Verified solution · Exam FM

SOA Exam FM Sample Question #381 Solution

This Exam FM sample reference tests Bond Valuation. The purchase price exceeds redemption, so the earliest permitted call gives the lowest investor yield; solving the year-18 price equation gives 7.985%, choice C.

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 Bond Valuation question

Setup

The bond is purchased at a premium relative to its call amount.

1321>1111\Longrightarrow n_{\mathrm{worst}}=18

Model

For a premium bond, the earliest return of redemption amortizes the premium fastest and produces the lowest yield.

1321=111.10a_{\overline{18}|\,i}+1111(1+i)^{-18}

Compute

Solve the annual yield from eighteen coupons followed by the call payment.

i=0.07985

Answer

The minimum possible annual effective yield is 7.985%, corresponding to choice C.

\boxed{i_{\min}=7.985\%\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 18 N; 1321 PV; 111.10 +/- PMT; 1111 +/- FV; CPT I/YI/Y = 7.985Use the year-18 call because the bond is purchased at a premium.

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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.

AChoice A is inconsistent with the premium bond's year-18 call-yield equation; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the premium bond's year-18 call-yield equation; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the premium bond's year-18 call-yield equation; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the premium bond's year-18 call-yield equation; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: coupon implied by a protected earliest-call yield

A callable face-1,000 bond sells for 1,100 and may be called at par in years 6, 7, or 8. Determine the annual coupon that makes its protected yield 7% effective.

A
70.98
B
80.98
C
90.98
D
100.98
E
110.98

Variant answer in brief

At a premium the year-6 call is limiting; solving its 7% price equation gives annual coupon 90.98, choice C.

Setup

Because price exceeds call value, use the earliest allowed redemption for the protected yield.

1100=Ca_{\overline{6}|\,0.07}+1000(1.07)^{-6}

Model

Coupons form a six-payment annuity and par is paid with the final coupon.

C=\frac{1100-1000(1.07)^{-6}}{a_{\overline{6}|\,0.07}}

Compute

Solving the linear price equation gives 90.9796.

C=90.9796

Answer

The required annual coupon is 90.98, corresponding to choice C.

\boxed{C=90.98\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 6 N; 7 I/Y; 1100 PV; 1000 +/- FV; CPT PMTPMT = -90.98

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #381 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Bond Valuation 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: coupon implied by a protected earliest-call yield

Variant answer in brief

Setup

Model

Compute

Answer

BA II Plus keystrokes

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution