Worked solution · Exam FM

SOA Exam FM Sample Question #214 Solution

This Exam FM sample reference tests Equivalent Interest Measures. Equating the nominal-discount accumulation with the force-of-interest accumulation gives n = 16.568 years, which rounds to choice B.

Independent analysis by ActuaryProof · reviewed October 6, 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 Equivalent Interest Measures question

Setup

A 12% nominal discount rate convertible quarterly has quarterly discount rate 3%, so each quarter accumulates by 1 divided by 0.97.

d^{(4)}/4=0.03

Model

Equate the two account balances after n years. Fund X has 4n quarterly periods, and Fund Y accumulates under force 0.08.

100(0.97)^{-4n}=200e^{0.08n}

Compute

Take natural logarithms and isolate n.

n[-4\ln(0.97)-0.08]=\ln 2

n=16.5679

Answer

The balances meet after approximately 16.6 years, so the answer is B.

\boxed{n\approx16.6\quad\text{(B)}}

Test the method on unseen problems

Financial Mathematics Practice Examination I

30 original Exam FM questions across the syllabus, to be worked in 150 timed minutes, with a full worked solution for each one. Written for Exam FM, not copied from the SOA set. One-time $39 PDF.

See the cover and sample pages

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 treats the nominal discount rate as a nominal interest rate and uses accumulation factor 1.03 per quarter.
CChoice C rounds the logarithmic coefficient before solving for n.
DChoice D uses four times 3% as an annual effective rate rather than applying four quarterly discount factors.
EChoice E converts the force of interest to a simple annual rate instead of using exponential accumulation.

Original practice · fully worked

Original variant: initial deposit under two accumulation laws

Fund A earns a nominal annual discount rate of 8% convertible semiannually. Fund B receives 500 and earns a constant force of interest of 6%. Determine the deposit in Fund A that makes the two balances equal exactly seven years from now.

A
396.18
B
412.64
C
429.71
D
447.92
E
468.35

Answer and calculation

Equating the seven-year accumulation factors gives an initial Fund A deposit of 429.71, which is choice C.

Setup

The half-year discount rate in Fund A is 4%, so its half-year accumulation factor is 1 divided by 0.96.

d_{1/2}=0.08/2=0.04

Model

Seven years contain 14 half-years. Equate Fund A's accumulated deposit X to Fund B's force-of-interest balance.

X(0.96)^{-14}=500e^{0.06(7)}

Compute

Move Fund A's accumulation factor to the other side and evaluate.

X=500e^{0.42}(0.96)^{14}=429.7055

Answer

The required initial deposit is approximately 429.71, so choice C is correct.

\boxed{X\approx429.71\quad\text{(C)}}

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How to solve this Equivalent Interest Measures question

Setup

Model

Compute

Answer

Financial Mathematics Practice Examination I

Why the other letters tempt

Original variant: initial deposit under two accumulation laws

Answer and calculation

Setup

Model

Compute

Answer

Related Exam FM solutions

Next steps for Exam FM Time Value of Money