Say that consuming 2,000 calories per day will cause a person to maintain weight is there a formula to determine how rapidly that person will lose weight if they consume, say 1,500 calories per day (or 500 calories under the level required to maintain current weight)? Does current weight play a part in this calculation?

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The weight loss clinic I attended stated that 3400 extra calories add one pound of fat. You have to get an accumulation of 3400 calories less that what it takes to maintain your weight before you lose.
At first, you will loose fluid but after that you need to reduce calorie level by 3400 accumulative per pound loss.
A normal man uses 1800 calories per day maintenance , a woman 1600 on the average.

3500 calories = 1 pound, so if your body uses 2000 a day and you start eating 1500 a day you would burn 500 calories a day, you do that for a week or 7 days, and that = 500 X 7 for 3500 calories lost in a week or 1 pound loss for a week

Yes, there is a formula. In general, if your maintenance is X number of calories, you will want to reduce your intake to (X - 500).
It is a scientific fact that one pound of fat equates to about 3500 calories. Thus, if you cut out 500 calories from your daily diet, you should, in theory, lose 1 lb per week, since you're cutting down your calories by 3500 in that time.
Current weight gives you a reference point to start with so yes, it is part of the calculation.

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