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Cram Session By TJ Chukwueke

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**Calculate the total amount in the two funds at the end of 2 years**

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

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

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**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

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4. You are given: Determine 29.52

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**5. The rate of inflation is a constant r per annum**

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 Determine r. 2.75

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**6. Harvey invests X in a fund earning 4% annual effective**

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

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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

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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 Determine X. 5.7

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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

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**10. A company must pay a benefit of 1000 to a customer in two years**

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

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-2.53

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**12. A non-dividend paying stock has a current price of 82**

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

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DM Sample Question #9

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