Discussion
The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:
Answer: A
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
\[ \text{CI} - \text{SI} = P\left(\frac{R}{100}\right)^{2} \]
\[ 1 = P(0.04)^{2} = 0.0016P \quad\Longrightarrow\quad P = \text{Rs. } 625 \]
Checking: simple interest is Rs. 50 and compound interest Rs. 51. The Re. 1 gap is 4% of the Rs. 25 earned in the first year, which is exactly what the squared-rate formula encodes.
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