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 $182,105 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 25-year mortgage interest rates have dropped to 3.387% (APR), what is the lowest monthly payment you could make for the remaining life of your loan that would be attractive to the bank? The new payment is?

Your son has been accepted into college. This college guarantees that your son's tuition will not increase for the four years he attends college. The first $7,500 tuition payment is due in six months. After that, the same payment is due every six months until you have made a total of eight payments. The college offers a bank account that allows you to withdraw money every six months and has a fixed APR of 4% (semiannual) guaranteed to remain the same over the next four years. How much money must you deposit today if you intend to make no further deposits and would like to make all the tuition payments from this account, leaving the account empty when the last payment is made?

Therefore the 4% APR (semiannual) implies a semiannual discount rate of __%?