First, we need to calculate the outstanding balance at time 48, which is after the end of 4 years with monthly payments.
Go here: Principal and Interest Paid Home Loan Amortization Table
Enter your information. Your selected time is 48. That's the time we want to calculate the outstanding balance immediately after our payment.
Scroll down through the rows of amortization table. It starts at "Now show the math work for the principal paid, interest paid, and balance at time = 48". After that, it will show you how to calculate the outstanding balance.
You should get 114901.93.
Now we need the new monthly payment at 6.5% for 21 more years.
Go here: Mortgage Payment Calculator
Enter your info, and I match your answer to the penny.