Problem 1. A loan of $10,000 at a fixed annual effective interest is being repaid by level annual payments. The outstanding balance immediately after the 9th pay- ment is $6,665.29 and the outstanding balance immediately after the 18th payment is $1492.11. Determine the outstanding balance immediately after the 19th payment.

Problem 2. David purchases a 15-year, $2,000 par value bond with an annual nom- inal coupon rate of 10% payable semiannually. The purchase price will generate a nominal yield to maturity of 12% convertible semiannually. Exactly 2 months after the 10th coupon, David sells the bond at the market price with the same yield rate. Calculate the market/clean price on the sale date.

Problem 3. David borrows an amount at an annual effective interest rate of 7.25% and will repay all interest and principal in a lump sum at the end of 12 years. He uses the amount borrowed to purchase a 10-year semiannual coupon bond with face amount of $1,000. The bond has a nominal coupon rate of 10% and a nominal yield to maturity of 8% both convertible semiannually. All coupon payments and the redemption amount are reinvested at an annual effective interest rate of 6%. The redemption amount is paid at the end of the maturity date. Calculate the redemption amount needed such that David is just able to repay the loan.

Problem 4. Joey purchases a 15-year par value bond with semiannual coupons of $60 and a redemption value of $1,200. The bond can be called at $1,300 on any coupon date prior to maturity, starting at the end of year 10. Calculate the maximum price of the bond to guarantee that Joey will earn an annual nominal interest rate of at least 8% convertible semiannually.

Problem 5. David purchases a 15-year bond which pays semiannual coupons at a discount. The amount for amortization of the discount in the 14th coupon payment is 578.58. The amount for amortization of the discount in the 28th coupon payment is 1145.55. What is the value of the discount?