Worked solution · Exam FM
This Exam FM sample reference tests Coupon Bond Anchored by a Zero Price. The zero price fixes the n-period discount factor at 0.60. Coupons at half the yield contribute one-half of the discounted interest margin. The second price is therefore 0.80F, so F = 750 and choice B.
Independent solution
Setup
Normalize the zero-coupon price by face value.
Model
Let F be the second face value. Its coupon is Fi/2.
Compute
Use i times a-angle-n equal to one minus v to the n.
Answer
The second face value is 750, choice B.
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30 original bonds problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Error diagnosis
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Original practice · fully worked
A 1,000 face-value zero-coupon bond sells for 700. A second bond has the same maturity and yield, a face value of 875, and the same 700 price. Its annual coupon rate is alpha times the yield. Determine alpha.
The maturity discount is 0.70. The second price equation is 700 = 875[0.70 + alpha(0.30)], giving alpha = one-third, choice C.
Setup
The zero price fixes the common maturity discount factor.
Model
Price the second bond using coupon alpha times 875i.
Compute
Insert the known discount and solve.
Answer
The coupon rate is 33.3% of yield, choice C.
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