Verified solution · Exam FM

SOA Exam FM Sample Question #136 Solution

This Exam FM sample reference tests Bond Valuation. Because the coupon rate exceeds the required yield, the lowest price over allowable calls occurs at the earliest call; valuing 16 annual payments and par gives 1,542, choice B.

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

A coupon rate above yield makes the bond a premium instrument, so postponing redemption preserves more above-market coupons.

c=10\%>i=5\%\Longrightarrow\text{earliest call is limiting}

Model

For the buyer's guaranteed yield, the least valuable permitted outcome is therefore the earliest call date.

P=100a_{\overline{16}|\,0.05}+1000v^{16}

Compute

Discounting 16 coupons of 100 and the 1,000 call payment at 5% gives approximately 1,542.

P=100(10.0378)+458.11=1542

Answer

That is the maximum safe purchase price, corresponding to choice B.

\boxed{P_{\max}=1542\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 16 N; 5 I/Y; 100 PMT; 1000 FV; CPT PVPV = -1541.89END mode; I/Y is the annual effective required yield and the earliest call supplies 16 coupons.

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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 callable-bond price at the earliest call date; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the premium callable-bond price at the earliest call date; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the premium callable-bond price at the earliest call date; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the premium callable-bond price at the earliest call date; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: identify the yield-to-worst call date

A cinema bond pays annual coupons of 80 on face 1,000 and is purchased for 1,111.65. It can be called at par after years 7, 8, 9, or 10. Which call date produces the yield to worst, and what is that annual effective yield?

A
Year 7 at 6.00%
B
Year 8 at 6.19%
C
Year 9 at 6.33%
D
Year 10 at 6.45%
E
Every call date gives 6.00%

Variant answer in brief

Solving to each call date gives the minimum yield of 6.00% at year 7, choice A.

Setup

Use the actual purchase price in a separate yield equation for every permitted redemption date.

1111.65=80a_{\overline n|\,i_n}+1000(1+i_n)^{-n}

Model

The year-seven and year-eight solutions are 6.000% and 6.189%.

i_7=6.000\%,\qquad i_8=6.189\%

Compute

Later redemption raises the yield further because the premium is amortized over more above-market coupons.

i_9=6.335\%,\qquad i_{10}=6.451\%

Answer

The minimum is the year-seven yield of 6.00%, corresponding to choice A.

\boxed{\text{year 7 at }6.00\%\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 7 N; 1111.65 +/- PV; 80 PMT; 1000 FV; CPT I/YI/Y = 6.0000END mode; I/Y is the annual yield if called in year 7.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 8 N; 1111.65 +/- PV; 80 PMT; 1000 FV; CPT I/YI/Y = 6.1886END mode; I/Y is the annual yield if called in year 8.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 9 N; 1111.65 +/- PV; 80 PMT; 1000 FV; CPT I/YI/Y = 6.3345END mode; I/Y is the annual yield if called in year 9.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 10 N; 1111.65 +/- PV; 80 PMT; 1000 FV; CPT I/YI/Y = 6.4505END mode; I/Y is the annual yield if held to year 10.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #136 — 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: identify the yield-to-worst call date

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