Question
'P' invested Rs. 2,00,000 at compound interest of ___%
p.a., compounded once every 4 months. If he kept the amount invested for 12 months, then interest earned by 'P' at the end of 12 months is Rs. ___. 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, 11,230Solution
ATQ, Compound interest = Sum × {1 + (rate of interest/100) }time period in years - 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) × 3 = 3 terms So, sum at the end of 12 months = 200000 × {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) × 3 = 3 terms So, sum at the end of 12 months = 200000 × {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) × 3 = 3 terms So, sum at the end of 12 months = 200000 × {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.
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