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Question

The difference between C.I and S.I for 2 years at 10% per annum is Rs. 50. Find the sum.

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Solution

Let the value of the sum be P.

First let us calculate simple interest obtained in the period of 2 years at rate of 10% per year,
S.I=PRT100=P102100=P5=0.2P

Now we will calculate the compound interest gained in the period of 2 years compounded annually at the rate of 10%,
C.I=AP
=P(1+r)tP
=P((1+0.1)21)
=P((1.1)212)
=P(1.1+1)(1.11)
=P(2.1)(0.1)
=0.21P

Now it is given that the difference between C.I and S.I is equal to Rs. 50. So,
C.IS.I=500.21P0.2P=500.01P=50P=Rs. 5000

So, the sum is equal to Rs. 5000.

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