Question
"R" made certain investments with a 40% annual compound
interest rate that is compounded quarterly. If, 9 months later, he receives Rs. 1,99,650, then the amount invested by 'R' is equal to: I. Interest earned on Rs. 1,25,000 invested for four years at a simple interest rate of 30% per annum. II. The cost of an item that sells for Rs. 2,40,000 after a 40% profit. III. The difference between 'P' and 'Q''s' savings, assuming that each of them spends 40% of their respective salaries of Rs. (a + 406320) and Rs. (a + 156320).Solution
ATQ, Effective rate of interest = 40 ÷ 4 = 10% p.a. And effective time period = (9/12) X 4 = 3 terms We know that for compound interest, Amount = Sum X {1 + (rate of interest/100) }time period Let the sum invested be Rs. 'S' So, 199650 = S X {1 + (10/100) }3 Or, 199650 = S X (1.1)3 Or, 199650 = 1.331S So, S = 1,50,000 Therefore, sum invested = Rs. 1,50,000 For I: Interest received = (125000 X 0.3 X 4) = Rs. 1,50,000 Therefore, statement I is true. For II: Cost price of the article = (240000/1.4) = Rs. 171428.57 Therefore, statement II is false. For III: Difference between savings of 'P' and 'Q' = 0.6 X (a + 406320) - 0.6 X (a + 156320) = 0.6 X (406320 - 156320) = 0.6 X 250000 = Rs. 1,50,000 Therefore, statement III is true.
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