My wife and I are both PAYG employee in the same job for 5 plus years each. Our home loan is with CBA and the rate is 4.39% - loan is $720,000, could we get a better rate and by how much
Yes, definitely, there are much cheaper rates with a combination for fixed and variable.
Fixed for 2 years starts at 3.75%, while the variable is not far off,
the best way is to get in touch, find out what you are looking for and find the best options for you given the income, existing liabilities, value of property and so on.
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As Michael said, there are plenty of options that are well under 4% for owner occupied loans.
There are other variables such as your income and expenses, any other debts and the loan to valuation ratio (LVR).
Perhaps your first step is to meet with an experienced broker and see how your finances stack up and structure your loan to meet both current and future objectives
Best of luck
Have you asked CBA for a better deal?
This is always the first thing any borrower should do.
Tell them you are dissatisfied with the rate as you have seen other banks offering rates around the 3.60%.
Let them know that if they don't give you a better deal you will say "adios amigo".
I'm sure any professional finance broker would be delighted to have you and your wife as valued and life-long clients.