How does a cash out refinance work?

[Devlin Melvin]

Since numbers help me lets give an example. I buy a 100k house using a 20k downpayment and over a period of a few years i pay down 20k of the loan. So i have 20k in equity. But at the same time the homes value has gone up to 200k. The bank will give me a new loan for 75% of my homes new value or 200k*.75= 150k.

So i take out the new loan of 150k and payoff my existing loan of 80k which leaves 70k in cash. But did I actually make 50k in cash if i take 70k-20k downpayment? Do i still have the 20k of equity somewhere? What happens to that equity or did i just convert it to cash? Thank you