currency's fair value as well as its expected value is the forward price. In brownian motion, dS = mu*S
+s*sigma*dw, we only look as the drift term, which will be the "most fair" price of the currency. The drift term mu is the interest rate differential. Based on risk neutral assumption, high yield currency's value against low yield currency should decrease as time passes by, such as usdjpy, and the fact that usdjpy has been staying relatively high to its forward price is the carry trade.
depending on the interest rate u have, we have continously compounding and s.a compounding etc. here we assume conitunous compounding.
Fwd = Spot*Exp[-1*(Rf-Rd)*t), or = spot*df(for)/df(dom)
spot: spot price
Rf: interest rate of foreign ccy, eg USD
Rd: interest rate of domestic ccy, eg JPY
t: time to maturity of the forward
df: discount factor
in case of inflation, i suppose we look at the effective interest rate which will be Rf-Inflation(for) and Rd-Inflation(dom) respectively.
so the eurusd*1.02 is a simple version assuming linear compounding and t=1 with equal eur and usd interest rate.