why do we add (deduct) the option payoff and FV of premium option when computing for the effective annual rate of a put (call) option?

The option payoff offsets the interest received or interest paid… That obviously affects the “effective” interest rate, which is the bottom line. For example, if you pay $1500 mortgage a month but uncle joe credits you $500 for being a good boy each month, you might consider that you really only pay $1000 effective mortgage a month… That would be your effective rate.

The FV premium is a cost that you need to factor into the base aka principle. You add to the base if you’re lending and subtract if you’re borrowing.
Knowing whose perspective the options are does make sense. Thabks!