The note payable was originated in 2004, is due in four years, and carries simple interest at 7%annually. Interest for each year is paid annually on January 4 of the following year. The payment on January 4, 2007 was properly recorded, but no other entry regarding interest has been made in 2007.
Base on the balance sheet the note payable is $100,000
Note payable $100,000
Interest is 0.07 $7,000 interest expense(income statement)

Based on the question only the interest expenses is recorded on the income statement and no adjusted entry is needed to liabilities on the balance sheet site please advise.

I'm not quite sure what the problem is asking you to do. You're giving me information about the loan, but does it want information about the loan, or just the adjusting entry or what? You didn't actually say. ("Based on the question"... i.e. what question. I don't see a question.)

As for your comment, though, you cannot just record an expense on the income statement and not record anything else. There are always at least two sides to everything. If you are going to record an expense, what are you planning to balance that with?

If the interest was last paid back in January and it is now the end of 2007, does the company not owe a year's worth of interest? And has it been paid yet? When is it going to get paid? And where do things go that haven't been paid yet?

Let me clarify my assumption

The first part states that " the payment on January 4, 2007 was properly recorded", so my understanding is that following entry had been made:

Cr-cash
Dr - interest payable

The second part states that "but no other entry regarding interest has been made in 2007".
So my understanding is that the following entry is necessary:

Dr - interest expenses
Cr- interest payables

Is my thinking right?

The second entry -- the adjusting entry -- is correct. You're recording the interest accrued for the year into the expense, but since it hasn't been paid goes into the payable.

The first entry would be correct, assuming no reversing entry was made Jan 1. If you have no clue what I'm talking about then, then we'll assume not.