FRM Part I · FRM Exam Part I · Bond Yields and Return Calculations
Annually compounded spot rates are 3% for 1 year and 4% for 2 years. A 2-year bond pays a 5% annual coupon on a par value of 100. What is its price, closest to?
The bond is worth about 101.9, so the closest option is 101.89. Each cash flow is discounted at its own spot rate: the first coupon at 3% and the final coupon plus principal at 4% over two years. Pricing at par would ignore the coupon exceeding the par yield.
- A101.89Correct
- B100.00
- C103.80
- D101.40
Explanation
Price = 5/1.03 + 105/1.0816 = 4.8544 + 97.0828 = 101.937. Recompute: 105/1.0816 = 97.0784, so the total is 101.93. The closest option is 101.89. Using the 4% rate for both cash flows gives 5/1.04+105/1.0816 = 101.89, which coincides here only approximately, so check the discounting of the first coupon at 3%: the result is 101.93.
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