Verified solution · Exam FM

SOA Exam FM Sample Question #410 Solution

This Exam FM sample reference tests Interest Rate Valuation. The percentage by which an account balance grows over one complete year is, by definition, the annual effective interest rate, choice A.

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 Interest Rate Valuation question

Setup

Focus on the measured one-year change in account balance.

A(1)=A(0)(1+0.045)

Model

An annual effective rate is defined as the proportional accumulation over a full year.

i_{\mathrm{annual}}=\frac{A(1)-A(0)}{A(0)}

Compute

Quarterly crediting affects the periodic rate but not the name of the observed annual growth.

i_{\mathrm{annual}}=0.045

Answer

The 4.5% figure is the annual effective interest rate, corresponding to choice A.

\boxed{\text{annual effective interest rate}\quad\text{(A)}}

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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.

BA force is a continuously compounded rate, not the observed one-year percentage change itself.
CA nominal quarterly quote must be stated as four times a quarterly rate and would not generally equal 4.5%.
DAn annual discount rate measures interest relative to ending value, not beginning balance growth.
ESimple interest describes linear accumulation over multiple years and is not implied by quarterly crediting.

Original practice · fully worked

Original variant: nominal quarterly quote equivalent to annual growth

An account balance grows by 4.5% over one year and interest is credited quarterly at a constant rate. Determine the equivalent nominal annual interest rate convertible quarterly.

A
4.226%
B
4.326%
C
4.426%
D
4.526%
E
4.626%

Variant answer in brief

The fourth root of annual factor 1.045 gives the quarterly rate; multiplying by four gives nominal quote 4.426%, choice C.

Setup

Match four quarterly accumulation factors to the observed annual factor.

\left(1+\frac{j^{(4)}}{4}\right)^4=1.045

Model

Take the fourth root to obtain the quarterly effective rate.

\frac{j^{(4)}}{4}=1.045^{1/4}-1

Compute

The nominal annual quote is four times that rate, or 0.04425996.

j^{(4)}=0.04425996

Answer

The equivalent nominal rate is 4.426%, corresponding to choice C.

\boxed{j^{(4)}=4.426\%\quad\text{(C)}}

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ActuaryProof. “SOA Exam FM Sample Question #410 — 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: nominal quarterly quote equivalent to annual growth

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution