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Choose correct option from the following Quantity 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 money Quantity 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 

Choose correct option from the following Quantity 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 money Quantity 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  Correct Answer 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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