I’ve recently started learning options. How the expected premium is calculated for option writers?

**Values**

Current Underlying Price @ 100

CALL Option Premium = 5

Delta of the option = + 0.50

Assuming Underlying Price will rise to 108

**CALL Option Buyer**

Change in Underlying = 108-100 = +8 Points

Change in Premium = 8*(+0.5) = 4

New Premium = 5+4 = 9

**CALL Option Seller**

Change in Underlying = 108-100 = +8 Points

Change in Premium = 8*(-0.5) = -4

CALL Option seller Delta value taken as negative (-0.5)

New Premium = 5-4 = 1 ???

When underlying increases the CALL premium should increase but in this case it’s not

Can anyone help me with this, I’m confused

Update: As we’ve written the the option the value is negative for option writers.

New Premium = 5-(-4) = 9