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?

1 Answer
Apr 8, 2018

Answer:

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#