I have been reading online about the FX carry trade and how this can be profitable (in general). From my understanding, the idea is to be long (lend) the currency with higher interest rate and short (borrow) the currency with lower interest rate. This is effectively borrowing at the lower rate and lending at the higher one. However, say that 1 NZD = 1USD today. If yearly interest rates are 10% in NZ and 1% in US, then doesnt that mean that 1 year from now, 1.1 NZD = 1.01 USD so it takes more NZD than before to purchase a single dollar?
If you would want to lock in a Forward USDNZD rate then both the 10% and 1% are taken into account like you suggested.
But if you would enter the fx carry trade like you suggested without trying to lock in a forward rate. Then the spot rate 1 year from now is still a random variable from todays perspective.
You might get lucky and the rate does not change, giving you a 9% (10 -1) rate differential. You might get even luckier and the fx spot moves in your favour. Or you might get unlucky. But as said earlier, if you want to remove this randomness of the fx spot by entering into a Fwd you will give up all your interest rate gains as there is no free lunch.
You wrote "doesnt that mean that 1 year from now, 1.1 NZD = 1.01 USD". This is true if the UIP (Uncovered Interest Parity) is true, or in other words if the forward rate is an unbiased predictor of the future exchange. However empirical research has cast doubts on this theoretical proposition. It seems, for reasons that are not entirely clear yet, that high interest rate currencies on average depreciate less than your statement indicates, making the carry trade on average profitable over long historical periods. [As mbison points out sometimes you lose and sometimes you gain]. A good overview article (though somewhat old) is Froot K.A. and Thaler R.H., 1990.“Foreign Exchange,” Journal of Economic Perspectives,vol 4.pp.179-192.