Use formula method to solve the problem. Tedros borrowed $2 million and planned to repay the loan by making equal month-end payments over a period of 10 years. The interest rate on the loan is 6%, compounded monthly. *

(a) Tedros plans to pay off the loan immediately after making the 60th payment. What should the size of the lump-sum (pre-)payment be?

(b) Immediately after the 60th repayment, the central bank increased the market interest rate and the bank subsequently raised the loan's interest rate to 8% p.a., compounded monthly. If Tedros decides to keep the number of remaining payments unchanged, what is the size of the new monthly repayments?

(c) Calculate the total amount of principal repaid and interest paid in the first 60 monthly payments. Assume that the relevant interest rate is still 6%, compounded monthly (that is, not 8%).[Hint: One make-sense way to think about this is by focusing on the relationships between amount borrowed, total amount repaid to the bank and the amount still owed to the bank after the 60th payment is made. You may think of the total amount of principal repaid first].

(d) Suppose that if the bank allows Tedros to only pay the first five years of interests at t=60 in a single payment (with principal repayment only to be made at the end of Year 10). How much interests will Tedros has to pay at t=60? What explains the difference in the total amount of interests paid in part (c) and here [part (d)]? Assume that the relevant interest rate is still 6%, compounded monthly (that is, not 8%).