An investment of $\$ 4000.05$ earns interest at 2.5 \%$ per annum compounded quarterly for 3 years. At that time the interest rate is changed to $19.8 \%$ compounded monthly. How much will the accumulated value be 2.5 years after the change?
The accumulated value is $\$$
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：Given that the principal amount (P) is $4000.05, the annual interest rate for the first 3 years (r1) is 2.5% or 0.025 in decimal, the number of times that interest is compounded per year for the first 3 years (n1) is 4 (quarterly), and the time the money is invested for the first 3 years (t1) is 3 years.

Step 2 ：We use the formula for compound interest A = P (1 + r/n)^(nt) to calculate the accumulated value after 3 years. Substituting the given values, we get A1 = 4000.05 (1 + 0.025/4)^(4*3) = 4310.584277054068 dollars.

Step 3 ：Then, the annual interest rate is changed to 19.8% or 0.198 in decimal, the number of times that interest is compounded per year is changed to 12 (monthly), and the time the money is invested is 2.5 years.

Step 4 ：We use the formula for compound interest again to calculate the accumulated value after 2.5 years with the new interest rate. This time, the principal amount is the accumulated value from the first part (A1). Substituting the values, we get A2 = 4310.584277054068 (1 + 0.198/12)^(12*2.5) = 7043.0 dollars.

Step 5 ：\(\boxed{7043.0}\) dollars will be the accumulated value 2.5 years after the change.