This Exam FM sample reference tests Callable Bond Redemption Value. Solving 1,722.25 = X[0.04a-angle-30 + v³⁰] gives X = 1,440. The result agrees with the published answer key, choice C.
How to solve this Callable Bond Redemption Value question
Setup
Setup
Work in semiannual periods: the yield is 3% per half-year and the earliest call date is 30 periods away. Let X be the redemption amount, so each coupon is 4% of X.
j=0.03,n=30
Model
Model
Price equals the present value of thirty coupons plus X at the call date. Both cash-flow components are proportional to X, leaving a direct linear equation.
1722.25=0.04Xa30∣j+Xv30
Compute
Compute
Solving 1,722.25 = X[0.04a-angle-30 + v³⁰] gives X = 1,440.
X=1440
Answer
Answer
The calculation gives 1440 for callable bond redemption value, matching published choice C.
X=1440(C)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (1400) does not match the checked callable bond redemption value result (1440); no distinct standard one-step error is identifiable.
BChoice B (1420) does not match the checked callable bond redemption value result (1440); no distinct standard one-step error is identifiable.
DChoice D (1460) does not match the checked callable bond redemption value result (1440); no distinct standard one-step error is identifiable.
EChoice E (1480) does not match the checked callable bond redemption value result (1440); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: earliest-call par value
A callable bond pays semiannual coupons equal to 3% of par. It is priced at 1,300 and may first be called after ten years. At a required 4% nominal yield convertible semiannually, find par.
A 1050
B 1100
C 1117
D 1150
E 1200
Variant answer in brief
Solving gives X = 1,117.3047, or 1,117. This selects choice C.
Setup
Setup
Use twenty half-year periods at 2% and let X be redemption; each coupon is 3% of X.
j=0.02,n=20
Model
Model
Price is X times the coupon-annuity and redemption factors.
1300=X(0.03a20∣j+v20)
Compute
Compute
Solving gives X = 1,117.3047, or 1,117.
X=1117.3047
Answer
Answer
The requested value is 1117, so the correct choice is C.
X=1117(C)
Calculator reproduction
BA II Plus keystrokes
2nd CLR TVM; 20 N; 2 I/Y; 3 PMT; 100 FV; CPT PV−116.35Scale 1,300/116.35 to recover the redemption amount.
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.
