Please post with mathematical formulas please, not an excel sheet!

1. Mr. X is repaying a loan by monthly payments of $146.75 at a nominal annual rate of 9% compounded monthly. Immediately after one of the pay- ments is made, when Mr. X has still 50 payments ahead of him, the lender lowers the interest rate to 7.8% nominal annual rate compounded monthly. Mr. X chooses to keep the same monthly payments, except the last payment that is larger than the regular ones. How many months from the time of the interest change will it take for Mr. X to repay the loan and what will be the total amount of the last payment