Finding someone's birthdate

What is your birthdate?
You might want to take a piece of paper to try this.
Write the numbers 1 through 12 down the side of your paper.
Then write your answer next to each number.

Write number of the month in which you were born.
Multiply it by 4.
Add 13.
Multiply by 100.
Divide by 4.
Subtract 200.
Add the day of the month you were born.
Multiply by 2.
Subtract 40.
Multiply by 50.
Take the last two digits of the year you were born and add it to the total so far.
Subtract 10,500.
Your result should be a number telling (from left to right) the month, day of the month, and year you were born.
Does it match your birthdate? If not, can you retrace your steps and find your error?
Can you explain why it works?