<span>I think the answer to this equation is26.7</span>

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That's a 33% increase.
I calculated this using the formula:

Where n = the new value (16 in your question), o = the old value (12 in your question) and the result is outputted as a percent increase. You can check that this is correct by finding 33% of 12, adding the result to 12, and checking that the result equals your "new" number.
Note that 33% is only an approximation as your question requires a number rounded to the nearest whole.
You add 1/4 each year:
800 to 1000 in one year
1000 to 1250 in 2
1250 to around 1812.5
3.6 goes into both of them. Hope this helps