 2,00,000 = Rs. 38,203.2 So, statement I is true. For II: Effective rate of interest = 15 ÷ 3 = 5% per term Effective time period = (12/12) X 3 = 3 terms So, sum at the end of 12 months = 200000 X {1 + (5/100) }³ = Rs. 2,31,525 So, interest earned = 2,31,525 - 2,00,000 = Rs. 31,525 So, statement II is true. For III: Effective rate of interest = 30 ÷ 3 = 10% per term Effective time period = (12/12) X 3 = 3 terms So, sum at the end of 12 months = 200000 X {1 + (10/100) }³ = Rs. 2,66,200 So, interest earned = 2,66,200 - 2,00,000 = Rs. 66,200 So, statement III is false.