(adsbygoogle = window.adsbygoogle || []).push({}); Why do we take the "no. of years to compound the interest" as power?

Suppose interest is given at 12% annually, compounded once a year. At the end of the year we will have (A = starting amount):

[tex]A( 1 + 0.12 )[/tex]

But if it is compoundedtwicea year, then at the end of the year we will have:

[tex]2A \left( 1 + \frac{0.12}{2} \right)[/tex]

Why is the above wrong? Why it should be [tex]A \left( 1 + \frac{0.12}{2} \right)^2[/tex] instead of [tex]2A \left( 1 + \frac{0.12}{2} \right)?[/tex]

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# Why do we take the no. of years to compound the interest as power?

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