This Exam FM sample reference tests Coupon Rate Interpolation. The third coupon rate is 96.8/1,320 − 0.044 = 0.02933, or 2.93%. The result agrees with the published answer key, choice B.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (2.46%) does not match the checked coupon rate interpolation result (2.93%); no distinct standard one-step error is identifiable.
CChoice C (3.52%) does not match the checked coupon rate interpolation result (2.93%); no distinct standard one-step error is identifiable.
DChoice D (3.67%) does not match the checked coupon rate interpolation result (2.93%); no distinct standard one-step error is identifiable.
EChoice E (4.00%) does not match the checked coupon rate interpolation result (2.93%); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: coupon-rate interpolation by redemption amount
For a family of otherwise comparable bonds, coupon rate has the form r = x/F + y, where F is redemption amount. A bond with F = 1,000 has r = 5%, and a bond with F = 1,250 has r = 4%. Find r when F = 800.
A 5.50%
B 5.75%
C 6.00%
D 6.25%
E 6.50%
Variant answer in brief
The parameters are x = 50 and y = 0, so redemption 800 implies coupon rate 50/800 = 6.25%. The coupon rate is 6.25%, which is choice D.
Setup
Setup
Use the two observed bonds to solve the linear relationship in reciprocal redemption amount.
0.05=x/1000+y,0.04=x/1250+y
Model
Model
Subtracting the equations isolates x; back-substitution then gives y.
x=50,y=0
Compute
Compute
The parameters are x = 50 and y = 0, so redemption 800 implies coupon rate 50/800 = 6.25%.
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
