The appraised value of your home limits how much you can borrow. It's your income that limits whether or not you can afford a 15-year mortgage. I'm going to assume it's the appraisal issue that's keeping you from refinancing. Otherwise, you could refinance with a longer-term loan, capture the interest rate savings and prepay principal to shorten the life of the loan.
President Barack Obama recently announced the start of a mortgage loan program for homeowners who wouldn't qualify using conventional mortgage underwriting standards. This program seems to fit your needs in refinancing your loans. It's a modification on the Home Affordable Refinance Program, or HARP. Operational details of the plan won't be available until Nov. 15, and banks aren't expected to start refinancing loans under this program until at least Dec. 1, but one of the goals of the plan is to help homeowners refinance into shorter mortgages at today's lower interest rates.
If you don't qualify under the modified HARP plan and you have the cash, I'd recommend a cash-in refinance versus making additional principal payments over time. A cash-in refinancing has you bring money to closing to reduce the size of the mortgage loan you need to refinance the property. Additional principal payments will help you build equity and will eventually help you qualify for that refinancing, but you run the risk that mortgage rates will start trending higher, and you would lose the ability to take advantage of today's low rates.
I'm not a fan of biweekly payments. You can do as well on your own by making additional principal payments equal to two mortgage payments per year. You don't need the added structure, and you don't need to make the payments contractual as they would be with a biweekly mortgage.
It should go without saying that you should make any additional principal payments on the 8 percent mortgage loan before paying down the 5.8 percent first mortgage.
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