r=.06/4=.015 (assuming that 6% is nominal annual interest rate, compounded quarterly)..
If there are 10 payments left, you have made p=30 payments. Then the value on the outstanding loan, assuming that you have just made the 30th payment, is;
Similiar to (1). L=1200000, n=25, r=.04.
So she has received p=15 payments. Then the amount outstanding in the annuity is calculated as (1) was..
Assuming that the 100th payment was just made (there is a full month until the next payment is due), after 100 payments on the mortage, the outstanding balance is;
The monthly repayment on the mortgage is calculated using the formula
So under the original contract, the monthly payment was;
L=$500000, r=.07/12=.005833, n=180
If they refinance the outsanding loan balance of $286644.1 at 6% for the remaining 80 periods, the repayment will be;
so they will save $274.857 a month.
The PV of this saving is, at 6% discount rate (Im not sure if you should use 6%?), less the rate modification fee;
I hope this helps/is correct.