Discussion

At what rate of interest is an amount doubled in two years, when compounded annually?

Answer: B

Compounded annually, doubling in two years means

\[ \left(1 + \frac{R}{100}\right)^{2} = 2 \]

\[ 1 + \frac{R}{100} = \sqrt{2} = 1.4142 \]

\[ R = 41.42 \approx 41.4\% \]

Under simple interest the answer would be 50%; compounding needs less, because the first year's interest itself earns in the second.

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