Aman invested ₹2,00,000 at an annual compound interest rate of ___%, with interest compounded every 4 months. If the investment was held for a total duration of 12 months, ________ would be the interest earned by Aman at the end of this period. The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true?
I. 18, 38,203.2
II. 15, 31,525
III. 30, 11,230

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.