Final answer:
The forward price at this time is $3.4269. The forward price is the price at which the asset will be delivered in the future. We can calculate it by discounting the future cash flows generated by the asset.
Step-by-step explanation:
To calculate the forward price at a later time, we can use the concept of present value. The forward price is the price at which the asset will be delivered in the future. We can calculate it by discounting the future cash flows generated by the asset.
In this case, the asset provides an income of $2 at the end of the 3-month and $2 at the end of the 9-month. We need to discount these cash flows to the present using the risk-free rate for all maturities, which is 10%.
Using the formula for present value of cash flows, we can calculate the present value of $2 received at the end of 3 months, and the present value of $2 received at the end of 9 months. Then, we sum these present values to get the present value of the asset. This present value represents the forward price at the time of entering the contract.
Now, let's calculate the present value of the asset. The present value of $2 received at the end of 3 months is calculated as: PV1 = $2 / (1 + 10%/4)^(3 * 4), which equals $1.8446. The present value of $2 received at the end of 9 months is calculated as: PV2 = $2 / (1 + 10%/4)^(9 * 4), which equals $1.5823.
The present value of the asset is the sum of PV1 and PV2: PV = PV1 + PV2, which equals $3.4269. Therefore, the forward price at this time is $3.4269.