FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage
The 1-year spot rate is 3.00% and the 2-year spot rate is 4.00%, both annually compounded. What is the price today of a zero-coupon bond paying 1,000 in 2 years?
The price is 924.56. A 2-year zero-coupon bond is discounted using the 2-year spot rate of 4.00%, so the price is 1,000 divided by 1.04 squared, or 1.0816, which equals 924.56. The 1-year rate is not used for this cash flow.
- A924.56Correct
- B961.54
- C915.14
- D970.87
Explanation
Price = 1,000/1.04^2 = 1,000/1.0816 = 924.56. The 961.54 figure uses the 2-year rate for only one year. The 915.14 figure wrongly uses 1.03 x 1.04... actually 1.03 x 1.04 = 1.0712 gives 933.53, so it is not that; the correct computation uses only the 2-year spot rate.
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