1 - Purdue University



(9 points) Ahmad buys a 20 year zero coupon bond for 5000. The bond will mature for 15,000 in 20 years. Calculate the annual effective yield rate of the bond.

1. (10 points) A loan is being repaid using the sinking fund method. Rob has paid 100 at the end of each month into the sinking fund earning 6.6% compounded monthly for the last 120 months. The amount in the sinking fund immediately after the 120th payment will exactly repay Rob’s loan. How much was his loan?

2. (11 points) Liz is receiving quarterly annuity payments for the next 30 years. During the first year, the payments are 10 at the end of each quarter. During the second year, payments are 20 at the end of each quarter. The payments continue to increase until 300 is paid at the end of each quarter during the 30th year. Calculate the present value of this annuity at an annual effective interest rate of 6%.

3. (11 points) An 8 year bond pays semi-annul coupons. The bond has a par value of 7000 and a semi-annual coupon of 140. The bond was purchased at issue to yield 7% convertible semi-annually. The bond is now 4 years and 2 months old. Calculate the difference between the theoretical Dirty Value and the practical Clean Value.

4. (10 points) A 20 year continuous annuity pays at a rate of t at time t. Interest is at a rate of δ = 0.05. Calculate the accumulated value of the annuity.

5. (11 points) Kenji Corporation borrows 500,000. Kenji has the option of repaying the loan using one of two methods:

a. The loan can be repaid with annual payments using the sinking fund method over the next 10 years. The interest rate on the loan is 6%. Payments will be made into a sinking fund so the amount in the sinking fund at the end of 10 years equals the amount of the loan. The sinking fund will earn 5%.

b. The loan can be repaid using the amortization method at an annual effective interest rate of i.

If the annual payment under either option is equal, calculate i.

6. (11 points) A 20 year bond with annual coupons is redeemable at its par value of 10,000. The bond was purchased to yield 8% annually. If the amount of premium amortized in the 7th coupon is 100, calculate the purchased price.

7. (11 points) Tim borrows 30,000 from Dustin to buy a new car. Tim agrees to repay the loan with monthly payments over 5 years at a nominal interest rate of 9% compounded monthly. Dustin takes each of Tim’s payments and deposits a portion into a fund earning interest at a nominal interest rate of 6% compounded monthly. The amount that Dustin deposits into the fund is the amount necessary to exactly replace his capital of 30,000 at the end of 5 years. Dustin retains the rest of Tim’s monthly payment for his use. Calculate the annual effective yield rate that Dustin earns on this loan.

8. (10 points) A loan being repaid with level annual payments of 1000 has an annual effective interest rate of 4%. The principal in the 5th payment is 333.47. Calculate the interest in the 20th payment.

9. (11 points) Michael purchases a 10 year bond with a par value of 10,000. The bond matures for 10,500 and has a coupon rate of 6% convertible semi-annually. Michael purchases the bond for P to yield 7% convertible semi-annually.

Andrew purchases a 10 year bond with a par value of 10,000. The bond is redeemable at par and has a semi-annual coupon of 325. Andrew also pays P for his bond. Calculate the yield convertible semi-annually that Andrew will earn on his bond.

10. (10 points) A loan is being repaid with payments of 100 per month for 60 months followed by payments of 200 per month for the next 60 months. Calculate the amount of interest and principal in the 75th payment if the interest rate on the loan is 12% compounded monthly.

11. (11 points) Jennifer is going to purchase a 20 year callable bond. The bond has a redemption value of 10,000 at the end of 20 years. It pays annual coupons of 800. The bond is callable at 10,500 at the end of years 12, 14, and 16. It is also callable at par at the end of year 18. Calculate the price that Jennifer should pay to assure an annual yield of 7%.

12. (11 points) A loan is being repaid with level annual payments of for four years. The total interest paid in those four payments is 2009.72. The total principal paid in those four payments is 10,000. List the amortization table for this loan.

13. (11 points) A 25 year bond matures for 1000 and pays annual coupons. The coupons are 10 in the first year, 20 in the second year, etc., until 250 is paid in the 25th year. The bond was bought to yield 10% annually. Calculate I24 and P24.

14. (11 points) The present value of a continuous perpetuity assuming compound interest is 1/δ2 + 1/δ. What is the rate of payment at time t for this perpetuity?

15. (10 points) A callable bond has a par value of 1000 and annual coupons of 60. The bond matures at par after 15 years. However, it can be called at anytime after 10 years at par. Wang-Jun buys the bond at 1077.22. What is the maximum yield that Wang-Jun is assured of receiving? What is the maximum yield that Wnag-Jun could receive?

16. (11 points) A continuous annuity pays at the rate of t2+1 at time t for 15 years. Calculate the present value of this annuity if v(t) = 1-.001t2.

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