A $25-$year annuity with monthly payments makes payments of $1000$ at the end of each month during the first year. The payments during the second year are $1200$ per month. The payments during the third year are $1400$ per month. The payments continue to increase by $200$ in each year with $5800$ being paid each month during the $25$ th year. Calculate the present value of this annuity at an annual effective interest rate of $8\%.$

Answer: $$351,078\mathrm{.}21$