According to the Schwab website, the margin requirement for a credit spread on a broad-based index is:
Difference in strike prices x 100 x number of contracts
Using that formula, your margin requirement would be $10K.
I don’t think you’ll find a US broker that will allow anything less.
However, in most cases, the cash generated from selling the spread will be applied to the margin requirement. In your example, I’m guessing that the premium you collect from selling the spread might be somewhere around $2300. So the amount you need to open the position might be around $7700.
That amount is “something between 15 percent and 100 percent of the spread.” 
There was a rather lengthy debate about this in a different thread over a year ago. The cash that you collect from establishing a credit spread generally cannot be used for something else, i.e., you can’t withdraw it, and you can’t use it to buy GNMA bonds or an Ethereum ETF. And it cannot be used to satisfy the margin requirement of some other position.
But it does get applied to the margin requirement of the spread that generated the cash. This is precisely why it cannot be used for anything else. It is tied up as part of the $10K that you need to maintain the credit spread.
The earlier thread was not about credit spreads, but rather about cash-secured puts. But the issue is the same. When you sell a cash-secured put, in a cash account with no margin privileges, how much cash do you actually need?
The answer is: The cost of the stock in the event of assignment, i.e., the strike price of the put x 100, minus the premium you collect from selling the put.
Here’s the earlier thread:
https://www.elitetrader.com/et/threads/broker-silently-changed-the-conditions.374402/
Incredibly, the thread went on for over a month, and occupies 19 pages. My comments, with screenshots from Schwab, are here:
https://www.elitetrader.com/et/thre…ed-the-conditions.374402/page-14#post-5813241
