Discussion
A sum of money at simple interest doubles itself in 10 years. Find out the rate of interest per cent per annum.
Answer: B
The rate is 10% per annum.
If the sum doubles, the simple interest earned equals the principal \(P\) itself, over 10 years.
\[ \begin{aligned} \frac{P \times R \times 10}{100} &= P \\ R &= \frac{100}{10} = 10 \end{aligned} \]
The general rule: a sum doubles at simple interest in \(\frac{100}{R}\) years, so 10 years means 10%. At 8% doubling takes 12.5 years, at 12% about 8.3 years and at 15% about 6.7 years, so none of the other rates fits 10 years.
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