Interest over time

If certain sum at compound interest becomes double in 5 years, then, in how many years, it will be 16 times at the same rate of interest?

Correct answer:

n =  20

Step-by-step explanation:

$$\begin{gathered} r_1=2 \\ {t}_1=5 \\ r=16 \\ r=16=2\cdot 2\cdot 2\cdot 2=2^4=r_1^4 \\ r=r_1^4 \\ n=t_1\cdot 4=5\cdot 4=20 \end{gathered}$$

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