FRM Part I · FRM Exam Part I · Interest Rates
A zero-coupon bond with a face value of 1,000 matures in exactly 3 years. The yield to maturity is 5% per year, compounded annually. What is the bond's price today?
The price is 863.84. A zero-coupon bond is worth its face value discounted at the yield for the full term: 1,000 divided by 1.05 cubed, or 1.157625. Simple-interest or continuous-compounding shortcuts give different, incorrect values.
- A863.84Correct
- B850.00
- C860.71
- D952.38
Explanation
Price = 1,000 / 1.05^3 = 1,000 / 1.157625 = 863.84. The 850.00 option wrongly uses simple interest (1,000 x (1 - 0.05 x 3)). The 860.71 option uses continuous compounding, which does not match the stated annual compounding. The 952.38 option discounts for only one year.
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