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

A 2-year zero-coupon bond with a face value of 1,000 has a yield to maturity of 5.00% per year, quoted with semiannual compounding. What is its price?

The price is 905.95. A semiannual yield of 5% means 2.5% per half-year over four half-years, so the price is 1,000 divided by 1.025 to the fourth power. Using annual compounding would wrongly give 907.03.

  1. A905.95Correct
  2. B907.03
  3. C951.81
  4. D900.00

Explanation

With semiannual compounding there are 4 periods at 2.5% each. Price = 1,000 / 1.025^4 = 1,000 / 1.103813 = 905.95. The 907.03 option uses annual compounding (1,000 / 1.05^2). The 951.81 option uses only 2 periods at 2.5%.

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