Verified solution · Exam FM

SOA Exam FM Sample Question #226 Solution

This Exam FM sample reference tests Bond Pricing and Yields. The zero-coupon price ratio implies yield 0.6218%. Pricing the coupon bond at the same 0.80 ratio and solving for term gives 72 years, which is choice D.

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 Pricing and Yields question

Setup

Use the first bond to recover the common annual yield from its price-to-face ratio.

0.8=(1+i)^{-36}

i=0.0062176820

Model

The second bond's annual coupon per unit face is four-ninths of that yield.

c=\frac49i=0.0027634142

0.8=ca_{\overline{n}|i}+(1+i)^{-n}

Compute

Solving the bond-price equation at the recovered yield gives term 72.0000 years.

n=72.000000

Answer

The second bond matures in 72 years, so choice D is correct.

\boxed{n=72\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

2ND · CLR TVM · 36 · N · 0.8 · +/- · PV · 0 · PMT · 1 · FV · CPT · I/YI/Y = 0.6218Use values per unit of face.
0.621768 · I/Y · 0.8 · +/- · PV · 0.276341 · PMT · 1 · FV · CPT · NN = 72

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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 (45) does not satisfy the common-price bond equation using the yield implied by the 36-year zero; no distinct standard one-step error is identifiable.
BChoice B (54) does not satisfy the common-price bond equation using the yield implied by the 36-year zero; no distinct standard one-step error is identifiable.
CChoice C (63) does not satisfy the common-price bond equation using the yield implied by the 36-year zero; no distinct standard one-step error is identifiable.
EChoice E (81) does not satisfy the common-price bond equation using the yield implied by the 36-year zero; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: zero-coupon term equivalent to a known coupon bond price

A 30-year bond pays annual coupons equal to 1% of face and yields 2% annually. A zero-coupon bond has the same face amount, the same 2% yield, and the same price. Calculate the zero-coupon bond's term.

A
10.88 years
B
11.52 years
C
12.16 years
D
12.80 years
E
13.44 years

Variant answer in brief

The coupon bond price is 0.776035 per unit of face. Equating this with a zero-coupon discount factor at 2% gives a term of 12.80 years, choice D.

Setup

Price the 30-year coupon bond per unit of face at the stated yield.

p=0.01a_{\overline{30}|0.02}+(1.02)^{-30}

Model

Set the equal-priced zero-coupon discount factor equal to that price ratio.

(1.02)^{-m}=p

Compute

The coupon bond price ratio is 0.77603544, and logarithms give term 12.8042 years.

m=-\frac{\ln p}{\ln(1.02)}=12.80421432

Answer

The equivalent zero-coupon term is 12.80 years, selecting choice D.

\boxed{m\approx12.80\text{ years}\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVM · 30 · N · 2 · I/Y · 1 · +/- · PMT · 100 · FV · CPT · PVPV = -77.60Scale face to 100.

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ActuaryProof. “SOA Exam FM Sample Question #226 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Bond Pricing and Yields 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: zero-coupon term equivalent to a known coupon bond price

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