stock question about covered calls

I'm wondering how a premium for a covered call price is calculated.
For example let's say a stock is worth $100 and the premium is 1$ a week out from experation or 100$ received for the contract.
If that same stock a year later is now worth 400$ will the premium scale with the price increase of the stock and now be $4 a week out from expiration?
Basically I'm asking does the percentage of premium increase the same as the stock price? Or are there many more variables involved? Thanks