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Unformatted text preview: 1. A 20 year bond has a par value of 2000 and matures for 2500. The semiannual coupons are paid
at a rate of 6% convertible semiannually. Calculate the price of this bond to yield 8% convertible semiannually. A 20 year annuity has annual payments at the end of each year. The first payment is 1000. The
second payment is 1200. Each subsequent payment is 200 greater than the previous payment
until 4800 is paid at the end of the 20th year. Calculate the accumulated value of this annuity at the end of 20 years using i = 0.075. 3. You are given the following table: — 2000 i
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_— _— Nancy invests X on January 1, 1997 in a fund which credits interest using the investment year
method. Nancy also invests X on January 1, 2001 into a fund earning the portfolio interest rate. 1 On December 31, 2004, Nancy has a total of 3735.05 in the two funds combined. Calculate X. 4. Brian is receiving a level continuous annuity at a constant rate ofX per year for 20 years. Lifan is receiving an increasing continuous annuity at a rate of 50’: at time t for a period of 20 years. You are given that 5 = 0.10. The present value of Brian’s annuity is equal to the present value of Lifan’s annuity. Calculate X. 5. An 8 year bond with annual coupons of 200 matures for 3500. If this bond is bought at a premium
of 500, calculate the annual effective yield rate used to determine the price ofthe bond. 6. A ten year annuity pays 15 at the end of each month during the first year. It pays 30 at the end of
each month during the second year. The payments are level during each year, but continue to
increase year to year until 150 is paid at the end of each month during the 10th year. The interest rate is 12% compounded monthly. Calculate the present value of this annuity. l l l 7. Emily is repaying a 10,000 loan with annual payments of 900. The final payment will be for an
amount less than 900 (a drop payment). The annual effective rate on the loan is 5%. Calculate the amount of the drop payment. 8. A loan of 50,000 is being repaid using the sinking fund method. Payments are made annually at
the end of each year for 10 years. The interest rate on the loan is 6%. The interest rate earned by
the sinking fund is 4%. ‘ Calculate the interest paid each year on the loan and the annual sinking fund deposit. 9. A bond has a book value immediately after the fifth coupon of 1000. The next semi—annual coupon
is 45. The bond was purchased to yield 8% convertible semiannually. Calculate the book value immediately after the sixth coupon. 10. The present value of an increasing perpetuity immediate is 650. The perpetuity pays 1 at the end
of the first year, 2 at the end of the second year, etc. Calculate i. 11. The book value of a bond immediately after the 5th coupon is 1200. The bond was purchased to
yield 6% convertible semiannually. The bond pays semiannual coupons of 80. Calculate the Clean Value of the Bond at 2 months after the 5th coupon. made monthly. The sinking fund earns 12% compounded monthly. Calculate the amount in the E
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12. A loan is being repaid using the sinking fund method. Sinking fund payments of 1000 are being l sinking fund at the end of two years. 13. A bond matures in 30 years for 100,000. The bond pays an increasing annual coupon. The coupon
at the end of the first year is 500. The coupon at the end of the second year is 1000. Each
subsequent coupon increases by 500 until a coupon of 15,000 is paid at the end of the 30th year. If the bond is bought to yield 10% annually, calculate the price of this bond. 14. A loan is being repaid with periodic payments of Q. The principal in the 10th payment is 89.00. The
principal in the 50th payment is 229.83. The interest in the 60th payment is 708.66. Calculate Q. 15. A zero coupon bond maturing for 100,000 in 30 years was purchased for 10,000. Calculate the yield rate on the bond. I
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 Spring '08
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 Math, Nancy

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