Hello again IndiansFan,
There really is no way to completely "avoid" th capital gains tax. There are ways that you can "defer" the tax, and pay it at a later time, but using the proceeds to pay down your rental property mortgage would not be one of them.
The only way to defer capital gains tax on investment property is when you participate in what is called a 1031 Exchange. With a 1031 Exchange, you use the proceeds from the sale of one investment property to purchase another "like kind" property. The taxes on the sale then do not become due until such time as you sell that replacement property.
The property you purchase must be "like kind", meaning you would have to purchase another land lot. You could not purchase a business or other type of investment. When you participate in a 1031 exchange, there are strict rules
that must be followed. An intermediary must be used to handle the money from both transactions. The replacement property must be identified prior to the sale of the first property, and the replacement property must be purchased within 60 days of the first sale.
That is the only way to defer taxes on the capital gains you would have from the sale of this property.
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Thank you IndiansFan.