Greg bought a gold coin for $9,000. If the value of the coin increases at a constant rate of 12% every 5 years, how many years will it take for the coin to be worth $20,000?

1 Answer
Aug 24, 2017

Answer:

Approximately 35 years (35.23).

Explanation:

If the price increases by 12% every five years, to get the value after five years we multiply by #1.12#. To get the value after another five years we multiply by #1.12# again, ie we multiply the original value by #1.12^2#.

So the value after #5n# years will be given by

#9000*(1.12)^n#

So we now want to find out when the value will be $20000. So

#20000 = 9000*1.12^n#

#implies 20000/9000 = 20/9 = 1.12^n#

Take logs of both sides and use rules of logs on LHS to bring down the n:

#log(20/9) = n*log(1.12)#

#therefore n = log(20/9)/log(1.12) ~= 7.046#

The coin reaches $20000 value after roughly 35 years.