Verified solution · Exam FM

SOA Exam FM Sample Question #406 Solution

This Exam FM sample reference tests Interest Rate Valuation. Real growth is nominal accumulation divided by inflation accumulation; 1.09/1.05 − 1 = 3.81%, nearest 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.

Read the solution Open official source

Independent solution

How to solve this Interest Rate Valuation question

Setup

Compare purchasing power using accumulation factors rather than subtracting rates.

1+i_{\mathrm{nom}}=(1+i_{\mathrm{real}})(1+r)

Model

Remove the 5% price-level growth from the 9% nominal investment growth.

1+i_{\mathrm{real}}=\frac{1.09}{1.05}

Compute

The factor ratio gives real rate 0.038095.

i_{\mathrm{real}}=0.038095

Answer

The real annual effective return is about 3.8%, corresponding to choice B.

\boxed{i_{\mathrm{real}}\approx3.8\%\quad\text{(B)}}

Continue without hunting through PDFs

All 461 Exam FM sample solutions in syllabus order

The searchable 2210-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.

See inside the Exam FM study manual PDF

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 nominal-real-inflation factor equation; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the nominal-real-inflation factor equation; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the nominal-real-inflation factor equation; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the nominal-real-inflation factor equation; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: inflation inferred from nominal and real investment returns

An investment earns 10% nominally and 4% in real purchasing-power terms. Determine the annual effective inflation rate.

A
4.77%
B
5.27%
C
5.77%
D
6.27%
E
6.77%

Variant answer in brief

Dividing 1.10 by 1.04 gives inflation accumulation 1.057692, or 5.77%, choice C.

Setup

Represent nominal return as real growth compounded with inflation.

1.10=(1.04)(1+r)

Model

Divide the nominal factor by the real factor.

1+r=\frac{1.10}{1.04}=1.0576923

Compute

The remaining price-level growth rate is 0.0576923.

r=0.0576923

Answer

Annual effective inflation is 5.77%, corresponding to choice C.

\boxed{r=5.77\%\quad\text{(C)}}

Keep practicing

Turn this solution into a complete study sequence

The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.

See the Exam FM study manual PDF — $49 More Exam FM Time Value of Money practice problems Free Exam FM formula sheet

Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #406 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Interest Rate Valuation question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: inflation inferred from nominal and real investment returns

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution