oldex3 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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1 UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 210 P r o f . R i c k G o r v e t t Theory of Interest Fall, 2008 Exam # 3 Problems from a Past Math 210 Offering 1) Assume that the term structure of interest rates (the yield curve) has the following form: r( t ) = 3 t , where r( t ) is the spot rate of interest for an investment of length t , expressed as an annual percentage rate. What is the yield-to-maturity of a three-year, 1,000 face value, 8% annual coupon bond? 2) Consider a three-year bond, with a 1,000 face value and a 10% annual coupon rate, which was bought to yield 8% annually. What is the “amount for amortization of premium” during the second year of the bond’s life? 3) You are given the following information: The two-year spot rate is 6.00%. The three-year spot rate is 8.00%. The one-year forward rate one year from now is 7.50%. What is the one-year spot rate? 4) What is the modified duration (or the “volatility”) of a 20-year, 1,000 face value, 12% annual coupon bond? Assume an effective annual interest rate of 10%. 5)
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oldex3 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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