Question

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?

Answer 1

The coin will be worth `$271.65`

Explanation:

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`