The verb "ponder" means to think about (something) carefully and at length.
Some examples of synonyms are the following:
Think about, consider, ruminate on, etc.
I find that this verb is generally used before a crucial decision. Therefore, at the moment, Walter ponders (thinks about) the price of a new car. You may infer, for example, that the vehicle is a tad pricey, but it could be worth the extra money.