Two debts, the first of $\$ 1800$ due nine months ago and the second of $\$ 900$ borrowed two years ago for a term of five years at $8.8 \%$ compounded annually, are to be replaced by a single payment one year from now. Determine the size of the replacement payment if interest is $8.2 \%$ compounded quarterly and the focal date is one year from now.

The size of the replacement payment is $\$ \square$. (Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：Given two debts, the first of $1800 due nine months ago and the second of $900 borrowed two years ago for a term of five years at 8.8% compounded annually, are to be replaced by a single payment one year from now.

Step 2 ：We need to determine the size of the replacement payment if interest is 8.2% compounded quarterly and the focal date is one year from now.

Step 3 ：The first debt is simple, it's just the principal amount since it's already due. So, the future value of the first debt is \( \$1800 \).

Step 4 ：The second debt involves calculating the future value of a loan with compound interest. The formula for future value is \( FV = P(1 + r/n)^{nt} \), where P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

Step 5 ：Substituting the given values into the formula, we get \( FV = \$900(1 + 0.088/1)^{1*2} = \$2130.7392000000004 \).

Step 6 ：The future value of the second debt is therefore \( \$2130.7392000000004 \).

Step 7 ：The total future value of the two debts is the sum of the future values of the individual debts, which is \( \$1800 + \$2130.7392000000004 = \$3930.7392000000004 \).

Step 8 ：However, we need to calculate the future value of this total debt one year from now with an interest rate of 8.2% compounded quarterly.

Step 9 ：Using the future value formula again, we get \( FV = \$3930.7392000000004(1 + 0.082/4)^{4*1} = \$918.5923195966762 \).

Step 10 ：The size of the replacement payment is therefore \( \$918.5923195966762 \).

Step 11 ：Rounding to the nearest cent, the final answer is \(\boxed{\$3049.33}\).