In a small neighborhood community, it has been documented that home sales vary quarterly throughout the year and that the sales have been consistently increasing over the past $5$ years. The quarterly indexes were found to be $0\mathrm{.}73$ for quarter $1,0\mathrm{.}90$ for quarter $2,$ and $1\mathrm{.}4$ for quarter $3.$ Also, a trend analysis revealed the following model yt$=10+3\mathrm{.}04$t would reflect how the number of sales have been gradually increasing each year. What would be the forecast for the number of home sales for the second quarter of year $6?$