The value of a gold coin picturing the head of the Roman Emperor Domitian is increasing at the rate of 6% per year. If the coin is worth $135 now, what will it be worth in 12 years?

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Answer 1 · 2018-04-08T18:10:05

The coin will be worth $$271.65$

We could model this by a geometric sequence,

$a_n=a(r)^n$ , where $n>=0$ , $a$ 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

$a_n=135(1.06)^n$

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

$a_12=135(1.06)^12 approx 271.65$

The coin will be worth $$271.65$