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After how many years the deposited sum of K-euros will triple itself if the interest percentage of capitalization is 12%, the capitalization is annual.

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up vote 1 down vote accepted

$$K\cdot 1.12^n=3K \implies n = \frac{\log(3)}{\log(1.12)} \approx 9.6 \text{ years}$$

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If you multiply it by $1 + 0.12$ every year for $t$ years, you've multiplied it by $1.12^t$, so you want $1.12^t=3$. That implies $\log(1.12^t)=\log 3$, so $t\log1.12=\log3$. Solve that for $t$.

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