How do I calculate the delivery price for a forward contract? How do I calculate the delivery price for a forward contract? In the time interval $[0,t]$ the interest rate is $r_1$ and in the time interval $[t,T]$ the interest rate is $r_2$. Determine the delivery price $F(0,T)$ for a forward contract on an underlying asset whose price at time $0$ is equal to $S(0)$.

Denote $r_2^C$ and $r_1^C$ to be the continuously compounded interest rate equivalent of $r_2$ and $r_1$, resp.

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Discount $F(0,T)$ from time $T$ to time $t$:

$$F(0,T)e^{-r_2^C(T-t)} \tag{*}$$

Discount $F(0,T)e^{r_2^C(T-t)}$ from time $t$ to time $0$:

$$F(0,T)e^{-r_2^C(T-t)}e^{-r_1^C(t-0)}$$

The above term is supposed to be equal to $S_0$.

Thus we have:

$$F(0,T) = S_0e^{r_2^C(T-t)}e^{r_1^C(t-0)}$$

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I think $(*) = S_t$ and $S_T = F(0,T)$