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Choose correct option from the followingQuantity I: On a certain sum of money difference between compound interest compounded every 6 month at 20% p.a. and simple interest at same rate of interest for one year is Rs 150 then calculate sum of moneyQuantity II: Calculate sum of money on which difference between compound interest and simple interest for period of three years at 20% p.a. rate of interest is Rs 1280 1. Quantity I ≥ Quantity II2. Quantity I ≤ Quantity II3. Quantity I < Quantity II4. Quantity I = Quantity II5. Quantity I > Quantity II |
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Answer» Correct Answer - Option 5 : Quantity I > Quantity II Given: 20% p.a. = compounded bi yearly Difference between compound interest and simple interest = Rs 150 20% p.a. = 3 years C.I. – S.I. = 1280 Formula used: Net effect formula for CI = x + y + (x × y)/100 Calculation: Quantity I : Compound Interest (Half yearly compounded) = 10% (∵ 20/2 = 10) ⇒ Effective rate of percentage = 10 + 10 + (100/100) ⇒ Effective rate of percentage = 21% Simple interest = 20% Now, C.I – S.I. = Rs 150 ⇒ 1% of sum = Rs 150 ⇒ Sum = 150 × 100 ⇒ Sum = 15,000 Quantity II: Compound interest for three years = 20% ⇒ Effective percentage rate of first and second year = 20 + 20 + (400/100) ⇒ Effective percentage = 44% ⇒ Effective percentage of previous an third year = 44 + 20 + (880/ 100) ⇒ Effective percentage = 72.8% Simple interest for three years = 20 × 3 ⇒ Simple interest for three years = 60% Now, (72.8 – 60%) of sum = 1280 ⇒ 12.8% of sum = 1280 ⇒ sum = 1280 × 100/12.8 ⇒ sum of money = Rs 10,000 ∴ Quantity I > Quantity II |
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