How are the Prices of Options are Affected by the Time to Expiration?

The price of an option has two components, the intrinsic value and the time value. The intrinsic value of an option is the difference between the actual price of the underlying security and the strike price of the option. The time value is determined by the remaining lifespan of the option, the volatility and the cost of refinancing the underlying asset (interest rates).

Longer term call, both American and European, typically values more than short term call because there is more time to have an event that can occur to make them go in the money. For American put, same as call.

European puts can only be exercised on the maturity date. If the put were to go into the money, one could exercise that option and receive the funds before the maturity date - that money could then be invested in another asset. Consequently, with the European put an investor has to wait to receive the funds and loses those extra days to earn additional income.