Verified solution · Exam FM

SOA Exam FM Sample Question #227 Solution

This Exam FM sample reference tests Duration and Convexity. The four-year zero-coupon price implies annual yield 4.6635%. Dividing its four-year Macaulay duration by 1 + i gives modified duration 3.82, 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 Duration and Convexity question

Setup

For a zero-coupon bond, Macaulay duration equals the four-year maturity.

D_M=4

Model

Recover the annual yield from the purchase price and maturity payment.

1000(1+i)^4=1200

i=0.0466351394

Compute

Modified duration is Macaulay duration divided by the annual accumulation factor, giving 3.82177 years.

D_{\mathrm{mod}}=\frac{4}{1+i}=3.82177117

Answer

The modified duration is approximately 3.82 years, so choice B is correct.

\boxed{D_{\mathrm{mod}}\approx3.82\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

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

2ND · CLR TVM · 4 · N · 1000 · +/- · PV · 0 · PMT · 1200 · FV · CPT · I/YI/Y = 4.6635

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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 (3.33) does not satisfy the zero-coupon price equation followed by Dmod = 4/(1+i); no distinct standard one-step error is identifiable.
CChoice C (3.86) does not satisfy the zero-coupon price equation followed by Dmod = 4/(1+i); no distinct standard one-step error is identifiable.
DChoice D (4.00) does not satisfy the zero-coupon price equation followed by Dmod = 4/(1+i); no distinct standard one-step error is identifiable.
EChoice E (4.19) does not satisfy the zero-coupon price equation followed by Dmod = 4/(1+i); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: redemption amount recovered from price and modified duration

A six-year zero-coupon security is priced at 900. Its modified duration is 5.7 years under annual effective yield quotation. Calculate the security's maturity payment.

A
1,224.34
B
1,285.55
C
1,346.77
D
1,407.99
E
1,469.20

Variant answer in brief

Modified duration first gives yield 5.2632%. Accumulating the 900 price for six years at that yield produces a maturity payment of 1,224.34, choice A.

Setup

Use the six-year Macaulay duration and the stated modified duration to recover yield.

5.7=\frac{6}{1+i}

Model

A zero-coupon maturity payment is the current price accumulated for the full term.

F=900(1+i)^6

Compute

The inferred yield is 5.2632%, giving maturity value 1224.34.

i=0.05263158

F=1224.336728

Answer

The maturity payment is 1,224.34, selecting choice A.

\boxed{F\approx1224.34\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVM · 6 · N · 5.263158 · I/Y · 900 · +/- · PV · 0 · PMT · CPT · FVFV = 1224.34

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #227 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Duration and Convexity 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: redemption amount recovered from price and modified duration

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