If I started out with $1000 and at the end of three years I have $1800 what is my APR?
Depends on the number of compounding periods.
See here.
It’s not a well-defined question, since APR has varying definitions. The nominal APR will indeed depend on the number of compounding periods in a year, but the effective APR is calculable from this information. For this, use the linked compound interest formula with n = 1 and t = 3.
As noted above, the rate depends on the number of compounding periods and the exact definition of APR that you use. Assuming annual compounding, 21.6% in this case.
(1- (1.8 ^ 1/3)) * 100 = 21.6%