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Question

The difference between the simple interest and the compound interest (compounded annually) on Rs. 1250 for 2 years at 8% per annum will be?

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Solution

Let P be the principal amount

r be the rate of interest, Then

Compound interest in two years is,

C.I =P(1+r100)2P --(1)

Simple interest in 2 years is,

S.I =2Pr100 ---(2)

Now, The difference between the simple interest and the compound interest (compounded annually),

=C.PS.P

=P(1+r100)2P2Pr100

=P((1+r100)212r100)

=P(1+(r100)2+2r10012r100)

=P(r100)2

Difference of S.I & C.Ifor 2 years is P(r100)2

It is given that, P=Rs. 1250 and r=8% and two years

Difference =p(r100)2
=1250(8100)2

=1250(225)2

=1250×225×225

=2×2×2

=8

Hence, the required amount is Rs. 8


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