Fixed-Rate Home Equity Loan?

Does the principal and interest payment remain the same each month?

Yes, if you can find a fixed rate equity loan. Most are ARM, interst only, or prime plus 2 when you lock in.

I just refinanced and got 4.875

Yes, they stay the same each month. As you pay down the loan, the portion of your payment that gets applied to principal will increase and the portion that gets applied to interest will decrease, but the payment will stay the same.

By contrast, with home equity line of credit, the payments can change with each advance or when the interest rate is changed.

It's still possible to get a fixed-rate home equity loan. It's more common to find this product at a credit union than a bank these days.

yes fixed note is fixed. The problem is home equity loans are revolving so you need just a simple second deed of trust closed end fixed note rather than a home equity line of credit