When Refinance I Borrow More or Less from Bank if My House Value Increased?

refinance

I borrowed a $300, 000 house with 20% down payment and a 5/1 ARM loan. The current sale price of the akin house is $330,000. I am wondering if I refinance the house, how many I have to borrow from bank: $240,000 [$300,000 (sale’s price) - $60,000 (my downpay)] or more (330.000 – $60,000)?
Thank you very much in advance.

A confused lady.

Can We Refinance a House That Is Now Worth Less Than the Mortgage?

refinance

We bought the house in 2006 for about $251,000, place 20% down and have a mortgage of about $194,000 left for 30 years at 6.6% interest. Looking at the house value, it is now probably only worth about $190,000 or so and want to refinance with new rates at about 5%. We have never been late on the payments and cannot show a financial hardship. Any suggestions?