I need help with the following assignment, I would like to see how the problems are done please. Thank you

1. Matt purchased a 20-year par value bond with an annual coupon rate of 8% compounded semiannually for a price of 1722.25. The coupons begin paying 6-months after the bond is purchased, and the bond can be called at par value X on any coupon date starting at the end of year 15, after the coupon is paid. The price guarantees that Matt will receive a nominal annual yield rate of at least 6% compounded semiannually. Note: The price guarantees that the yield will be a minimum of 6%. Find X. (a) 1460 (b) 1440 (c) 1420 (d) 1400 (e) 1380 Answer: ____________________ 2. John borrows 1000 for 10 years at an annual effective interest rate of 10%. He can repay this loan using the amortization method with equal size payments of P at the end of each year. Instead, John repays the 1000 using a sinking fund that pays an annual effective rate of 14%. The deposits to the sinking fund are equal to P minus the interest on the loan and are made at the end of each year for the next 10 years. Determine the balance in the sinking fund immediately after the repayment of the loan. (a) 213 (b) 218 (c) 223 (d) 230 (e) 237 Answer: ____________________ 3. Lori borrows 10000 for 10 years at an annual effective interest rate of 9%. At the end of each year, she pays the interest on the loan and deposits the level amount necessary to repay the principal into a sinking fund earning an annual effective interest rate of 8%. The total of all payments (i.e. interest payments and sinking fund payments) made by Lori over the 10-year period is X. Find X. (a) 15803 (b) 15853 Answer: ____________________ (c) 15903 (d) 15953 (e) 16003 4. A loan is being amortized by means of level monthly payments at an annual nominal rate of 9% compounded monthly. The amount of principal repaid in the 12 th payment is 1000 and the amount of principal repaid in the tth payment is 3700. Calculate t. (a) 176 (b) 187 (c) 195 (d) 204 (e) 212 Answer: ____________________ 5. Jason and Margaret each take out a 17-year loan for L. Jason repays his loan using the amortization method, at an annual effective interest rate of i. He makes an annual payment of 500 at the end of each year. Margaret repays her loan using the sinking fund method. She pays interest annually, also at an annual effective interest rate of i. In addition, Margaret makes level annual deposits at the end of each year for 17 years into a sinking fund. The annual effective rate on the sinking fund is 4.62%, and she pays off the loan after 17 years, depleting the sinking fund entirely. Margaret's total annual outlay is equal to 10% of the original loan amount. Calculate the original loan amount L. (a) 4844 (b) 4943 (c) 5040 (d) 5141 (e) 5239 Answer: ____________________ 6. A 1000 par value 5-year bond with an annual coupon rate of 8.0% compounded semiannually was bought to yield 7.5% convertible semiannually. The bond will redeem at par value at maturity. Determine the amount of premium amortized in the 6th coupon payment? Hint: What is the principal adjustment in the 6th coupon period? (a) 2.00 (b) 2.08 Answer: ____________________ (c) 2.15 (d) 2.25 (e) 2.34 7. The current price of a bond is 100. The instantaneous rate of change or derivative of the price of the bond with respect to the yield rate is -700. The yield rate is an annual effective rate of 8%. Calculate the Macaulay duration of the bond. Note: Recall that it is customary to drop the negative when computing volatility or modified duration. (a) 7.00 (b) 7.49 (c) 7.56 (d) 7.69 (e) 8.00 Answer: ____________________ 8. A fund earned a net investment income (i.e. Ending Balance - (Starting Balance + Deposits/Withdrawals)) of 9200 during 1999. The beginning and ending balances of the fund were 100000 and 129200, respectively. A deposit was made at time K during the year. No other deposits or withdraws were made. The fund earned 8% in 1999 using the dollar-weighted method. Determine then date corresponding to time K. (a) April 1 (b) May 1 (c) July 1 (d) Sept. 1 (e) Oct. 1 Answer: ____________________ 9. Melissa borrows an amount at an annual effective interest rate of 9% and will repay all interest and principal in a lump sum at the end of 15 years. She uses the amount borrowed to buy a 1000 par value 15-year bond with a coupon rate of 10% convertible semiannual. The bond redeems at par value and it is purchased to yield 12% convertible semiannually. All coupons are then reinvested at an annual nominal rate of 5% convertible semiannually. Coupons are paid-out at the end of each 6-month period. Calculate the net gain or (loss) to Mellissa at the end of 15 years. (a) 82 (b) 54 Answer: ____________________ (c) 12 (d) (18) (e) (35) 10. A 1000 par value 20-year bond with annual coupons is redeemable at maturity for 1050. The bond is purchased for P to yield an annual effective rate of 8.25%. The first coupon is 75. Each subsequent coupon is 3% greater than the preceding coupon. Determine P. Round your answer to two decimal places. Answer: ____________________ 11. An investor purchases a 1000 bond redeemable at par that pays semiannual coupons at a nominal rate of 8% compounded semiannually and matures in ten years. The bond will yield an annual rate of 7% convertible semiannually to maturity. If the bond is called in five years, immediately after the 10th coupon payment, the minimum redemption value the investor needs to realize the same yield would be X. Determine X. Round your answer to two decimal places. Answer: ____________________ 12. Jim purchases a 10-year 1000 par value bond with annual coupons of 5%. The bond redeems at par value at maturity and is purchased to yield an annual rate of 8%. The bond is purchased on January 1st 2000 and pays coupons each January 1st, starting in 2001. On January 1st, 2008, immediately after receiving the coupon payment, Jim sells the bond to Gary for 983.48. After the sale of the bond to Gary, Jim realizes an overall annual yield rate of j% on the bond during his ownership. After the purchase of the bond from Jim, Gary holds the bond until maturity and realizes an overall annual yield rate of i% on the bond during his ownership. Find i + j. Give your answer as a percentage rounded to one decimal place. Answer: ____________________ 13. John takes out a 2000 10-year loan with an annual effective interest rate of 20%. The principal amount of the loan will be repaid with 10 equal size yearly payments made at the end of each year. The interest accrued on the loan will be repaid with yearly payments occurring at the end of each year. The first interest payment is for X and each subsequent interest payment will be twice as large as the previous interest payment. After 10 years, the loan and interest accrued are completely paid off. Note: The resulting size of X will result in a capitalization of interest on this loan. Find X. Give your answer rounded to two decimal places. Answer: ____________________ 14. Tim takes out a loan of L and agrees to pay it back in equal size monthly payments over the next 25 years. Payments of size 500 are made at the end of each month and Tim is charged an annual nominal rate of 12% compounded monthly. Over the 25 years, how much interest in total does Tim end up paying back on the loan? Give your answer rounded to the nearest whole number. Answer: ____________________ 15. 2000 is deposited into a newly opened fund on January 1, 1999. Another deposit is made into the fund on July, 1 1999. On January 1, 2000, the balance in the fund is 6000. The time-weighted rate of return in 1999 is 8.0% and the dollar-weighted rate of return is 4.8%. Calculate the balance of the fund on July 1, 1999, immediately before the deposit is made. Give your answer rounded to the nearest whole number. Answer: ____________________ 16. The following two investment options are viewed under an annual effective interest rate of i. Investment A is a 10-year zero coupon bond which redeems at par-value 250. Investment B is a perpetuity-immediate paying an annual payment starting with 4 and having each successive payment increase by X% from the previous payment. If the volatility of each investment is 8, then find the value of X. Give your answer as a percentage rounded to two decimal places. Answer: ____________________ 17. Jack purchases a corporate bond with par-value 30000 on January 15, 2000. The bond matures at par-value on January 15, 2030 and pays semiannual coupons at an annual nominal rate of 5% compounded semiannually every January 15 and July 15. The first coupon payment comes on July 15, 2000, and Jack immediately begins investing his coupon payments into a Money Market account which earns an annual interest rate of 2% compounded semiannually. The bond is originally priced to yield an annual rate of 6% compounded semiannually. On June 15, 2020, Jack sells the bond at a price that is 8% higher than the stated market price (i.e. clean price) at that time. Factoring in the sale of the bond and the coupon investments, what is Jack's overall yield on his original investment at the time that he sells the bond? Give your answer as an annual interest rate compounded semiannually. Round your percentage answer to two decimal places. Note: Between January 15, 2020 and June 15, 2020 a period of five months has passed. And, between January 15, 2020 and July 15, 2020 a period of six months has passed. Hint: Find the price at which the bond was purchased and the price at which the bond was sold, and use these along with the invested coupons to determine the rate that needs to be applied to the original purchase price in order to have it equal the value of the invested coupons and the selling price. Answer: ____________________