12% or 1.12 is your dollar after 16 months of investment (16/12 is about ~1.33 years)
In otherwords, (1+x%)^(16/12)= 1.12 or 12%
Solve for x by raising 1.12 to (12/16) and subtracting 1 to give 0.0887 or 8.87%.
I think your first answer was the equivalent of saying 12 percent was a stated (non-compounded) rate (like an APR but for 16 months). However, it really was some rate, (x), compounded over 16 months to give you 12% return over the period.
There are a few interest rates we know to be nominal:
In each case, we’re told (or know by convention) how to convert them to an effective rate:
LIBOR: the tenor of the LIBOR rate is the period over which it is effective (e.g., a 60-day LIBOR rate of 4.5% is an effective rate for 60 days: 4.5%(60/360) = 0.75% effective for 60 days
BEY: this is twice the semiannual effective rate (e.g., a BEY of 3.8% means an effective semiannual rate of 1.9%)
Mortgage rate: in the US, this is 12 times the monthly effective rate (e.g., a mortgage rate of 4.8% is a monthly effective rate of 0.4%)
Without being told explicitly the compounding period, or having an interest rate (such as LIBOR or BEY) with a known convention on its compounding period, we have no choice but to treat the rate as effective.
Furthermore, as a practical matter, if you were told that over a period of 16 months someone had earned 12% on a $100 investment, wouldn’t you take that to mean that 16 month after they invested $100 their portfolio was worth $112? If you divide the ending balance by the beginning balance, the result is always (1 + r), where r is the effective rate for the holding period. That’s what effective rate means.