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That means I won't receive any rewards for seven days after I delegate. Will my rewards start arriving after seven days? How much liquid steem can I earn per thousand per day?

Yes, as you know steem pays for user's posts after 7 days, so you'll start receiving the daily payout after 7 full days of delegation.
Obviously this means that you will continue to receive your daily pay even 7 days after the delegation is eventually removed.

For 1k SP delegated you should get around 0.25/0.35 Steem daily, it's not a fixed income as it can vary depend on the curation service.

Cur8 Team

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