The standard no-arbitrage price $F_{t,T}$ for currency forwards when the spot price is $S_t$, the domestic rate is $r_d$ and the foreign rate is $r_f$ is
$$F_{t,T} = S_t (1 + (r_d-r_f)(T-t) )$$
and the price time $\delta t$ later is
$$F_{t+\delta t, T}$$