Question about "gotta"

I know "I gotta" is grammatically incorrect. It is more of a spoken form. 'got to' is shortened to 'gotta'.

But, Could anybody explain me what is the meaning of "gotta"? Because it doesn't make sense for me. For example, with the next sentence I think I can say the same with other sentence, are they correct?

"I gotta manage my money." - I have to manage my money - I have managed my money
"I gotta obey the laws." - I have to obey the laws - I have obeyed the laws
"I gotta move to a bigger house." - I have to move to a bigger house - I have moved to a bigger house
"I gotta impress my boss." - I have to impress my boss - I have impressed my boss
"I gotta brush my teeth." - I have to brush my teeth - I have brushed my teeth

<em>Each pair of sentences can be explained in the same way.  The first one indicates obligation in the present tense : "I have to = I have got to = I gotta.  The second one is the normal present perfect.  </em>