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Whether you're refinancing your current home or buying a new one, something worth considering is a 15 year loan rather than a 30 year term. The payments will be a little higher but you'll get a lower interest rate and you'll build equity much faster.
Let's look at an example of a $200,000 mortgage with the choice of a 30 year term with a 3.75% rate compared to a 15 year term with a 2.875% rate. The payments would be $442.94 higher on the shorter term but the equity would be considerably higher even after you adjust for the higher payments.
Another benefit is that the shorter term loan creates a forced savings situation where the savings on a longer term loan might end up being spent rather than being saved and invested. Contact me if you'd like a recommendation of a trusted lender.