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FRM Part I · FRM Exam Part I · Properties of Interest Rates

A 2-year bond with face value 100 pays an annual coupon of 6%. The continuously compounded zero rates are 4% for 1 year and 5% for 2 years. What is the bond's theoretical price?

The bond is worth about 101.68. The 6 coupon is discounted for one year at 4% and the 106 final payment for two years at 5%, both continuously compounded. Using one rate for every cash flow gives wrong answers, because each cash flow needs its own maturity-matched zero rate.

  1. A101.68Correct
  2. B101.34
  3. C103.62
  4. D100.00

Explanation

Discount each cash flow at its own zero rate: 6e^(-0.04) + 106e^(-0.10) = 5.765 + 95.913 = 101.68. The 101.34 option discounts both cash flows at the 2-year rate. The 103.62 option discounts both at the 1-year rate. The 100.00 option assumes the bond prices at par.

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