Discussion
The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?
Answer: B
Simple interest of Rs. 40 over two years means Rs. 20 in each year. Compound interest exceeds it by Re. 1, and that excess is one year's interest on the first year's Rs. 20:
\[ 20 \times \frac{R}{100} = 1 \quad\Longrightarrow\quad R = 5\% \]
The principal never has to be found. This shortcut - the two-year excess is always one year's interest on one year's interest - solves the whole family of these questions.
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