FRM Part I · FRM Exam Part I · Interest Rates
A zero-coupon bond with a face value of 1,000 matures in 5 years. The yield to maturity is 4% per year, compounded annually. What is the bond's price?
The price is 821.93. A zero-coupon bond is worth its face value discounted at the annually compounded yield for five years, so 1,000 divided by 1.04 to the fifth power gives 821.93. Simple discounting or continuous compounding would give different values.
- A800.00
- B818.73
- C821.93Correct
- D833.33
Explanation
Price = 1,000 / 1.04^5 = 1,000 / 1.216653 = 821.93. The 833.33 figure comes from simple interest discounting, 1,000 / (1 + 5 x 0.04), which ignores compounding. The 818.73 figure uses continuous compounding, which does not match the stated annual compounding.
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