To solve these problems, we can use different compound and simple interest formulas. Let's address each question:

1. Accumulated Value of ₱10,000:

   • Years 1-2: $7\%$ compounded annually. $A_1 = 10000 \times (1 + 0.07)^2$
   • Years 3-4: $8\%$ compounded quarterly. $A_2 = A_1 \times \left(1 + \frac{0.08}{4}\right)^{4 \times 2}$
   • Years 5-7: $6\%$ compounded monthly. $A_3 = A_2 \times \left(1 + \frac{0.06}{12}\right)^{12 \times 3}$
   • Years 8-10: $10\%$ compounded semi-annually. $A_4 = A_3 \times \left(1 + \frac{0.10}{2}\right)^{2 \times 3}$

2. Simple Interest for Peter:

   • Calculate how much he will have with simple interest from December 1, 2022, to June 1, 2025.
   • Duration = 2 years + 6 months = 2.5 years. $A = 1000000 \times (1 + 0.06 \times 2.5)$
   • Calculate how much time in years: $2.5 \text{ years} = 2 + \frac{6}{12}$.

   For compound interest: $A = 1000000 \times \left(1 + \frac{r}{4}\right)^{4 \times 2.5}$ Solve for $r$ using equality of simple and compound interest accumulations.

3. Effective Rate for Mr. Chan:

   • Given: principal $P = 45500$, amount $A = 50543$, time = 5.5 years. $A = P \times \left(1 + \frac{r}{12}\right)^{12 \times 5.5}$ Solve for $r$, and then calculate the effective annual rate (EAR): $\text{EAR} = \left(1 + \frac{r}{12}\right)^{12} - 1$

Calculations for exact numerical answers need additional processing.