Discussion
The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
Answer: A
Over two years the gap between compound and simple interest is
\[ \text{CI} - \text{SI} = P\left(\frac{R}{100}\right)^{2} \]
\[ 96 = 15000 \times \frac{R^{2}}{10000} = 1.5R^{2} \]
\[ R^{2} = 64 \quad\Longrightarrow\quad R = 8\% \]
The rate is fully determined, so "cannot be determined" is a trap: for a two-year period the difference, the principal and the rate are locked together by that single relation.
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