The equity in your house will reflect any growth in the value of your home. The down payment you make may provide you with some initial equity but the cost of closing the deals does not.
Equity can increase in several ways.
First, the value of a house may increase due to home improvements. Also, inflation and local supply and demand for homes may increase value. During times of inflation, the largest portion of the country's net worth is in home equity. Third, as you steadily repay your mortgage, you are building equity. When looking at improvements as a means to increase the value of the house, consider carefully what you choose to do.