FRM Part I · FRM Exam Part I · Interest Rates
A two-year bond with a face value of 100 pays a 6% annual coupon in two semiannual payments of 3. It is quoted at a yield to maturity of 8% on a semiannual (bond-equivalent) basis. What is its price?
The price is 96.37. With a 4% semiannual yield, the cash flows are 3, 3, 3 and 103, discounted over four half-years. Using annual compounding instead gives 96.43, and leaving out the final coupon gives 93.81.
- A96.37Correct
- B96.43
- C100.00
- D93.81
Explanation
The semiannual yield is 4% over 4 periods. Price = 3/1.04 + 3/1.04^2 + 3/1.04^3 + 103/1.04^4 = 2.88 + 2.77 + 2.67 + 88.04 = 96.37. Treating 8% as an annual rate with annual coupons gives 96.43, which is wrong because the quote is semiannual. 93.81 omits the final coupon of 3.
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