Discussion

A sum of money place at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself?

Answer: C

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

Eight is \( 2^{3} \), so three doubling periods are needed:

\[ \left(1 + \frac{R}{100}\right)^{12} = 2^{3} = 8 \]

\[ 3 \times 4 = 12 \text{ years} \]

Multiplying the four years by eight would give 32 - the mistake of treating compound growth as if it were proportional to time.

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