1 - Purdue University



(10 points) You are given the following table:

| |Year 1 |Year2 |Year 3 |Year 4 |Year 5 |Portfolio |Year |

|1995 |.0850 |.0825 |.0800 |.0780 |.0760 |.0730 |2000 |

|1996 |.0825 |.0800 |.0775 |.0755 |.0735 |.0705 |2001 |

|1997 |.0800 |.0775 |.0750 |.0730 |.0710 |.0680 |2002 |

|1998 |.0750 |.0725 |.0071 |.0690 |.0670 |.0650 |2003 |

|1999 |.0700 |.0675 |.0655 |.0640 |.0635 |.0610 |2004 |

|2000 |.0650 |.0630 |.0610 |.0590 |.0580 |.0570 |2005 |

|2001 |.0600 |.0575 |.0560 |.0540 |.0530 |.0520 |2006 |

|2002 |.0550 |.0530 |.0510 |.0500 |.0510 |.0525 |2007 |

|2003 |.0500 |.0480 |.0490 |.0500 |.0515 |.0540 |2008 |

|2004 |.0450 |.0470 |.0495 |.0520 |.0550 | | |

|2005 |.0500 |.0535 |.0550 |.0575 | | | |

|2006 |.0550 |.0575 |.0600 | | | | |

|2007 |.0600 |.0620 | | | | | |

|2008 |.0650 | | | | | | |

Elmer invests 3000 on January 1, 2001 in a fund which credits interest using the investment year method.

Herman invests 3000 on January 1, 2000 in a fund which credits interest using the portfolio method.

On December 31, 2007, how much will Herman’s fund exceed Elmer’s fund.

1. (12 points) Ken borrows money to buy a house. Under the loan, Ken agrees to make monthly payments for the next 20 years. His first payment is 20. His second payment is 40. His payments continue to increase each time until he pays 4800 as a final payment. Ken’s loan has an interest rate of 15% compounded monthly. Calculate the amount that Ken borrowed.

2. (10 points) Wozny-Wiggins Corporation wants to borrow 500,000 to be repaid with annual payments over ten years.

Dummitt Bank offers a loan using the sinking fund method. The interest rate on the loan is i and the sinking fund will earn 5%. Each year, Wozny-Wiggins must pay the interest on the loan and make a payment into the sinking fund. The payments into the sinking fund are such that the amount in the sinking fund after 10 years will exactly repay the loan.

Lumley Bank offers a loan based on the amortization method and an annual effective interest rate of 6.5%. The amount of the payment under this loan is exactly equal to the sum of the interest payment and sinking fund deposit on the loan from Dummitt Bank.

Calculate i, the annual effective interest rate on the loan from Dummitt Bank?

3. (10 points) A 20 year continuous annuity pays 1000t2 – 10 at time t. Calculate the present value of this annuity if v(t) = 1/(t+0.1).

4. (12 points) William is the beneficiary of a trust. Under the trust, he will receive payments at the end of each quarter for 30 years. The payments are 1000 per quarter in the first year. The payments are 2000 per quarter in the second year. The payments continue to increase until 30,000 is paid each quarter in the 30th year. Calculate the present value of the payments that William will receive based on a nominal interest rate of 5% compounded quarterly.

5. (6 points) A zero coupon bond which matures for 100,000 is bought for 37,511.68. The yield on the bond is 8% convertible semi-annually. Calculate the term of the bond in years.

6. (12 points) Erin received payments from a 20 year continuous annuity which paid at a rate of 10 per year. John received payments from a 20 year continuous annuity which paid at a rate of t at time t. The interest rate is 10% compounded continuously. Calculate the accumulated value at the end of 20 years of Erin’s annuity less the accumulated value at the end of 20 years of John’s annuity.

7. (12 points) A four year loan is being repaid with annual payments. The first payment is 3000. The second payment is 4000. The third payment is 5000. The final payment is 6000. The annual effective interest rate is 10%. Create an amortization table for this loan.

8. (12 points) A twenty year bond has a redemption value of 2000 and pays semi-annual coupons of 48. The bond was purchased for 1366.63. Complete the following table if it is now 4 months after the 15th coupon.

| |Practical Method |Theoretical Method |

|Clean Value | | |

| | | |

| | | |

| | | |

| | | |

| | | |

9. (10 points) A 20 year callable bond has a redemption value of 10,000. The bond pays semi annual coupons of 500. The bond is callable at the end of the 12th, 14th, and 16th years. The call price is listed in the following table.

|Call Date |Call Price |

|12th Year |11,150 |

|14th Year |10,900 |

|16th Year |10,650 |

Calculate the price that Nancy should pay in order to assure a yield of 8% convertible semi-annually.

10. (9 points) A loan is being repaid with annual payments for 20 years. The principal in the 5th payment is $4236.99. The principal in the 10 payment is $5670.05. Calculate the amount of the loan to the nearest dollar.

11. (10 points) A bond with a par value of 1000 is bought to yield 8% convertible semi-annually. The bond pays semi-annual coupons at a rate of 6% compounded semi-annually. The bond matures for C. If the Book Value of the Bond immediately after the 5th Coupon is 1100, fill in the following table:

|Time |Coupon |Interest |Principal |Book Value |

|5th Coupon | | | |1100 |

|6th Coupon | | | | |

12. (12 points) Hannah is considering buying two bonds both priced to produce the same yield rate.

The first bond is a 20 year bond with annual coupons of 500. The bond matures for 10,500. The purchase price of this bond is 7,000.

The second bond is a 15 year bond which matures for 8,000 and pays annual coupons of 100t in year t. In other words, the coupon is 100 in the first year, 200 in the second year, etc until it is 1,500 in year 15.

Calculate the amount of premium or discount in the purchase of the second bond. Be sure to state whether it is discount or premium.

13. (7 points) Josh has repaid a loan with 4 annual payments of 950 each. The total interest repaid in those four payments was 800. Calculate the annual effective interest rate on the loan.

14. (6 points) Matt is receiving a continuous perpetuity which pays at a rate of 1000t at time t. The perpetuity has a present value of 100,000. Calculate the annual effective interest rate used to calculate the present value.

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