An investor purchased a 5-year bond with quarter coupons (a quarter = 3 months) , redeemable at par value $500,000. The nominal interest rate is 8% converted quarterly, and the coupon rate is 16% (nominal rate convertible quarterly). Find: (1) The price is of the bond at issue. (2) The theoretical dirty) price after 1 month of the bond issue? (3) The price after 1 year of the bond issue? (after the coupon paid) (4) The theoretical dirty) price after 35 months of the bond issue? (5) If the nominal interest rate converted quarterly changes and under the new rate i(4), the price of the bond at issue is 520,000. Find the new nominal interest rate i(4). (Hint: find the periodical effective interest for one quarter, then find i(4).)