#### Explanation:

We could model this by a geometric sequence,

${a}_{n} = a {\left(r\right)}^{n}$, where $n \ge 0$, $a$ is the first term, $r$ is the common ratio between terms.

We know the first term in our sequence, when $n = 0 ,$ or when no years have elapsed, is $135.$

Furthermore, we're told that the value of the coin increases by 6% per year. Or, by a ratio of 100%+6%=106%=1.06

So, the common ratio is $r = 1.06$

So, we can define our sequence as

${a}_{n} = 135 {\left(1.06\right)}^{n}$

Then, after $12$ years, $n = 12 ,$ and

${a}_{12} = 135 {\left(1.06\right)}^{12} \approx 271.65$

The coin will be worth \$271.65