The covered interest parity (CIP) is a non-arbitrage condition. It postulates that the nominal interest differential between two countries () should equal the forward premium (Ft+1/St)1. CIP assumes perfect capital mobility, and that debt instruments denominated in domestic and foreign currency have similar risk. If , then the forward price of the foreign currency will be greater (lower) than the spot price.
In formulas: 
                                                           1+it =1/s (1+it*)Ft                        (1)

where the LHS is the return from purchasing and holding a domestic financial asset and the RHS is the determinist return – known at time t – obtained through the investment on the forward market. Equation (1) can be rewritten as follows:
                          1+it = [( Ft - St )/ St] +1+[(Ft - St)/St] it* + it* =>it* +[(Ft - St)/St]    (2)

It is needless to say that if the equality does not hold, it would give rise to an arbitrage opportunity. Let’s suppose for example that equation (1) does not hold because of a relatively low domestic interest rate (LHS)

1. by borrowing national currency at interest it for, let's say, n periods;
2. by selling it spot for the foreign currency (yielding 1/St units of foreign currency for each unit on the domestic one);
3. by lending the foreign currency at rate it* ;
4. by selling the amount (1+it*)/S in the n-period on the forward market against the national currency.
At the end of the n-period, the arbitrageur will repay (1+it) for each unit of national currency borrowed, but they will obtain an amount of domestic currency equal to  for each unit of foreign currency lent. The difference between these two amounts is the riskless profit earned by the arbitrageur.

1 Here F is the forward exchange rate and S is the spot exchange rate.

Editor: Lorenzo CARBONARI