Discussion

An amount becomes 4 times in 6 years. In how many years will it become 64 times if the rate of interest remains unchanged?

Answer: B

Compound growth multiplies, so express 64 as a power of the known growth factor.

\[ \left(1 + \frac{R}{100}\right)^{6} = 4 = 2^{2} \quad\Longrightarrow\quad \left(1 + \frac{R}{100}\right)^{3} = 2 \]

So the money doubles every 3 years. Since \( 64 = 2^{6} \), six doublings are needed:

\[ 6 \times 3 = 18 \text{ years} \]

Equivalently \( 64 = 4^{3} \), and three quadruplings take \( 3 \times 6 = 18 \) years - the same answer by a different route.

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