Question

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?

Answer 1

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.