The no-arbitrage link between spot, forward and interest rates

In short

• Route 1: invest one unit of domestic currency at $r_d$. Route 2: convert at spot, invest at $r_f$, and sell the proceeds forward. Both are riskless, so they must pay the same.
• With quotes in foreign/domestic (f/d) form: $1 + r_d = S_{f/d}(1 + r_f)\frac{1}{F_{f/d}}$, which gives $F_{f/d} = S_{f/d}\frac{1 + r_f}{1 + r_d}$.
• In price/base terms: the forward is above spot when the price currency's interest rate is higher. The higher-rate currency trades at a forward discount.
• A forward quote that breaks the equation creates riskless arbitrage: borrow in the route with the lower return, invest in the one with the higher return.
• Forwards are sometimes read as expected future spot rates, but they are poor predictors in practice; treat them as the output of the arbitrage equation.