This Exam FM sample reference tests Callable Discount Bond. Solving the linear price equation gives X = 1,200. The result agrees with the published answer key, choice E.
Use the earliest relevant call date of twenty half-year periods and a yield of 3% per half-year. Let X be the unknown redemption amount; each coupon equals 2% of X.
j=0.03,n=20
Model
Model
The bond’s price is X times the sum of the coupon-annuity factor and the discounted redemption factor. Because the coupon rate is below yield, the price is below X as expected.
1021.50=0.02Xa20∣j+Xv20
Compute
Compute
Solving the linear price equation gives X = 1,200.
X=1200
Answer
Answer
The calculation gives 1200 for callable discount bond, matching published choice E.
X=1200(E)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (1120) does not match the checked callable discount bond result (1200); no distinct standard one-step error is identifiable.
BChoice B (1140) does not match the checked callable discount bond result (1200); no distinct standard one-step error is identifiable.
CChoice C (1160) does not match the checked callable discount bond result (1200); no distinct standard one-step error is identifiable.
DChoice D (1180) does not match the checked callable discount bond result (1200); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: discount callable par
A ten-year callable bond pays semiannual coupons equal to 1% of par and is priced at 900. The guaranteed nominal yield is 4% convertible semiannually. If the adverse call is at year ten, find par.
A 1000
B 1050
C 1076
D 1100
E 1150
Variant answer in brief
Solving gives X = 1,075.9300, or 1,076. This selects choice C.
Setup
Setup
At 2% per half-year, price twenty coupons equal to 1% of redemption X plus redemption.
j=0.02,n=20
Model
Model
Factor X from the complete bond-price equation.
900=X(0.01a20∣j+v20)
Compute
Compute
Solving gives X = 1,075.9300, or 1,076.
X=1075.9300
Answer
Answer
The requested value is 1076, so the correct choice is C.
X=1076(C)
Calculator reproduction
BA II Plus keystrokes
2nd CLR TVM; 20 N; 2 I/Y; 1 PMT; 100 FV; CPT PV−83.65Scale the observed price by the per-100 price.
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.
