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What is the relationship between risk-free interest rate and futures price and futures value?
Futures and spot prices are closely linked, so there is a pricing formula for the price between them.

Theoretical value of futures = spot value+cost × risk-free interest rate+storage cost+handling fee.

The actual price of futures closely revolves around the theoretical value, because the relationship between spot arbitrage and intertemporal arbitrage forces will basically keep the price difference between them within a reasonable range.

Simply put, the risk-free interest rate will affect the theoretical value of futures, and then affect the actual futures price.