Question on Compounding premium of Interest rate option

I am reviewing Study Session 15 Risk Management Applications of Option Strategies - Interest Rate Options. CFAI Book Page 309, Using Interest Rate with Borrowing.

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I do not really understand why we compound the premium using that rate. Anyone could explain?

you are buying the call option today - so that you can exercise it X days later. And it is LIBOR + Spread.

And you get the Loan X days later.

So X days later - you are getting (Loan Amount - what the Call Premium would be X days later)

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