1. Suppose you have a loan of $300,00. The terms of the loan are that the yearly interest is 9% compounded monthly. You are to make equal monthly payments to repay this loan over 20 years.
(a) How much is the monthly payment?
(b) After 10 years' payments, what principal remains to be paid?
(c) How much interest is paid in the first month of the 11th year?
(d) How much is the total interest paid over the 20 years?
(e) If you have a lump sum payment of $25,000 at the end of 10 years, and you maintain the same amount of monthly payments, how many years in total will you take to repay your loan?
2. Consider two 5-year bonds: one has a 5% coupon and sells for $97; the other has a 8% coupon and sells for $103. What is the price of a 5-year zero coupon bond? (Assume that the coupons are paid annually and the face values of all the bonds are $100)