If you are just trying to refinance the loan you already have, and not take out any equity, the type of loan you are looking for is called a Rate and Term loan. With this type of refinance you can change the term (or length of your loan) and you can also change the interest rate. The purpose of a rate/term refinance is to change to a lower interest rate or change the term of a loan without advancing new money on the loan. Closing costs can be rolled in. The borrower may receive a maximum 1% of the loan amount in cash at closing.
Your new interest rate will depend on how much money you are borrowing and for what length of time. Mortgage companies use something called a 'loan to value' ratio to calculate this. For instance, if you had an $80,000 home and an existing mortgage of $40,000, you would have a loan to value ratio of 50%. Basically, the higher your loan to value (LTV) ratio, the higher the interest rate.