Kate invests $2500$ into the Adams Fund at the end of each year for the next $13$ years. The Adams Fund earns an annual effective interest rate of $7\%.$ At the the end of each year, the interest earned in the adams fund is transferred to the Baker Fund. The Baaker fund earns an annual effective interst rate of $8\%.$ Determine the amount that Kate will have at the end of $13$ years when she combines the amount in the Adams Fund and the amount in the Baker Fund.