The lottery will make annual payments at the beginning of each year for the next $25$ years. The first payment is $100,000.$ The second payment is $150,000.$ The third payment is $200,000.$ The same pattern continues with each payment being $50,000$ more than the prior payment until a payment of $1,300,000$ is made at the start of the $25$th year. Calculate the present value of these payments at an annual effective interest rate of $9\%.$