Please explain step by step process, would this require the present annuity formula??? please be clear in explanation thank u!

You are a loan manager at Royal Bank. Your client, Jorda, is setting up a new small business and takes out a loan from your bank for $100,000 on October 1, 2023. You offer Jorda the following repayment scheme:

Payments are to be made at the beginning of each month, starting October 1, 2024.

The loan accrues interest at a reduced APR of 7%, compounding at the end of each month in the first year.

The loan then accrues interest at an APR of 10%, compounding at the end of each month starting in the second year (October 2024) and onward.

(a) Jorda wants his last payment to be on September 1, 2039. Calculate Jordans monthly payment. (Round your answer to the nearest cent.)

(b) After five years, Jordas business is very successful, and he can afford to pay more each month. Suppose he doubles his monthly payments starting October 1, 2029. When would Jordas last payment be?