Discussion
Find the principal amount invested if the difference between Compound Interest and Simple Interest obtained for 3 years at rate of interest of 25% is Rs. 320?
Answer: B
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
Over three years,
\[ \text{CI} - \text{SI} = P\left[(1.25)^{3} - 1 - 0.75\right] \]
\[ = P(1.953125 - 1.75) = 0.203125P \]
\[ 320 = 0.203125P \quad\Longrightarrow\quad P = \text{Rs. } 1575.38 \]
At a rate as high as 25% the gap is large relative to the principal - over 20% of it - which is why the answer is so much smaller than in the usual low-rate versions of this question.
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