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

The size of the replacement payment is $\mathrm{\$}◻$. (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 $1800dueninemonthsagoandthesecondof$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 $\mathrm{\$}1800$.

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 $FV=\mathrm{\$}900(1+0.088/1{)}^{1\ast 2}=\mathrm{\$}2130.7392000000004$.

Step 6 ：The future value of the second debt is therefore $\mathrm{\$}2130.7392000000004$.

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

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 $FV=\mathrm{\$}3930.7392000000004(1+0.082/4{)}^{4\ast 1}=\mathrm{\$}918.5923195966762$.

Step 10 ：The size of the replacement payment is therefore $\mathrm{\$}918.5923195966762$.

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