Verified solution · Exam FM

SOA Exam FM Sample Question #29 Solution

This Exam FM sample reference tests Yield to Maturity. The root is i = 0.0890. Substitution returns the price to cents, so the annual effective yield is 8.9%. The result agrees with the published answer key, choice E.

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 Yield to Maturity question

Setup

Use the verified bond price 926.03 as the time-0 value. The bond pays three annual coupons of 60 and redeems 1,000 with the third coupon.

P=926.03

Model

Yield to maturity is the single rate i that discounts this promised cash-flow stream to its price, so solve 926.03 = 60a-angle-3 + 1,000v³.

926.03=60a_{\overline3|\,i}+1000(1+i)^{-3}

Compute

The root is i = 0.0890. Substitution returns the price to cents, so the annual effective yield is 8.9%.

i=0.089

Answer

The calculation gives 8.9% for yield to maturity, matching published choice E.

\boxed{i=8.9\%\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 3 N; 926.03 +/- PV; 60 PMT; 1000 FV; CPT I/Y8.90END mode; the display is the annual effective yield in percent.

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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 (8.1%) does not match the checked yield to maturity result (8.9%); no distinct standard one-step error is identifiable.
BChoice B (8.3%) does not match the checked yield to maturity result (8.9%); no distinct standard one-step error is identifiable.
CChoice C (8.5%) does not match the checked yield to maturity result (8.9%); no distinct standard one-step error is identifiable.
DChoice D (8.7%) does not match the checked yield to maturity result (8.9%); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: yield on a spot-priced note

A two-year 1,000 par bond pays 5% annual coupons and is priced at 982.5732. Find its annual effective yield to maturity.

A
5.50%
B
5.75%
C
5.95%
D
6.10%
E
6.25%

Variant answer in brief

The economically admissible root is i = 0.0594985, or 5.95%. This selects choice C.

Setup

Use price 982.5732, coupon 50, and redemption 1,000 in a two-year yield equation.

982.5732=50v+1050v^2

Model

Multiplying by (1 + i)² gives a quadratic equation in 1 + i.

982.5732(1+i)^2=50(1+i)+1050

Compute

The economically admissible root is i = 0.0594985, or 5.95%.

i=0.0594985

Answer

The requested value is 5.95%, so the correct choice is C.

\boxed{i=5.95\%\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 2 N; 982.5732 +/- PV; 50 PMT; 1000 FV; CPT I/Y5.95Annual periods and END mode.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #29 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Yield to Maturity 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 on a spot-priced note

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