FX Forward Pricing

Consider the spot exchange rate at date $t = 0$ denoted $S_0$, defined by:

Let $r_{\text{USD}}$ be the risk-free rate in USD and $r_{\text{EUR}}$ the risk-free rate in EUR over the period $[0, T]$. Assume no arbitrage opportunities exist.

An FX forward is a contract that fixes at date $t = 0$ a rate $F_{0,T}$ at which two counterparties commit to exchange, at a future date $T$, one currency against the other. Here, the contract stipulates: at time $T$, exchange 1 USD against $F_{0,}$ EUR. No cash flows occur at inception.

Question: Using a replication strategy, derive the forward rate $F_{0,T}$.