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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.

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Presentation on theme: "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."— Presentation transcript:

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 41 st 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 20 th 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 13 th 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 5 th 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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