Your mortgage has

years left, and has an APR of

(with semiannual compounding) with monthly payments of

.

a. What is the outstanding balance?

b. Suppose you cannot make the mortgage payment and you are in danger of losing your house to foreclosure. The bank has offered to renegotiate your loan. The bank expects to get

for the house if it forecloses. They will lower your payment as long as they will receive at least this amount (in present value terms). If current

-year

mortgage interest rates have dropped to

(APR with semiannual compounding), what is the lowest monthly payment you could make for the remaining life of your loan that would be attractive to the bank?