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Cram Session

Cram Session. By TJ Chukwueke. 1 . You are given: Fund X accumulates at an interest rate of 8% compounded quarterly Fund Y accumulates at an interest rate of 6% compounded semiannually At the end of 10 years, the total amount in the two funds combined is 1000

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Cram Session

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  1. Cram Session By TJ Chukwueke

  2. 1. You are given: • Fund X accumulates at an interest rate of 8% compounded quarterly • Fund Y accumulates at an interest rate of 6% compounded semiannually • At the end of 10 years, the total amount in the two funds combined is 1000 • At the end of 5 years, the amount in Fund X is twice that in Fund Y • Calculate the total amount in the two funds at the end of 2 years • 560

  3. 2. You are given: • Determine the force of interest at time t = ½ • .097

  4. 3. Susan and Jeff each make deposits of 100 at the end of each year for 40 years. • Starting at the end of the 41st year, Susan makes annual withdrawals of X for 15 years and Jeff makes annual withdrawals of Y for 15 years. Both funds have a balance of 0 after the last withdrawal. • Susan’s fund earns 8% annual effective. Jeff’s fund earns 10% annual effective. • Calculate Y-X • 2792

  5. 4. You are given: • Determine • 29.52

  6. 5. The rate of inflation is a constant r per annum. A 10-year annuity-immediate provides for annual payments that increase with inflation. The first payment is 1000(1+r). The present value of this annuity at 7% effective is 8056. Determine r. • 2.75

  7. 6. Harvey invests X in a fund earning 4% annual effective. In return, he receives 1 at the end of each quarter in the first year, 2 at the end of each quarter in the second year,…, and 20 at the end of each quarter in the 20th year. Determine X. • 508.07

  8. 7. A corporation borrows 10,000 for 25 years, at an effective annual interest rate of 5%. A sinking fund is used to accumulate the principal by means of 25 annual deposits earning an effective annual interest rate of 4%. Calculate the sum of the net amount of interest paid in the 13th installment and the increment in the sinking fund for the ninth year. • 684.30

  9. 8. A company pays 100 for a bond with annual coupons X to get an effective annual yield rate of 5%. The amount of interest in the 5th coupon is 4.85. Determine X. • 5.7

  10. 9. An annuity-immediate has payments of 1000, 3000, and 7000 at the end of one, two, and three years, respectively. Determine the convexity of the payments evaluated at I = 10%. • 7.63

  11. 10. A company must pay a benefit of 1000 to a customer in two years. To provide for this benefit, the company will by one-year and three-year zero-coupon bonds. The one-year and three-year spot rates are 8% and 10% respectively. The company wants to immunize itself from small changes in interest rates on either side of 10%. What amount should it invest in the one-year bonds? • 420

  12. -2.53

  13. 12. A non-dividend paying stock has a current price of 82. The premium for a one year European call is 10.424 and the premium for the corresponding put is 8.993. The risk-free interest rate is 5.5% annual effective. Find the strike price. • 85

  14. DM Sample Question #9

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