Discussion

Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?

Answer: D

The sum more than doubles once \( (1.25)^{n} > 2 \).

\[ (1.25)^{2} = 1.5625, \qquad (1.25)^{3} = 1.953125 \]

\[ (1.25)^{4} = 2.4414 \]

The third year still falls just short of doubling, so the answer is 4 years.

The near miss at year 3 - 1.953, only 2.3% below 2 - is exactly what the question is testing.

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