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FRM Part I · FRM Exam Part I · Bond Yields and Return Calculations

A 2-year bond with face value 100 pays an annual coupon of 5%. The 1-year spot rate is 3.00% and the 2-year spot rate is 4.00%, both annually compounded. What is the bond's arbitrage-free price?

The price is 101.93. Each cash flow is discounted at the spot rate matching its maturity: the 5 coupon at 3% gives 4.854, and the final 105 at 4% for two years gives 97.078. Their sum is 101.93.

  1. A101.89
  2. B101.93Correct
  3. C103.78
  4. D103.83

Explanation

Discount each cash flow at the spot rate for its own maturity: 5/1.03 = 4.8544 and 105/1.04^2 = 105/1.0816 = 97.0784. The total is 101.93. The 101.89 option discounts the first coupon at 4%. The 103.83 option discounts both cash flows at 3%. The 103.78 option reverses the two rates.

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