$4)$ Currently the premium of a put option is $ $1\mathrm{.}25.$ This put option is written on a stock whose current price is $34.$ The exercise price of the put option is K $=33$ and it has a remaining maturity of $45$ days.

a$)$ What is the current time premium of that put?

b$)$ Re$-$calculate the time premium assuming that the current price of stock is $31\mathrm{.}9($K $=33$ again$)$ and the premium is $ $1\mathrm{.}42$