Verified solution · Exam FM

SOA Exam FM Sample Question #72 Solution

This Exam FM sample reference tests Callable Bond Guaranteed Price. Pricing twenty half-year coupons of 50 plus redemption of 1,000 gives 885.30, or 885. The result agrees with the published answer key, choice A.

Independent analysis by ActuaryProof · reviewed August 4, 2026

Official wording withheld. Read the problem in the official SOA sample-question PDF. This page provides only our independently written analysis.

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Independent solution

How to solve this Callable Bond Guaranteed Price question

Setup

The required nominal yield is 12% convertible semiannually, or 6% per half-year. Evaluate the price under the redemption date that is least favorable for this discount bond.

j=0.12/2=0.06

Model

With coupon rate below yield, a later redemption keeps the below-market coupons outstanding longer, so the latest permitted date controls the guaranteed price.

P_{\rm latest}=50a_{\overline{20}|\,0.06}+1000(1.06)^{-20}

Compute

Pricing twenty half-year coupons of 50 plus redemption of 1,000 gives 885.30, or 885.

P_{\max}=885.30

Answer

The calculation gives 885 for callable bond guaranteed price, matching published choice A.

\boxed{P=885\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

2nd CLR TVM; 20 N; 6 I/Y; 50 PMT; 1000 FV; CPT PV−885.30The latest permitted redemption controls the guaranteed price.

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Error diagnosis

Why the other letters tempt

These notes identify the calculation error associated with each wrong letter when that error is reproducible.

BChoice B (892) does not match the checked callable bond guaranteed price result (885); no distinct standard one-step error is identifiable.
CChoice C (926) does not match the checked callable bond guaranteed price result (885); no distinct standard one-step error is identifiable.
DChoice D (965) does not match the checked callable bond guaranteed price result (885); no distinct standard one-step error is identifiable.
EChoice E (982) does not match the checked callable bond guaranteed price result (885); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: yield guaranteed by a known callable-bond price

A callable bond costs 900 and pays semiannual coupons of 22. It may be redeemed for 1,080 after 12 years or 1,000 after 18 years. Calculate the nominal annual yield convertible semiannually that the purchase price guarantees.

A
4.74%
B
5.00%
C
5.27%
D
5.53%
E
5.79%

Variant answer in brief

The two scenario yields are 6.047% and 5.267%; the guaranteed yield is 5.27%. The guaranteed nominal yield is 5.27%, which is choice C.

Setup

The market price is given, so find the yield under each possible redemption schedule.

900=22a_{\overline{24}|j}+1080v^{24},\qquad900=22a_{\overline{36}|j}+1000v^{36}

Model

Solve in half-year periods, double the roots for nominal annual quotes, and retain the smaller result.

i_{12}=6.047344\%,\quad i_{18}=5.266652\%

Compute

The two scenario yields are 6.047% and 5.267%; the guaranteed yield is 5.27%.

i_{worst}=\min(i_{12},i_{18})=5.266652\%

Answer

The guaranteed nominal yield is 5.27%, which is choice C.

\boxed{i_{worst}=5.27\%\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #72 — Verified Solution.” Verified 2026-07-31.

Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.

How to solve this Callable Bond Guaranteed Price question

Setup

Model

Compute

Answer

BA II Plus keystrokes

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: yield guaranteed by a known callable-bond price

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution