Since you do pose a slightly higher risk (and the degree of risk depends on your credit history, income and asset levels, etc.) you will have to pay some interest rate higher than the government does. This is typically considered index plus margin (the margin being the bank's profit margin plus a little extra to cover the additional risk).
The best rate you can get obviously depends on each banks evaluation of your risk to them, plus their profit margin. If they see you as a low risk and make no profit, you may get a great rate. If another bank wants to make 1% profit, your rate will reflect this too. You should contact a mortgage broker who can shop you around to different banks, who will each assess your risk to them (they each may see it slightly differently) and add in their profit (which depends on how hungry they are for your business) to come up with varying rates. Without knowing at least 5 things about your loan, no one can tell what YOUR best rate for refinancing should be, which is where the mortgage broker comes in.
Lastly, you can check bankrate.com to get a feel for current interest rates.
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