Verified solution · Exam FM

SOA Exam FM Sample Question #284 Solution

This Exam FM sample reference tests Interest Rate Measures. Losing the final nine months of interest after a three-year holding leaves only 2.25 years of 8% accumulation. Equating that factor to three years at rate j gives j = 5.94%, 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 Interest Rate Measures question

Setup

Under the interest-loss penalty, only three years minus nine months earns the original 8% rate.

A_1=(1.08)^{3-0.75}=(1.08)^{2.25}

Model

Under the reduced-rate penalty, the full three-year holding earns j.

A_2=(1+j)^3

Compute

Equating the two accumulation factors gives j = 5.941914%.

j=(1.08)^{2.25/3}-1=0.0594191443

Answer

The equivalent reduced annual rate is approximately 5.94%, selecting choice B.

\boxed{j\approx5.94\%\quad\text{(B)}}

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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 (5.74%) does not satisfy the equality of 2.25 years at 8% and three full years at the reduced rate; no distinct standard one-step error is identifiable.
CChoice C (6.14%) does not satisfy the equality of 2.25 years at 8% and three full years at the reduced rate; no distinct standard one-step error is identifiable.
DChoice D (6.34%) does not satisfy the equality of 2.25 years at 8% and three full years at the reduced rate; no distinct standard one-step error is identifiable.
EChoice E (6.54%) does not satisfy the equality of 2.25 years at 8% and three full years at the reduced rate; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: interest-forfeiture period implied by an equivalent reduced rate

A certificate normally earns 7% annually. If redeemed after four years, one penalty forfeits the final M months of interest; another credits 5.5% annually for all four years. Calculate M when the two penalties are equivalent.

A
9.52 months
B
10.02 months
C
10.52 months
D
11.02 months
E
11.52 months

Variant answer in brief

Equating 7% accumulation for four years minus M/12 years to four years at 5.5% and solving logarithmically gives 10.02 months, choice B.

Setup

Write the accumulation factor after forfeiting M months from the four-year original-rate term.

A_1=(1.07)^{4-M/12}

Model

Set it equal to four years at the reduced annual rate.

(1.07)^{4-M/12}=(1.055)^4

Compute

Taking logarithms and isolating M gives 10.015842 months.

M=12\left[4-\frac{4\ln(1.055)}{\ln(1.07)}\right]=10.01584172

Answer

The forfeited interest period is 10.02 months, selecting choice B.

\boxed{M\approx10.02\text{ months}\quad\text{(B)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #284 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Interest Rate Measures question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: interest-forfeiture period implied by an equivalent reduced rate

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution