An institutional lender is willing to make a Graduated Payment Mortgage for $1 million on an office building. The interest rate is 10%, but initially payments are calculated using an 8% pay rate. That means payments are calculated as if the interest rate were 8%. However, in reality, the required interest rate is 10%, and so the borrower is underpaying in this period. The loan term is 30 years and there are monthly payments. After the first five years the payments are to be adjusted so that the loan can be amortized over the remaining 25-year term at the actual interest rate. Note: In both the initial under-payment period, as well as after the adjustment, payments are calculated as a CPM with the respective pay rate.

(a) What is the initial payment?

(b) How much interest will accrue during the first year? Note: accrued interest is interest that is added to the loan balance (i.e. negative amortization).

(c) What will the balance be after five years?

(d) What will the monthly payments be, starting in year 6?

(e) Now suppose that the mortgage is paid off with a single balloon payment at the beginning of year 26. What is the amount of the balloon payment?