You are examining the silver market on December $1,2023.$ Given that silver is largely held as

an investment asset, has limited storage costs, and no intermediate income, the futures pricing

formula implies that F$0=$ S$0$e

rt$.$ You observe a spot price of $$25\mathrm{.}41$ per ounce, one$-$month

SOFR of $5\mathrm{.}31\%,$ two$-$month SOFR of $5\mathrm{.}40\%,$ and six$-$month SOFR of $5\mathrm{.}70\%($all continuously

compounding, expressed as annual rate$).$ Using the futures pricing formula, calculate the

arbitrage$-$free futures prices for the January $2024,$ February $2024,$ and June $2024$ contracts

that have January $1,2024,$ February $1,2024,$ and June $1,2024$ delivery dates, respectively.

Now, given your calculated futures price for the June $2024$ contract, show that attempting to

implement an arbitrage strategy $($i$.$e$.,$ similar to what you did for problem $1$ above$)$ produces

no net cash flows