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Periodic Compounding & Continuous Compounding; Present Value & Discount Factors

Hi all,

I know this is not covered on the lectures but I'm so confused on the difference between periodic compounding and continuous compounding. I know the formula but I don't know on where to use them? What is the difference on using one instead of the other?

Additionally, I'm so confused on the idea of discount factors. What is it used for?

Cheers!
Joshua