Why do we sometimes use save up, and sometimes save in the sentence about money? Is there any difference between them?
- Know how much money you have saved up.
- Know how much money you have saved.
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Firstly, I think your second example should be have saved, rather than have save.
To save up pretty much always means deliberately putting money aside for something. There will be a purpose, and a defined saving period: you choose when to start saving, and you finish when you (hopefully) reach a certain amount, and/or reach a deadline. The 'up' implies working towards something, even if it is not specified in the sentence.
To save can imply that you are putting money aside, gathering/gaining money, or not spending money. There may be a specific purpose, target amount, deadline, but there may not. It can be deliberate or not.
A simple rule: (in my experience of British English), if there is no target/purpose, you should say 'save', not 'save up'. If there is a target/purpose, 'save up' is more natural (although you can say 'save').
One of the numerous meanings of the verb save is not to waste, to prevent loss. And you can use save with that meaning when talking about money.
They use cheap material to save money on production.
You would not use up in that case.
Another meaning is to accumulate, to put aside, in order to collect a certain amount for a purpose. With money it means to spend less money than you get and collect up to a certain amount. In this sense save or save up can be used indifferently.
I must save money for my holiday.
I must save up money for my holiday.
Note that money is not compulsory. If you say:
I must save for my holiday / I must save up for my holiday.
everybody understands you are talking about money. If you meant something else you would express it:
I must save energy for my holiday.
The difference I would make between save and save up is that maybe the use of save "up" shows the gradual effort one makes to accumulate the required amount.
To go back to you examples you could use either :
I want to know how much money you have saved up.
I want to know how much money you have saved.
or if you want to ask a question:
How much (money) have you saved up?
How much (money) have you saved?
Putting up after a verb can do some interesting things. Sometimes it changes the meaning slightly, sometimes drastically, and sometimes not much at all.
For example, to grow means to get bigger, but to grow up means to age and mature.
Consider the word shut; I can say:
Also, consider the word work:
Here's an example where the two sentences pretty much mean the same thing, and the inclusion of up changes nothing more than the tone:
and sometimes up is used in place of an object, when that object is obvious from the context:
Now, back to save and save up. I don't think save up is really much different from save, although save by itself can be used in a broader array of contexts.
Both of these mean that I will start saving money. The word up may imply there is some long-range goal, but I don't think it's a necessary word (unlike in shut example – I cannot simply say I will shut the shop).
However, in this context:
The phrase save up would not be appropriate if I'm only referring to getting a good bargain.
In your two sentences:
If you are talking about how much money I've put aside for my new motorcycle, then either sentence will work. However, if you are talking about the amount of money I've saved by using coupons, then only the first sentence will work.
One last point: Regional variations may apply; sometimes the meaning of an included up can vary between American and British English, for example. Here's one example: in American English, knock up is coarse slang for getting a woman pregnant; in British English, the same expression means to knock at someone's door to wake them up. So, you want to be very careful before you say, "I want you to knock me up in the morning" – particularly if you are a woman.